Stanford Research Systems SR850 User Manual

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DSP Lock-In Amplifier

model SR850

1290 D Reamwood Avenue

Sunnyvale, CA 94089 USA

Phone: (408) 744-9040 • Fax: (408) 744-9049

www.thinkSRS.com • e-mail:info@thinkSRS.com

Revision 1.4 • 10/99

Stanford Research Systems

TABLE OF CONTENTS

GENERAL INFORMATION

Safety and Preparation for Use 1-3 Specifications 1-5 Abridged Command List 1-7

GETTING STARTED

Your First Measurements 2-1 The Basic Lock-in 2-3 Displays and Traces 2-7 Outputs, Offsets and Expands 2-13 Scans and Sweeps 2-17 Using the Disk Drive 2-23 Aux Outputs and Inputs 2-31 Trace Math 2-35

SR850 BASICS

What is a Lock-in Amplifier? 3-1 What Does a Lock-in Measure? 3-3 The SR850 Functional Diagram 3-5 Reference Channel 3-7 Phase Sensitive Detectors 3-9 Time Constants and DC Gain 3-11 DC Outputs and Scaling 3-13 Dynamic Reserve 3-17 Signal Input Amplifier and Filters 3-19 Input Connections 3-21 Intrinsic (Random) Noise Sources 3-23 External Noise Sources 3-25 Noise Measurements 3-27

OPERATION

FRONT PANEL 4-1

Power On/Off and Power On Tests 4-1 Video Display 4-1 Soft Keys 4-2 Keypad 4-2 Spin Knob 4-2 Disk Drive 4-2 Front Panel BNC Connectors 4-2

SCREEN DISPLAY 4-5 Default Display 4-5 Data Traces 4-6 Single/Dual Trace Displays 4-7 Bar Graphs 4-9 Polar Graphs 4-10 Strip Charts 4-11 Trace Scans, Sweeps and Aliasing 4-13 Settings and Input/Output Monitor 4-15 Menu Display 4-15 Status Indicators 4-16

KEYPAD 4-19 Normal and Alternate Keys 4-19 Menu Keys 4-19 Additional Menus 4-20 Entry Keys 4-20 START/CONT and PAUSE/RESET 4-20 CURSOR 4-21 ACTIVE DISPLAY 4-21 MARK 4-21 CURSOR MAX/MIN 4-21 AUTO RESERVE 4-22 AUTO GAIN 4-22 AUTO PHASE 4-22 AUTO SETUP 4-22 AUTOSCALE 4-22 PRINT to a PRINTER 4-23 PRINT to a FILE 4-23 HELP 4-23 LOCAL 4-23

REAR PANEL 4-25 Power Entry Module 4-25 IEEE-488 Connector 4-25 RS232 Connector 4-25 Parallel Printer Connector 4-25 PC Keyboard Connector 4-25 Rear Panel BNC Connectors 4-26 Aux Inputs (A/D Inputs) 4-26 Aux Outputs (D/A Outputs) 4-26 X and Y Outputs 4-26 Signal Monitor Output 4-26 Trigger Input 4-27 TTL Sync Output 4-27 Preamp Connector 4-27

USING SRS PREAMPS 4-27

MENUS

Menu Guide 5-1 Default Settings 5-2 Reference and Phase Menu 5-3 Input and Filters Menu 5-7 Gain and Time Constant Menu 5-9 Output and Offset Menu 5-15 Trace and Scan Menu 5-17 Display and Scale Menu 5-21 Aux Outputs Menu 5-25 Cursor Setup Menu 5-29 Edit Mark Menu 5-31 Math Menu 5-33 Disk Menu 5-41 System Setup Menu 5-49

Table of Contents

PROGRAMMING

GPIB Communications

6-1

RS232 Communications

6-1

Status Indicators and Queues

6-1

Command Syntax

6-1

Interface Ready and Status

6-2

GET (Group Execute Trigger)

6-2

DETAILED COMMAND LIST

6-3

Reference and Phase

6-4

Input and Filter

6-6

Gain and Time Constant

6-7

Output and Offset

6-9

Trace and Scan

6-10

Display and Scale

6-11

Cursor

6-13

Mark

6-14

Aux Input and Output

6-15

Math

6-16

Store and Recall

6-18

Setup

6-19

Print and Plot

6-21

Front Panel and Auto Functions

6-22

Data Transfer

6-23

Interface

6-28

Status Reporting

6-29

STATUS BYTE DEFINITIONS

6-30

Serial Poll Status Byte

6-30

Service Requests

6-31

Standard Event Status Byte

6-29

LIA Status Byte

6-32

Error Status Byte

6-32

PROGRAM EXAMPLES

Microsoft C, Nationall Instr GPIB

6-33

QUICKBASIC, Nationall Instr GPIB

6-39

TESTING

Introduction

7-1

Preset

7-1

Serial Number

7-1

Firmware Revision

7-1

General Installation

7-2

Necessary Equipment

7-3

If A Test Fails

7-3

PERFORMANCE TESTS

Self Tests

7-5

DC Offset

7-7

Common Mode Rejection

7-9

Amplitude Accuracy and Flatness

7-11

Amplitude Linearity

7-13

Frequency Accuracy

7-15

Phase Accuracy

7-17

Sine Output Amplitude

7-19

DC Outputs and Inputs

7-21

Input Noise

7-23

PERFORMANCE TEST RECORD

7-25

CIRCUITRY

Circuit Boards

8-1

Video Driver and CRT

8-1

CPU Board

8-3

Power Supply Board

8-5

DSP Logic Board

8-7

Analog Input Board

8-9

PARTS LISTS

Power Supply Board

8-11

Analog Input Board

8-13

DSP Logic Board

8-19

CPU Board

8-25

Chassis Assembly

8-29

Miscellaneous Parts

8-32

SCHEMATIC DIAGRAMS

CPU Board Power Supply Board DSP Logic Board Analog Input Board

SAFETY AND PREPARATION FOR USE

WARNING

Dangerous voltages, capable of causing injury or death, are present in this instrument. Use extreme caution whenever the instrument covers are removed. Do not remove the covers while the unit is plugged into a live outlet.

CAUTION

This instrument may be damaged if operated with the LINE VOLTAGE SELECTOR set for the wrong AC line voltage or if the wrong fuse is installed.

LINE VOLTAGE SELECTION

The SR850 operates from a 100V, 120V, 220V, or 240V nominal AC power source having a line frequency of 50 or 60 Hz. Before connecting the power cord to a power source, verify that the LINE VOLTAGE SELECTOR card, located in the rear panel fuse holder, is set so that the correct AC input voltage value is visible.

Conversion to other AC input voltages requires a change in the fuse holder voltage card position and fuse value. Disconnect the power cord, open the fuse holder cover door and rotate the fuse-pull lever to remove the fuse. Remove the small printed circuit board and select the operating voltage by orienting the printed circuit board so that the desired voltage is visible when pushed firmly into its slot. Rotate the fuse-pull lever back into its normal position and insert the correct fuse into the fuse holder.

LINE FUSE

Verify that the correct line fuse is installed before connecting the line cord. For 100V/120V, use a 1 Amp fuse and for 220V/240V, use a 1/2 Amp fuse.

LINE CORD

The SR850 has a detachable, three-wire power cord for connection to the power source and to a protective ground. The exposed metal parts of the instrument are connected to the outlet ground to protect against electrical shock. Always use an outlet which has a properly connected protective ground.

SERVICE

Do not attempt to service or adjust this instrument unless another person, capable of providing first aid or resuscitation, is present.

Do not install substitute parts or perform any unauthorized modifications to this instrument. Contact the factory for instructions on how to return the instrument for authorized service and adjustment.

1-3

1-4

1-5

SPECIFICATIONS

SIGNAL CHANNEL

Voltage Inputs

Single-ended (A) or differential (A-B).

Current Input

106 or 108 Volts/Amp.

Full Scale Sensitivity

2 nV to 1 V in a 1-2-5-10 sequence (expand off).

Input Impedance

Voltage:

10 MΩ+25 pF, AC or DC coupled.

Current:

1 kΩ to virtual ground.

Gain Accuracy

±1% from 20°C to 30°C (notch filters off).

Input Noise

6 nV/√Hz at 1 kHz (typical).

Signal Filters

60 (50) Hz and 120(100) Hz notch filters (Q=4).

CMRR

90 dB at 100 Hz (DC Coupled).

Dynamic Reserve

Greater than 100 dB (with no signal filters).

Harmonic Distortion

<-90 dB to 10 kHz, <-80 dB to 100 kHz.

REFERENCE CHANNEL

Frequency Range

1 mHz to 102 kHz

Reference Input

TTL (rising or falling edge) or Sine. Sine input is1 MΩ, AC coupled (>1 Hz). 400 mV pk-pk minimum signal.

Phase Resolution

0.001°

Absolute Phase Error

<1°

Relative Phase Error

<0.001°

Orthogonality

90° ± 0.001°

Phase Noise

External synthesized reference: 0.005° rms at 1 kHz, 100 ms, 12 dB/oct. Internal reference: crystal synthesized, <0.0001° rms at 1 kHz.

Phase Drift

<0.01°/°C below 10 kHz <0.1°/°C to 100 kHz

Harmonic Detect

Detect at Nxf where N<32767 and Nxf<102 kHz.

Acquisition Time

(2 cycles + 5 ms) or 40 ms, whichever is greater.

DEMODULATOR

Zero Stability

Digital displays have no zero drift on all dynamic reserves. Analog outputs: <5 ppm/°C for all dynamic reserves.

Time Constants

10 µs to 30 s (reference > 200 Hz). 6, 12, 18, 24 dB/oct rolloff. up to 30000 s (reference < 200 Hz). 6, 12, 18, 24 dB/oct rolloff. Synchronous filtering available below 200 Hz.

Harmonic Rejection

-90 dB

INTERNAL OSCILLATOR

Frequency

1 mHz to 102 kHz.

Frequency Accuracy

25 ppm + 30 µHz

Frequency Resolution

5 digits or 0.1 mHz, whichever is greater.

Frequency Sweeps

Linear and Log.

Distortion

f<10 kHz, below -80 dBc. f>10 kHz, below -70 dBc.1 Vrms amplitude.

Output Impedance

50 Ω

Amplitude

4 mVrms to 5 Vrms (into a high impedance load) with 2 mV resolution. (2 mVrms to 2.5 Vrms into 50Ω load).

Amplitude Accuracy

Amplitude Stability

50 ppm/°C

Outputs

Sine output on front panel. TTL sync output on rear panel. When using an external reference, both outputs are phase locked to the external reference.

SR850 DSP LOCK-IN AMPLIFIER

SR850 DSP Lock-In Amplifier

1-6

INPUTS AND OUTPUTS

Channel 1 Output

X, R, θ, or Trace 1-4. Traces are defined as A•B/C or A•B/C2 where A, B, and C are selected from the quantities Unity, X, Y, R, θ, Xnoise, Ynoise, Rnoise, Aux Inputs 1 through 4, or Frequency. Output Voltage: ±10 V full scale. 10 mA max output current.

Channel 2 Output

Y, R, θ, or Trace 1-4. Traces are defined as A•B/C or A•B/C2 where A, B, and C are selected from the quantities Unity, X, Y, R, θ, Xnoise, Ynoise, Rnoise, Aux Inputs 1 through 4, or Frequency. Output Voltage: ±10 V full scale. 10 mA max output current.

X and Y Outputs

Rear panel outputs of cosine (X) and sine (Y) components. Output Voltage: ±10 V. 10 mA max output current.

Aux. Outputs

4 BNC Digital to Analog outputs. ±10 V full scale, 1 mV resolution. May be set to a fixed voltage or swept in amplitude (linear or log). 10 mA max output current.

Aux. Inputs

4 BNC Analog to Digital inputs. Differential inputs with1 MΩ input impedance on both shield and center conductor. ±10 V full scale, 1 mV resolution.

Trigger Input

TTL trigger input triggers each data sample and/or start of scan.

Monitor Output

Analog output of signal amplifiers (before the demodulator).

DISPLAYS

Screen Format

Single or dual display.

Displayed Quantities

Each display may show one of the traces. Traces are defined as A•B/C or A•B/C2 where A, B and C are selected from the quantities Unity, X, Y, R, θ, Xnoise, Ynoise, Rnoise, Aux Inputs 1 through 4, or Frequency.

Display Types

Large numeric readout with bar graph, polar graph, and strip chart.

Chart Data Buffer

64k data points may be stored and displayed on strip charts. The buffer can be configured as a single trace with 64k points, 2 traces with 32k points each, or 4 traces with16k points each. The internal data sample rate ranges from 512 Hz down to 1 point every 16 seconds. Samples can also be triggered.

ANALYSIS FUNCTIONS

Smoothing

5 - 25 point Savitsky-Golay smoothing of trace regions.

Curve Fits

Line, Exponential, and Gaussian fits of trace regions.

Calculator

Arithmetic, trigonometric, and logarithmic calculations on trace regions.

Statistics

Mean and standard deviation of trace regions.

GENERAL

Monitor

Monochrome CRT. 640H by 480V resolution. Adjustable brightness and screen position.

Interfaces

IEEE-488, RS232 and Printer interfaces standard. All instrument functions can be controlled through the IEEE-488 and RS232 interfaces. A PC keyboard input is provided for additional flexibility.

Preamp Power

Power connector for SR550 and SR552 preamplifiers.

Hardcopy

Screen dumps to dot matrix and HP LaserJet compatible printers. Data plots to HP-GL compatible plotters (via RS232 or IEEE-488). Screens can also be saved to disk as PCX image files.

Disk

3.5 inch DOS compatible format, 720 kbyte capacity. Storage of data and setups.

Power

60 Watts, 100/120/220/240 VAC, 50/60 Hz.

Dimensions

17"W x 6.25"H x 19.5"D

Weight

40 lbs.

Warranty

One year parts and labor on materials and workmanship.

1-7

COMMAND LIST

VARIABLES

i,j,k,l,m

Integers

Frequency (real)

x,y,z

Real Numbers

String

REFERENCE and PHASE

page

description

PHAS (?) {x}

6-4

Set (Query) the Phase Shift to x degrees.

FMOD (?) {i}

6-4

Set (Query) the Reference Source to Internal (0), Sweep (1) , or External (2).

FREQ (?) {f}

6-4

Set (Query) the Reference Frequency to f Hz.Set only in Internal reference mode.

SWPT (?) {i}

6-4

Set (Query) the Internal Sweep Type to Linear (0) or logarithmic (1).

SLLM (?) {f}

6-4

Set (Query) the Start Frequency to f Hz.Set only in Internal Sweep mode.

SULM (?) {f}

6-4

Set (Query) the Stop Frequency to f Hz.Set only in Internal Sweep mode.

RSLP (?) {i}

6-4

Set (Query) the External Reference Slope to Sine(0), TTL Rising (1), or TTL Falling (2).

HARM (?) {i}

6-5

Set (Query) the Detection Harmonic to 1 ≤ i ≤ 32767 and i•f ≤ 102 kHz.

SLVL (?) {x}

6-5

Set (Query) the Sine Output Amplitude to x Vrms. 0.004 ≤ x ≤5.000.

INPUT and FILTER

page

description

ISRC (?) {i}

6-6

Set (Query) the Input Configuration to A (0), A-B (1) , or I (2).

IGAN (?) {i}

6-6

Set (Query) the Current Conversion Gain to 1 MΩ (0) or 100 MΩ (1).

IGND (?) {i}

6-6

Set (Query) the Input Shield Groungind to Float (0) or Ground (1).

ICPL (?) {i}

6-6

Set (Query) the Input Coupling to AC (0) or DC (1).

ILIN (?) {i}

6-6

Set (Query) the Line Notch Filters to Out (0), Line In (1) , 2xLine In (2), or Both In (3).

GAIN and TIME CONSTANT

page

description

SENS (?) {i}

6-7

Set (Query) the Sensitivity to 2 nV (0) through 1 V (26) rms full scale.

RMOD (?) {i}

6-7

Set (Query) the Dynamic Reserve Mode to Max (0), Manual (1), or Min (2).

RSRV (?) {i}

6-7

Set (Query) the Dynamic Reserve to i

reserve. Set will switch to Manual Reserve Mode.

OFLT (?) {i}

6-7

Set (Query) the Time Constant to 10 µs (0) through 30 ks (19).

OFSL (?) {i}

6-8

Set (Query) the Low Pass Filter Slope to 6 (0), 12 (1), 18 (2) or 24 (3) dB/oct.

SYNC (?) {i}

6-8

Set (Query) the Synchronous Filter to Off (0) or On below 200 Hz (1).

OUTPUT and OFFSET

page

description

FOUT (?) i {, j}

6-9

Set (Query) the CH1 (i=1) or CH2 (2) Output Source to XY,R,

,Trace 1, 2, 3, 4 (j=0...6).

OEXP (?) i {, x, j}

6-9

Set (Query) the X, Y, R (i=1,2,3) Offset to x percent and Expand to j. -105.00 ≤ x ≤ 105.00 and 1 ≤ j ≤ 256.

AOFF i

6-9

Auto Offset X, Y, R (i=1,2,3).

TRACE and SCAN

page

description

TRCD (?) i {, j, k, l, m}

6-10

Set (Query) the Definition of Trace i (1-4) to j•k/l and Store (m=1) or Not Store (0). j, k, l select 1, X, Y, R, q, Xn, Yn, Rn, Aux 1, Aux 2, Aux 3, Aux4, or F (j,k,l = 0...12). l=13-24 selects X

through F2.

SRAT (?) {i}

6-10

Set (Query) the Sample Rate to 62.5 mHz (0) through 512 Hz (13) or Trigger (14).

SLEN (?) {x}

6-10

Set (Query) the Scan Length to x seconds.

SEND (?) {i}

6-10

Set (Query) the Scan Mode to 1 Shot (0) or Loop (1).

TRIG

6-10

Software trigger command. Same as trigger input.

DISPLAY and SCALE

page

description

ASCL

6-11

Auto Scale the active display.

ADSP (?) {i}

6-11

Set (Query) the active display to Full (0), Top (1) or Bottom (2). Full screen is always active.

SMOD (?) {i}

6-11

Set (Query) the Screen Format to Single (0) or Up/Down dual (1) display mode.

MNTR (?) {i}

6-11

Set (Query) the Monitor Display to settings (0) or Input/Output (1).

DTYP (?) i {, j}

6-11

Set (Query) theFull (i=0), Top (i=1) or Bottom (i=2) Display Type to Polar (j=0), Blank (j=1), Bar (j=2) or Chart (j=3).

SR850 DSP Lock-In Amplifier

1-8

DTRC (?) i {, j}

6-11

Set (Query) theFull (i=0), Top (i=1) or Bottom (i=2) Display Trace to trace j (1,2,3,4).

DSCL (?) {x}

6-11

Set (Query) theFull (i=0), Top (i=1) or Bottom (i=2) Display Range to x.

DOFF (?) {x}

6-11

Set (Query) theFull (i=0), Top (i=1) or Bottom (i=2) Display Center value to x.

DHZS (?) {i}

6-12

Set (Query) theFull (i=0), Top (i=1) or Bottom (i=2) Display Horizontal Scale to 2 ms (0) through 200 ks (32) per div.

RBIN? i

6-12

Query the bin number at the right edge of the Full (i=0), Top (i=1) or Bottom (i=2) chart display.

CURSOR

page

description

CSEK (?) {i}

6-13

Set (Query) the active display Cursor Seek mode to Max (0), Min (1) or Mean (2).

CWID (?) {i}

6-13

Set (Query) the active display Cursor Width to Off (0), Narrow (1), Wide (2) or Spot (3).

CDIV (?) {i}

6-13

Set (Query) the active display Chart Divisions to 8 (0), 10 (1) or None (2).

CLNK (?) {i}

6-13

Set (Query) the Cursor Control Mode to Linked (0) or Separate (1).

CDSP (?) {i}

6-13

Set (Query) the active display Cursor Readout to Delay (0), Bin (1), Fsweep (2) or Time (3).

CMAX

6-13

Move active chart cursor to max or min. Same as pressing [CURSOR MAX/MIN] key.

CURS? i

6-13

Query the cursor horz,vert position of Full (0), Top (1) or Bottom (2) chart display.

CBIN (?) {i}

6-13

Set (Query) the center of the cursor region in the active chart display. i is the bin number.

MARK

page

description

MARK

6-14

Places a mark in the data buffer. Same as pressing [MARK] key.

MDEL

6-14

Delete the nearest mark to the left of the cursor. Same as pressing <Marker Delete> softkey.

CNXT

6-14

Move active chart cursor to next mark to the right.

CPRV

6-14

Move active chart cursor to next mark to the left.

MACT?

6-14

Query the number of active marks. Also returns the active mark numbers.

MBIN? i

6-14

Query the bin number of mark #i.

MTXT (?) i {,s}

6-14

Set (Query) the label text for mark #i.

AUX INPUT/OUTPUT

page

description

OAUX ? i

6-15

Query the value of Aux Input i (1,2,3,4).

AUXM(?) i{, j}

6-15

Set (Query) the Output Mode of Aux Output i (1,2,3,4). j selects Fixed (0), Log (1) or Linear (2).

AUXV (?) i {, x}

6-15

Set (Query) voltage of Aux Output i (1,2,3,4) to x Volts. -10.500 ≤ x ≤ 10.500. Fixed Output Mode only.

SAUX (?) i {, x, y, z}

6-15

Set (Query) the Aux Output i (1,2,3,4) Sweep Limits to Start (x), Stop (y) and Offset (z) voltages. 0.001 ≤ x,y ≤ 21.000 and

-10.500

≤ z ≤ 10.500.

TSTR (?) {i}

6-15

Set (Query) the Trigger Starts Scan? mode to No (0) or Yes (1).

MATH

page

description

SMTH i

6-16

Smooth the data within the active chart using 5 (0), 11 (1), 17 (2), 21 (3), 25 (4) point width.

COPR (?) {i}

6-16

Set (Query) the Calculator Operation to +, -, x, /, sin, cos, tan, √x, x

, log, 10x (i=0...10).

CALC

6-17

Do the Calculation selected by COPR with the argument set by CTRC or CARG.

CAGT (?) {i}

6-17

Set (Query) the Calculation Argument Type to Trace (0) or Constant (1).

CTRC (?) {i}

6-17

Set (Query) the Trace Argument to Trace i (1,2,3,4).

CARG (?) {x}

6-17

Set (Query) the Constant Argument value to x.

FTYP (?) {i}

6-17

Set (Query) the Fit Type to Linear (0), Exponential (1) or Gaussian (2).

FITT i, j

6-17

Fit the data within the chart region between i% and j% from the left edge. 0 ≤ i,j ≤ 100.

PARS ? i

6-17

Query the fit parameters a (0), b (1), c (2) or t0 (3).

STAT i, j

6-17

Statistically analyze the data within the chart region between i% and j% from the left edge. 0 ≤ i,j ≤ 100.

SPAR ? i

6-17

Query the Statistical results mean (0), standard dev (1), total (2) or delta time (3).

STORE AND RECALL FILE

page

description

FNAM (?) {s}

6-18

Set (Query) the current File Name to string s.

SDAT

6-18

Save the Active Display's Trace Data to the file specified by FNAM.

SASC

6-18

Save the Active Display's Trace Data in ASCII format to the file specified by FNAM.

SR850 DSP Lock-In Amplifier

1-9

SSET

6-18

Save the Settings to the file specified by FNAM.

RDAT

6-18

Recall the Trace Data from the file specified by FNAM to the active display's trace buffer.

RSET

6-18

Recall the Settings from the file specified by FNAM.

SETUP

page

description

OUTX (?) {i}

6-19

Set (Query) the Output Interface to RS232 (0) or GPIB (1).

OVRM (?) {i}

6-19

Set (Query) the GPIB Overide Remote state to Off (0) or On (1).

KCLK (?) {i}

6-19

Set (Query) the Key Click to Off (0) or On (1).

ALRM (?) {i}

6-19

Set (Query) the Alarms to Off (0) or On (1).

THRS (?) {i}

6-19

Set (Query) the Hours to 0≤ i ≤ 23.

TMIN (?) {i}

6-19

Set (Query) the Minutes to 0 ≤ i ≤ 59.

TSEC (?) {i}

6-19

Set (Query) the Seconds to 0 ≤ i ≤ 59.

DMTH (?) {i}

6-19

Set (Query) the Month to 1 ≤ 1 ≤ 12.

DDAY (?) {i}

6-19

Set (Query) the Day to 1 ≤ 1 ≤ 31.

DYRS (?) {i}

6-19

Set (Query) the Year to 0 ≤ 1 ≤ 99.

PLTM (?) {i}

6-19

Set (Query) the Plotter Mode to RS232 (0) or GPIB (1).

PLTB (?) {i}

6-19

Set (Query) the Plotter Baud Rate to 300 (0), 1200 (1), 2400 (2), 4800 (3), 9600 (4).

PLTA (?) {i}

6-19

Set (Query) the Plotter GPIB Address to 0 ≤ i ≤ 30.

PLTS (?) {i}

6-19

Set (Query) the Plot Speed to Fast (0) or Slow (1).

PNTR (?) {i}

6-19

Set (Query) the Trace Pen Number to 1 ≤ i ≤ 6.

PNGD (?) {i}

6-20

Set (Query) the Grid Pen Number to 1 ≤ i ≤ 6.

PNAL (?) {i}

6-20

Set (Query) the Alphanumeric Pen Number to 1 ≤ i ≤ 6.

PNCR (?) {i}

6-20

Set (Query) the Cursor Pen Number to 1 ≤ i ≤ 6.

PRNT (?) {i}

6-20

Set (Query) the Printer Type to Epson (0), HP (1) or File (2).

PRINT AND PLOT

page

description

PRSC

6-21

Print the screen. Same as the [PRINT] key.

PALL

6-21

Plot the display(s).

PTRC

6-21

Plot the trace(s) only.

PCUR

6-21

Plot the cursor(s) only.

FRONT PANEL CONTROLS AUTO FUNCTIONS

page

description

STRT

6-22

Start or continue a scan. Same as [START/CONT] key.

PAUS

6-22

Pause a scan. Does not reset a paused or done scan.

REST

6-22

Reset the scan. All stored data is lost.

ASCL

6-11

Auto Scale the active display.

ATRC (?) {i}

6-22

Set (Query) the active display to Top (0) or Bottom (1). Full screen is always active.

AGAN

6-22

Auto Gain function. Same as pressing the [AUTO GAIN] key.

ARSV

6-22

Auto Reserve function. Same as pressing the [AUTO RESERVE] key.

APHS

6-22

Auto Phase function. Same as pressing the [AUTO PHASE] key.

AOFF i

6-22

Auto Offset X,Y or R (i=1,2,3).

CMAX

6-22

Move Cursor to Max or Min. Same as pressing the [CURSOR MAX/MIN] key.

DATA TRANSFER

page

description

OUTP? i

6-23

Query the value of X (1), Y (2), R (3) or

(4). Returns ASCII floating point value.

OUTR? i

6-23

Query the value of Trace i (1,2,3,4). Returns ASCII floating point value.

SNAP?i,j{k,

l,m,n}

6-23

Records the values of 2,3,4,5, or 6 parameters at a single instant in time.

OAUX? i

6-23

Query the value of Aux Input i (1,2,3,4). Returns ASCII floating point value.

SPTS? i

6-23

Query the number of points stored in Trace i (1,2,3,4).

TRCA? i,j,k

6-23

Read k≥1 points starting at bin j≥0 from trace i (1,2,3,4) in ASCII floating point.

TRCB? i,j,k

6-23

Read k≥1 points starting at bin j≥0 from trace i (1,2,3,4) in IEEE binary floating point.

TRCL? i,j,k

6-24

Read k≥1 points starting at bin j≥0 from trace i (1,2,3,4) in non-normalized binary floating point.

FAST (?) {i}

6-25

Set (Query) Fast Data Transfer Mode On (2) for Windows programs, On (1) for DOS programs, or Off (0). On will transfer binary X and Y every sample during a scan over the GPIB interface.

SR850 DSP Lock-In Amplifier

1-10

SERIAL POLL STATUS BYTE

(6-28)

bit

name

usage

SCN

No data is being acquired

IFC

No command execution in progress

ERR

Unmasked bit in error status byte set

LIA

Unmasked bit in LIA status byte set

MAV

The interface output buffer is non-empty

ESB

Unmasked bit in standard status byte set

SRQ

SRQ (service request) has occurred

Unused

STANDARD EVENT STATUS BYTE

(6-29)

bit

name

usage

INP

Set on input queue overflow

Unused

QRY

Set on output queue overflow

Unused

EXE

Set when command execution error occurs

CMD

Set when an illegal command is received

URQ

Set by any key press or knob rotation

PON

Set by power-on

LIA STATUS BYTE

(6-29)

bit

name

usage

RESRV

Set when a RESRV overload is detected

FILTR

Set when a FILTR overload is detected

OUTPT

Set when a OUTPT overload is detected

UNLK

Set when reference unlock is detected

RANGE

Set when detection freq crosses 200 Hz

Set when time constant is changed

TRIG

Set when unit is triggered

PLOT

Set when a plot is completed

ERROR STATUS BYTE

(6-30)

bit

name

usage

Prn/Plt Err

Set when an printing or plotting error occurs

Backup Error

Set when battery backup fails

RAM Error

Set when RAM Memory test finds an error

Disk Error

Set when a disk error occurs

ROM Error

Set when ROM Memory test finds an error

GPIB Error

Set when GPIB binary data transfer aborts

DSP Error

Set when DSP test finds an error

Math Error

Set when an internal math error occurs

STATUS BYTE DEFINITIONS

STRD

6-25

Start a scan after 0.5sec delay. Use with Fast Data Transfer Mode.

INTERFACE

page

description

*RST

6-26

Reset the unit to its default configurations.

*IDN?

6-26

Read the SR850 device identification string.

LOCL(?) {i}

6-26

Set (Query) the Local/Remote state to LOCAL (0), REMOTE (1), or LOCAL LOCKOUT (2).

OVRM (?) {i}

6-26

Set (Query) the GPIB Overide Remote state to Off (0) or On (1).

TRIG

6-26

Software trigger command. Same as trigger input.

STATUS

page

description

*CLS

6-27

Clear all status bytes.

*ESE (?) {i} {,j}

6-27

Set (Query) the Standard Event Status Byte Enable Register to the decimal value i (0-255). *ESE i,j sets bit i (0-7) to j (0 or 1). *ESE? queries the byte. *ESE?i queries only bit i.

*ESR? {i}

6-27

Query the Standard Event Status Byte. If i is included, only bit i is queried.

*SRE (?) {i} {,j}

6-27

Set (Query) the Serial Poll Enable Register to the decimal value i (0-255). *SRE i,j sets bit i (0-

7) to j (0 or 1). *SRE? queries the byte, *SRE?i queries only bit i.

*STB? {i}

6-27

Query the Serial Poll Status Byte. If i is included, only bit i is queried.

*PSC (?) {i}

6-27

Set (Query) the Power On Status Clear bit to Set (1) or Clear (0).

ERRE (?) {i} {,j}

6-27

Set (Query) the Error Status Enable Register to the decimal value i (0-255). ERRE i,j sets bit i (0-7) to j (0 or 1). ERRE? queries the byte, ERRE?i queries only bit i.

ERRS? {i}

6-27

Query the Error Status Byte. If i is included, only bit i is queried.

LIAE (?) {i} {,j}

6-27

Set (Query) the LIA Status Enable Register to the decimal value i (0-255). LIAE i,j sets bit i (0-7) to j (0 or 1). LIAE? queries the byte, LIAE?i queries only bit i.

LIAS? {i}

6-27

Query the LIA Status Byte. If i is included, only bit i is queried.

GETTING STARTED

The sample measurements described in this section are designed to acquaint the first time user with the SR850 DSP Lock-In Amplifier. Do not be concerned that your measurements do not exactly agree with these exercises. The focus of these measurement exercises is to learn how to use the instrument.

It is highly recommended that the first time user step through some or all of these exercises before attempting to perform an actual experiment.

The experimental procedures are detailed in two columns. The left column lists the actual steps in the experiment. The right column is an explanation of each step.

Key Types

There are two types of front panel keys which will be referred to in this manual. Hardkeys are those keys with labels printed on them. Their function is determined by the label and does not change. Hardkeys are referenced by brackets like this - [HARDKEY]. The softkeys are the six gray keys along the right edge of the screen. Their function is labelled by a menu box displayed on the screen next to the key. Softkey functions change depending upon the situation. Softkeys will be referred to as the <Soft Key> or simply the Soft Key.

Hardkeys

The keypad consists of five groups of hardkeys. The ENTRY keys are used to enter numeric parameters which have been highlighted by a softkey. The MENU keys select a menu of softkeys. Pressing a menu key will change the menu boxes which are displayed next to the softkeys. Each menu groups together similar parameters and functions. The CONTROL keys start and stop actual data acquisition, select the cursor and toggle the active display. These keys are not in a menu since they are used frequently and while displaying any menu. The SYSTEM keys output the screen to a printer and display help messages. These keys can also be accessed from any menu. The AUTO keys perform auto functions such as Auto Gain and Auto Phase.

Softkeys

The SR850 has a menu driven user interface. The 6 softkeys to the right of the video display have different functions depending upon the information displayed in the menu boxes at the right of the video display. In general, the softkeys have two uses. The first is to toggle a feature on and off or to choose between settings. The second is to highlight a parameter which is then changed using the knob or numeric keypad. In both cases, the softkey selects the parameter which is displayed adjacent to it.

Knob

The knob is used to adjust parameters which have been highlighted by a softkey. Many numeric entry fields may be adjusted with the knob. In addition, many parameters are adjusted only with the knob. These are typically parameters with a limited set of values, such as sensitivity or time constant. In these cases, the parameter is selected by a softkey. The [CURSOR] key will set the knob function to scrolling the cursor within the active chart display.

2-1

YOUR FIRST MEASUREMENTS

Getting Started

2-2

The input impedance of the lock-in is 10 MΩ. The Sine Out has an output impedance of 50Ω. Since

The Basic Lock-in

THE BASIC LOCK-IN

This measurement is designed to use the internal oscillator to explore some of the basic lock-in functions. You will need BNC cables.

Specifically, you will measure the amplitude of the Sine Out at various frequencies, sensitivities, time constants and phase shifts. The "normal" lock-in display will be used throughout this exercise.

1. Disconnect all cables from the lock-in. Turn the power on while holding down the [ (backspace) key. Wait until the power-on tests are completed.

2. Connect the Sine Out on the front panel to the A input using a BNC cable.

←]

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

The display is the "normal" lock-in display. The lock-in setup is displayed across the top of the screen. The sensitivity, reserve, time constant, prefilters and input configuration are all easily visible. Watch how these indicators change as you change parameters. The upper numeric readout and bar graph shows the value of X (Rcosθ) and the lower graph shows the the value of Y (Rsinθ).

the Sine Output amplitude is specified into a high impedance load, the output impedance does not affect the amplitude.

The lock-in defaults to the internal oscillator reference set at 1.000 kHz. The reference mode (Intrnl) and frequency are displayed at the bottom of the screen. In this mode, the lock-in generates a synchronous sine output at the internal reference frequency.

3. Press [AUTO PHASE]

4. Press [REF/PHASE]

The sine amplitude is 1.000 Vrms and the sensitivity is 1 V(rms). Since the phase shift of the sine output is very close to zero, the upper display (X) should read close to 1.000 V and the lower display (Y) should read close to 0.000 V.

Automatically adjust the reference phase shift to eliminate any residual phase error. This should set the value of Y to zero.

Display the Reference and Phase menu. The phase shift (displayed in the top menu box) should be close to zero.

2-3

5. Press the <Rotate 90 deg> softkey.

50 Ω load).

The Basic Lock-in

This adds 90° to the reference phase shift. The value of X drops to zero and Y becomes minus the

magnitude (-1.000 V). Press the <deg.> softkey. Use the knob to adjust the phase shift until Y

is zero and X is equal to the positive amplitude.

Press [9] [0] [ENTER]

Press [AUTO PHASE]

6. Press <Ref. Frequency> Press [1] [2] [.] [3] [4] [5] [EXP] [3] [ENTER]

Press [1] [0] [0] [0] [ENTER]

Highlight the phase shift. The knob can be used to adjust parameters which

are continuous, such as phase, amplitude and frequency. The final phase value should be close to zero again.

Phase shifts can also be entered numerically. The knob is useful for small adjustments while

numeric entry is easier when changing to a precise value or by a large amount.

Use the Auto Phase function to return Y to zero and X to the amplitude.

Highlight the internal reference frequency menu. Enter 12.345 kHz in exponential form. The meas-

ured signal amplitude should stay within 1% of 1 V and the phase shift should stay close to zero (the value of Y should stay close to zero).

Parameters can be entered in real or integer form as well. In this case, the frequency is changed to

1.000 kHz.

7. Press <Sine Output> Use the knob to adjust the amplitude.

Press [.] [0] [1] [ENTER]

8. Press [GAIN/TC] Press [AUTO GAIN]

The internal oscillator is crystal synthesized with 25 ppm of frequency error. The frequency can be set with 5 digit or 0.1 mHz resolution, whichever is greater.

Highlight the sine output amplitude. As the amplitude is changed, the measured value

of X should equal the sine output amplitude. The amplitude may be entered numerically also. The sine amplitude can be set from 4 mV to 5 V

rms into high impedance (half the amplitude into a

Display the Gain and Time Constant menu. The Auto Gain function will adjust the sensitivity so

2-4

9. Press <Sensitivity>

Use the knob to change the sensitivity to 50 mV.

Change the sensitivity back to 20 mV.

10. Press <Time Constant>

Use the knob to change the time constant to 300 µs.

Change the time constant to 3 ms.

The Basic Lock-in

that the measured magnitude (R) is a sizable percentage of full scale.

Highlight the full scale sensitivity. Parameters which are discrete values, such as

sensitivity and time constant, can only be changed with the knob. Numeric entry is not allowed for these parameters.

Highlight the time constant. The values of X and Y become noisy. This is

because the 2f component of the output (at 2 kHz) is no longer attenuated completely by the low pass filters.

Let's leave the time constant short and change the filter slope.

11. Press the <Filter db/oct.> softkey until 6 dB/oct

is selected.

Press <Filter db/oct.> again to select 12 dB/oct.

Press <Filter db/oct.> twice to select 24 db/oct.

Press <Filter db/oct> again to select 6 db/oct.

12. Press [REF/PHASE]

Press <Ref. Frequency> Press [5] [0] [ENTER]

Parameters which have their available options displayed within the menu box are selected by pressing the corresponding softkey until the desired option is chosen.

The X and Y outputs are somewhat noisy at this short time constant and only 1 pole of low pass filtering.

The outputs are less noisy with 2 poles of filtering.

With 4 poles of low pass filtering, even this short time constant attenuates the 2f component reasonably well and provides steady readings.

Let's leave the filtering short and the outputs noisy for now.

Display the Reference and Phase menu. Highlight the internal reference frequency. Enter 50 Hz for the reference frequency. With a

3 ms time constant and only 6 db/oct of filtering, the output is totally dominated by the 2f component at 50 Hz.

2-5

The Basic Lock-in

13. Press [GAIN/TC] Press <Synchronous> to select <200 Hz.

Display the Gain and Time Constant menu again. This turns on synchronous filtering whenever the detection frequency is below 200 Hz.

Synchronous filtering effectively removes output components at multiples of the detection frequency. At low frequencies, this filter is a very effective way to remove 2f without requiring extremely long time constants.

The outputs are now very quiet and steady, even though the time constant is very short. The response time of the synchronous filter is equal to the period of the detection frequency (20 ms in this case).

This concludes this measurement example. You should have a feeling for the basic operation of the menus, knob and numeric entry. Basic lock-in parameters have been introduced and you should be able to perform simple measurements.

2-6

The input impedance of the lock-in is 10 MΩ. The tors have either a 50Ω or 600Ω output impedance.

Displays and Traces

DISPLAYS and TRACES

This measurement is designed to use the internal oscillator and an external signal source to explore some of the display types. You will need a synthesized function generator capable of providing a 100 mVrms sine wave at 1.000 kHz (the DS345 from SRS will suffice), BNC cables and a terminator appropriate for the generator function output.

Specifically, you will display the lock-in outputs when measuring a signal close to, but not equal to, the internal reference frequency. This setup ensures changing outputs which are more illustrative than steady outputs. The displays will be configured to show X, Y, R and θ in bar graph and polar formats. The example Scans and Sweeps demonstrates the use of the chart graph.

1. Disconnect all cables from the lock-in. Turn

the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

2. Turn on the function generator, set the fre-

quency to 1.0000 kHz (exactly) and the amplitude to 500 mVrms.

Connect the function output (sine wave) from the synthesized function generator to the A input using a BNC cable and appropriate terminator.

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

generator may require a terminator. Many generaUse the appropriate feedthrough or T termination if

necessary. In general, not using a terminator means that the function output amplitude will not agree with the generator setting.

The lock-in defaults to the internal oscillator reference set at 1.000 kHz. The reference mode (Intrnl) and frequency are displayed at the bottom of the screen. In this mode, the internal oscillator sets the detection frequency.

3. Press [REF/PHASE]

The internal oscillator is crystal synthesized so that the actual reference frequency should be very close to the actual generator frequency. The X and Y displays should read values which change very slowly. The lock-in and the generator are not phase locked but they are at the same frequency with some slowly changing phase.

Display the Reference and Phase menu.

2-7

Displays and Traces

Highlight the internal oscillator frequency. By setting the lock-in reference 0.2 Hz away from

the signal frequency, the X and Y outputs are

0.2 Hz sine waves (difference between reference and signal frequency). The X and Y output displays should now oscillate at about 0.2 Hz (the accuracy is determined by the crystals of the generator and the lock-in).

Display the Display and Scale menu. The SR850 collects data in the form of traces.

There are 4 definable traces and only these trace quantities may be displayed. The default definition of these traces is X, Y, R and θ for traces 1, 2, 3 and 4.

The Display Scale menu box shows the display parameters for the Full (screen), Top or Bottom (split screen) displays. In this case, the Top display parameters are shown.

Each display shows one of the data traces. The Top display defaults to showing trace 1 which has a default definition of X. Thus the top bar graph shows the X output.

Trace 3 has a default definition of R so showing trace 3 on the top graph will display the quantity R.

R is phase independent so it shows a steady value (close to 0.500 V).

[AUTO SCALE] automatically scales the active display. The top display is the active display (as indicated by the inverse trace identifier at the upper left of the display).

To modify the bottom graph, you must display the bottom graph's parameters in the Display Scale menu box. This also makes the bottom display the active display (for autoscaling). The trace indicator (at the upper left of each display) is highlighted on the active display.

The bottom display defaults to trace 2 (Y).

Trace 4 is θ. The phase between the reference and the signal changes by 360° every 5 sec (0.2 Hz difference frequency).

Press <Ref. Frequency> Use the knob to change the frequency to

999.80 Hz.

Press [DISPLAY/SCALE]

Press <Type/Trace> twice to highlight the displayed trace number.

Use the knob to change the trace number to 3.

Press [AUTO SCALE]

Press <Full, Top or Bottom> to select Bottom.

Press <Type/Trace> twice to highlight the displayed trace number.

Use the knob to change the trace number to 4.

2-8

Displays and Traces

[AUTO SCALE] automatically scales the active display. In this case, the trace data is moving and autoscaling may not do a very satisfactory job.

To manually set the graph scale, you set the range (±) and center value (@). The graph displays a scale equal to the center value plus and minus the range.

In this case, set the bar graph to ±180°. The bar graph should be a linear phase ramp at 0.2 Hz.

The monitor display at the top of the screen monitors either the lock-in settings (sensitivity, time constant, etc.) or the measured lock-in inputs and outputs (X, Y, R, θ and Aux In 1-4).

The Input/Output monitor allows you to see all of the measured quantities, even if they are not shown on the larger displays.

The screen is now setup for a single display. The default display type for the full screen display is a polar graph.

The polar graph plots the quantities X and Y on an X-Y axis. The resulting vector has a length equal to the magnitude R and has a phase angle relative to the positive X axis equal to θ. In this case, since the phase is rotating at the difference frequency, the vector rotates at 0.2 Hz.

Display the Reference and Phase menu. Highlight the internal oscillator frequency. As the internal reference frequency gets closer to

the signal frequency, the rotation gets slower and slower. If the frequencies are EXACTLY equal, then the phase is constant.

By using the signal source as the external reference, the lock-in will phase lock its internal oscillator to the signal frequency and the phase will be a constant.

Highlight the reference source. Select external reference mode. The lock-in will

phase lock to the signal at the Reference Input.

Press [AUTO SCALE]

Press the <± Range> softkey. This is the fifth softkey from the top.

Press [1] [8] [0] [ENTER]

Press <Monitor> to select Input/Output.

Press <Format> to select Single.

Press [REF/PHASE] Press <Ref. Frequency> Use the knob to adjust the frequency slowly to

try to stop the rotation of the signal vector.

Use a BNC cable to connect the TTL SYNC output from the generator to the Reference Input of the lock-in.

Press <Ref. Source> Use the knob to select External.

2-9

With a TTL reference signal, the slope needs to be set to either rising or falling edge.

The signal vector on the polar graph will not rotate since the phase is a constant. The actual phase depends upon the phase difference between the function output and the sync output from the generator.

The external reference frequency (as measured by the lock-in) is displayed at the bottom of the screen. The reference mode is shown as Ext+ for external TTL rising edge. The LOCK indicator should be on (successfully locked to the external reference).

Display the Display and Scale menu. Change the screen to dual display mode again.

Display the Trace and Scan menu. Trace 3 is defined as R and is displayed on the top

graph. Let's change the definition of trace 3 to something else.

Traces are defined as A•B/C. The quantities A, B, and C are selected from the various quantities measured by the lock-in.

Trace 3 has now been redefined to be X. The top graph now displays X. The trace definition is shown at the upper left of each graph.

Traces may be defined to be ratios and products of 2 or 3 quantities.

Trace 3 is now defined as X/R and is equal to cosθ, independent of the signal amplitude. The traces can be defined to display the most useful quantities for a given experiment. Trace data may be stored in the data buffers. Scans and chart graphs will be discussed in a later example.

Change the reference phase shift to check that trace 3 displays cosθ.

Automatically adjust the measured phase shift to zero. The top display should show cos0° or 1.

Highlight the phase shift.

Press <Ref. Slope> to select Rising Edge.

10.

Press [DISPLAY/SCALE] Press <Format> to select Up/Down.

11.

Press [TRACE/SCAN] Press <1 / 2 / 3 / 4> to select trace 3.

Press the second softkey, next to the trace definition, to highlight the R.

Use the knob to change the A parameter from R to X.

Press the second softkey to highlight the denominator (C) of the trace definition.

Use the knob to change the C parameter from 1 to R.

12.

Press [REF/PHASE]

Press [AUTO PHASE]

Press <deg.>

Displays and Traces

2-10

Displays and Traces

Using the keypad, enter a phase shift which is 45° greater than the displayed phase shift.

At a measured phase shift of 45°, trace 3 should equal cos45° or 0.707.

This concludes this measurement example. You should have a feeling for the basic operation of the display types and trace definitions.

2-11

Displays and Traces

2-12

The input impedance of the lock-in is 10 MΩ. The Sine Out has an output impedance of 50Ω. Since

Outputs, Offsets and Expands

OUTPUTS, OFFSETS and EXPANDS

This measurement is designed to use the internal oscillator to explore some of the basic lock-in outputs. You will need BNC cables and a digital voltmeter (DVM).

Specifically, you will measure the amplitude of the Sine Out and provide analog outputs proportional to the measurement. The effect of offsets and expands on the displayed values and the analog outputs will be explored.

1. Disconnect all cables from the lock-in. Turn

the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

2. Connect the Sine Out on the front panel to the

A input using a BNC cable.

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

the Sine Output amplitude is specified into a high impedance load, the output impedance does not affect the amplitude.

3. Connect the CH1 output on the front panel to

the DVM. Set the DVM to read DC Volts.

The CH1 output defaults to X. The output voltage is simply (X/Sensitivity - Offset)xExpandx10V. In this case, X = 1.000 V, the sensitivity = 1 V, the offset is zero percent and the expand is 1. The output should thus be 10 V or 100% of full scale.

2-13

4. Press [REF/PHASE]

Outputs, Offsets and Expands

Display the Reference and Phase menu. Press <Sine Output> Press [.] [5] [ENTER]

5. Press [OUTPUT/OFFSET]

Press <Auto Offset>

Highlight the sine output amplitude.

Enter an amplitude of 0.5 V. The top display

should show X=0.5 V and the CH1 output should

be 5 V on the DVM.

Display the Output and Offset menu. This menu

chooses which measured parameters or traces

are output on CH1 and CH2. In addition, the X, Y

and R offsets and expands are programmed in this

menu.

The Offset & Expand menu box displays the offset

and expand of either X, Y or R. In this case, the X

offset and expand is displayed. The <X,Y,R> soft-

key selects the which offset and expand is

displayed.

Auto Offset automatically adjusts the Xoffset (or Y

or R) such that X (or Y or R) becomes zero. The

offset should be about 50% in this case. Offsets

are useful for making relative measurements. In

analog lock-ins, offsets were generally used to

remove DC output errors from the lock-in itself.

The SR850 has no DC output errors and the offset

is not required for most measurements.

Press <Offset> Press [4] [0] [ENTER]

Press <Expand> Set the expand to 10 using the knob or the

numeric entry keys.

The offset affects both the displayed value of X

and any analog output proportional to X. The CH1

output should be zero in this case.

The highlighted OFFST indicator turns on at the

bottom left of the top display to indicate that the

displayed trace is affected by an offset.

Highlight the X offset.

Enter an offset of 40% of full scale. The output off-

sets are a percentage of full scale. The percent-

age does not change with the sensitivity. The dis-

played value of X should be 0.100 V (0.5 V - 40%

of full scale). The CH1 output voltage is

(X/Sensitivity - Offset)xExpandx10V.

CH1 Out = (0.5/1.0 - 0.4)x1x10V = 1 V

Highlight the X expand.

With an expand of 10, the display has one more

digit of resolution (100.XX mV).

2-14

Outputs, Offsets and Expands

The highlighted EXPD indicator turns on at the bottom left of the top display to indicate that the displayed trace is affected by an expand.

The CH1 output is (X/Sensitivity - Offset)xExpandx10V. In this case, the output voltage is

CH1 Out = (0.5/1.0 - 0.4)x10x10V = 10V The expand allows the output gain to be increased

by up to 256. The output voltage is limited to

10.9 V and any output which tries to be greater will turn on the OUTPT overload indicator at the bottom left of the screen.

With offset and expand, the output voltage gain and offset can be programmed to provide control of feedback signals with the proper bias and gain for a variety of situations.

Offsets do add and subtract from the displayed values while expand increases the resolution of the display.

6. Connect the DVM to the X output on the rear

panel.

7. Connect the DVM to the CH1 output on the

front panel again. Press <Expand> Press [1] [ENTER]

The X and Y outputs on the rear panel always provide voltages proportional to X and Y (with offset and expand). The X output voltage should be 10 V, just like the CH1 output.

The front panel outputs can be configured to output different traces quantities while the rear panel outputs always output X and Y.

Outputs proportional to X and Y (rear panel, CH1 or CH2) have 100 kHz of bandwidth. The CH1 and CH2 outputs, when configured to be proportional to R, θ, or a trace (even a trace defined as X or Y) are updated at 512 Hz and have a 200 Hz bandwidth. It is important to keep this in mind if you use very short time constants.

Let's change CH1 to a trace.

First, set the X expand back to 1.

Press <Offset> Press [0] [ENTER]

Set the X offset back to 0.0%. X Should be 0.500 V again and the CH1 output

should be 5.0 V.

2-15

Outputs, Offsets and Expands

Press <Source>

Use the knob to select Trace1.

8. Press [TRACE/SCAN]

Press the second softkey, next to the trace definition, to highlight the X.

Use the knob to change the numerator from X to 1.

Press the second softkey twice to highlight the denominator (C) of the trace definition.

Use the knob to change the denominator from 1 to X.

Highlight the CH1 source. The CH1 output is pro-

portional to this source.

CH1 can be proportional to X, R, θ, or Trace 1-4.

Choose Trace 1. Trace 1 has a default definition of

X so the CH1 output should remain 5.0 V (but its

bandwidth is only 200 Hz instead of 100 kHz).

Display the Trace and Scan menu.

Traces are defined as A•B/C. The quantities A, B,

and C are selected from the various quantities

measured by the lock-in.

Trace 1 is defined as X by default. Let's change it

to 1/X.

Trace 1 is now 1•1/1 and the top display shows

1.000

Change the denominator.

Trace 1 is now defined as 1/X. The top display

shows Trace 1. The trace definition is shown at

the upper left of the top display. The trace units

are shown at the bottom center of the top display

(1/V).

Remember, X was 0.5V. Thus, 1/X is 1/0.5 = 2.0

(1/V). The display should show 2.0 (or very close).

Displays use the actual measured quantities to

calculate the value of a trace. If X was 5 mV, the

value of Trace 1 would be 1/5 mV or 200 (1/V).

Traces are calculated using Volts, degrees, and

Hz for the units of A, B and C.

The CH1 output voltage is 0.2V. This is because

trace output voltages are calculated using the

output voltages of the A, B and C quantities rather

than their displayed values. In this case, X=0.5V.

As an analog output voltage, this would be 5.0 V

(1/2 scale of 1V full scale sensitivity). The 1/X

output voltage is 1/5.0V or 0.2 V.

See the DC Outputs and Scaling discussion in the

Lock-In Basics section for more detailed

information.

2-16

The input impedance of the lock-in is 10 MΩ. The Sine Out has an output impedance of 50Ω. Since

Scans and Sweeps

SCANS and SWEEPS

This measurement is designed to use the internal oscillator to explore some of the basic lock-in functions. You will need BNC cables.

Specifically, you will measure the response of the line notch filters by sweeping the internal reference frequency and measuring the sine output. Traces and strip chart displays will be used to record X, Y, R and θ as the signal is swept through the input notch filters.

1. Disconnect all cables from the lock-in. Turn

the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

2. Connect the Sine Out on the front panel to the

A input using a BNC cable.

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

the Sine Output amplitude is specified into a high impedance load, the output impedance does not affect the amplitude.

3. Press [INPUT/FILTERS]

Press the <Line Notches> softkey until Both filters are selected.

Display the Input and Filters menu. This menu allows the input configuration to be changed.

With the line notch filters engaged, signal inputs at 60 (50) Hz and 120 (100) Hz are removed. Note that the line filter indicators at the top of the screen are both on.

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4. Press [DISPLAY/SCALE]

Scans and Sweeps

Display the Display and Scale menu. This menu

configures and scales the different screen displays

and graphs. Press the <Type/Trace> softkey to select the

Trace number.

Use the knob to select Trace 3.

5. Press [REF/PHASE] Press <Ref. Source> Use the knob to select Internal Sweep.

6. Press <Sweep Menu>

Press <Start> Press [4] [0] [ENTER].

Highlight the trace number for the Top Bar graph. The SR850 acquires and displays data in the form of traces. The default definitions for the 4 traces are X, Y, R and θ. These definitions may be changed.

Display the magnitude R (Trace 3) on the top graph.

Display the Reference and Phase menu. Choose internal reference frequency sweep. In

this mode, the SR850 will sweep the internal oscillator from a start to a stop frequency.

Set the sweep start and stop frequencies in this submenu. Sweeps may be linear or logarithmic. In this case, let's use a linear sweep.

Highlight the start frequency. Set the start frequency to 40 Hz. The reference

changes to 40.000 Hz as shown in the frequency

readout at the bottom center of the screen. Press <Stop> Press [1] [6] [0] [ENTER].

7. Press [GAIN/TC] Press <Time Constant> and use the knob to

select 10 ms. Press <Synchronous> to select <200 Hz.

8. Press [TRACE/SCAN]

Highlight the stop frequency. Set the stop frequency to 160 Hz.

Display the Gain and Time Constant menu. Choose a short time constant so that the frequen-

cy can be swept in a reasonably short time. Since the sweep frequencies are below 200 Hz,

you can take advantage of the synchronous filter to remove the 2f component of the output without using a long time constant.

Display the Trace and Scan menu. This menu allows the trace definitions to be changed and the scan (sweep) to be configured. Trace data is sampled and stored in the buffers at the sample rate. Swept parameters (reference frequency in this case) are also updated at the sample rate (imme-

2-18

Scans and Sweeps

diately after the data is sampled). The scan time sets the amount of time the buffer will store and the length of any sweep.

In this measurement, let's leave the trace definitions equal to the defaults and just change the

sample rate and scan time. Press <Sample Rate> Use the knob to select 32 Hz.

Press <Scan Length> Press [1] [0] [0] [ENTER]

Press <1 Shot/Loop> to select 1 Shot.

Highlight the sample rate.

The trace data will be sampled at 32 Hz and

stored in the buffer. After each data point is

recorded, the reference frequency will be updated.

This determines the resolution of our data along

the time axis.

Highlight the scan length.

Set the scan length to 100 seconds (1:40). This

configures the data buffer to hold 3200 data points

(32 Hz sample rate x 100 second scan length).

The scan length is also the sweep time for the

internal frequency sweep. Sweeps are always

coordinated with the data acquisition. In this case,

the sweep range is 120 Hz (40 Hz to 160 Hz) and

will take 100 seconds and be updated 3200 times.

Each stored data point will represent a frequency

increment of 0.0375 Hz (120/3200).

Scans can repeat (Loop) or stop when finished (1

Shot). Let's take a single scan of data.

Now you're finally ready to start the scan.

9. Press [START/CONT]

The [START/CONT] key starts the scan and

sweep. The scan indicator at the bottom left corner

of the screen switches from STOP to Run 1 (single

scan in progress). The reference frequency read-

out at the bottom center displays the frequency

while sweeping.

As the frequency passes through 60 (50) Hz and

120 (100) Hz, the value of R should drop close to

zero as the signal sweeps through each input

notch filter.

When the scan is complete, the scan indicator

switches to DONE and the frequency should be

160 Hz.

Now let's try displaying the data in a more mean-

ingful way.

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Scans and Sweeps

10. Press [DISPLAY/SCALE] Press <Format> to select Single. Press <Type> Use the knob to select Chart. Press <Type> again to highlight the Trace

number. Use the knob to select Trace 3. Press [AUTO SCALE]

11. Press the <± Range> softkey. This is the fifth softkey from the top.

Use the knob to select 1.000 e0 (1 V) for the range.

Press the <± Range> softkey again to highlight the center value (@).

Display the Display and Scale menu. Choose a full screen display. Highlight the display type (the default is polar). Let's view the stored data on a chart graph. To view R on the chart, you need to display Trace

3. The chart now displays R vs time (frequency). Auto Scale the graph. To manually adjust the graph scale, you change

the center value and range. Highlight the range (±).

The graph displays a vertical scale equal to the center value plus and minus the range. The range can also be entered numerically to any value. The knob adjusts the range in a 1-2-5 sequence.

Highlight the center value.

Press [0] [ENTER]

12. Press [CURSOR]

Use the knob to read specific data points from the graph.

Press [CURSOR SETUP]

Set the center to zero. The graph always displays the center and range

below the chart in the units of the trace being displayed. The default horizontal scale is 10 seconds per division. This can be changed but let's leave it since the entire scan fits perfectly on the screen.

This key activates the cursor. The knob now controls the cursor. The cursor coordinates are displayed at the top right of the chart. When the cursor coordinates are surrounded by a box, the cursor is active and the knob will move the cursor.

The cursor horizontal position is displayed in units of seconds (time from the end of the scan) and the vertical position is in the trace units. Since this is an internal frequency sweep, let's read the frequency as the horizontal position.

Display the Cursor Setup menu. The cursor can be configured in many different modes. The cursor can be defined as a region where the marker seeks the max or min within the region. Cursors on split screen charts can also be linked together.

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Scans and Sweeps

Press <Cursor Readout> twice to select Fsweep.

Press <Cursor Seek> to select Min.

Use the knob to read the frequencies of the notch filter zeroes or minimums.

13. Press [DISPLAY/SCALE] Press <Type/Trace> to highlight the Trace

number again.

Set the cursor display to show the frequency and trace value of each data point. The reference frequency of each point is displayed in the cursor coordinate display.

The graph shows all 3200 data points at once. Since the screen resolution only has 640 pixels across, each X-axis value must represent multiple data points. The cursor reads the Max, Min or Mean of the data points graphed at each X-axis position.

To read the notch filter minimum frequencies, select Min.

The cursor displays the frequency and trace value of the smallest data point graphed at each horizontal X-axis position.

Show the Display and Scale menu again. The SR850 can store up to 4 traces simultaneously.

In the default configuration, all 4 traces are stored. Let's take a look at the other traces.

Use the knob to select Trace 1.

Use the knob to select Trace 2.

Use the knob to select Trace 4. Press [AUTO SCALE].

14. Press [PAUSE/RESET]

15. Press {START/CONT]

Trace 1 is X. This corresponds to the real part of the filter response.

Trace 2 is Y. This corresponds to the quadrature part of the filter response (or derivative of X).

Trace 4 is θ. This is the phase response of the filters. The phase approaches 180° at the exact filter notch frequencies and approaches zero at frequencies far from the notches. In many experiments, the phase (or quadrature) measurements yield a far more exact measure of the actual resonant or peak frequency than R.

Pressing the [PAUSE/RESET] key while DONE will reset the scan and sweep. The stored data is lost and the scan indicator shows STOP again. Swept parameters (frequency in this case) return to their start values and the graph is blanked.

Let's take the data again, this time while displaying the chart to show the scan data in progress. The data scrolls in from the right. New points are added at the right edge and the old points move to the left. This is a strip chart type of graph.

The buffers can be configured for a single scan (1 Shot) as in this measurement, or continuous

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16.

When the scan is complete, press [

TRACE/SCAN]. Press <1 Shot/Loop> to select Loop. Press [PAUSE/RESET] Press [START/CONT] to start the scan again.

17.

Press [PAUSE/RESET] ONCE.

Press [START/CONT]

18.

Press [DISPLAY/SCALE] Press <sec/div> (the last softkey). Use the knob to select 20 S/div.

looping (Loop). In the loop mode, scans repeat indefinitely and the entire data buffer is filled at the sample rate. When the end is reached, new points are added at the beginning again, overwriting the oldest data. This mode is convenient for always storing the last buffer full of data. If something worth saving occurs, simply pause the scan and save, print or plot the data.

Display the Trace and Scan menu.

Choose the loop buffer. Reset the scan and data buffer. This time, the scan and sweep will repeat at the

end. The buffer is capable of storing 16000 points (for 4 traces). Each scan is 3200 points so 5 complete sweeps can be stored in the buffer.

Pause the scan by pressing the [PAUSE/RESET] key once while the scan is in progress. The scan indicator shows PAUSE. Pressing this key again will reset the data!!!

Resume the scan with [START/CONT] key. Let the scan run for more than 100 seconds so data

scrolls past the left edge of the graph.

Show the Display and Scale menu. Highlight the horizontal chart scale. Twice as much data will now be shown on the

graph. 2 complete sweeps can now be displayed on the graph.

Scans and Sweeps

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The Disk Drive

Disconnect all cables from the lock-in. Turn the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

Connect the Sine Out on the front panel to the A input using a BNC.

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

The display is the "normal" lock-in display. The lock-in setup is displayed across the top of the screen. The upper numeric readout and bar graph shows the value of X (Rcosθ) and the lower graph shows the the value of Y (Rsinθ).

The input impedance of the lock-in is 10 MΩ. The Sine Out has an output impedance of 50Ω. Since the Sine Output amplitude is specified into a high impedance load, the output impedance does not affect the amplitude.

The lock-in defaults to the internal oscillator reference set at 1.000 kHz. The reference mode (Intrnl)

USING THE DISK DRIVE

The disk drive on the SR850 may be used to store 3 types of files.

1. Data File This includes the data in the active display trace. In addition to the data, the instrument state (sensitivity, input configuration, time constant, reference, scan parameters, aux outputs) and the trace definition of the stored trace are saved. Data files are recalled into the trace buffer of the active display. If the present trace buffer is configured to hold less points than the stored trace, then points are recalled starting with the oldest point in the stored trace until the trace buffer is filled. The stored instrument state and the trace definition of the recalled trace are recalled as well. When data is recalled from disk, the instrument state is changed to the state in effect when the data was stored!

2. ASCII Data File This file saves the data in the active display trace in ASCII format. These files may not be recalled to the display. This format is convenient when transferring data to a PC application. ASCII files are much larger than the binary data file for the same trace.

3. Settings File This files stores the lock-in settings. This includes the instrument state (see Data file) as well as the system setup (printer, plotter, etc.) Recalling this file will change the lock-in setup to that stored in the file.

The disk drive uses double-sided, double density (DS/DD) 3.5" disks. The disk capacity is 720k. The SR850 uses the DOS format. A disk which was formatted on a PC or PS2 (for 720k) may be used. Files written by the SR850 may be copied or read on a DOS computer.

This measurement is designed to familiarize the user with the disk drive. We will use the internal oscillator to provide a signal so that there is some data to save and recall. Specifically, you will save and recall a data file and a settings file.

STORING AND RECALLING DATA

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The Disk Drive

3. Press [AUTO PHASE]

4. Press [DISPLAY/SCALE] Press <Format> to select Single display. Press <Type> Use the knob to adjust the display type to

Chart.

and frequency are displayed at the bottom of the screen. In this mode, the lock-in generates a synchronous sine output at the internal reference frequency.

Automatically adjust the phase shift so that Y is zero and X is equal to the magnitude.

Show the Display and Scale menu. Change the screen to a full screen display. Highlight the display type. With the chart display, we can see the data stored

in the trace buffers.

5. Press [TRACE/SCAN] Press <Scan Length> Press [1] [0] [0] [ENTER]

Press <1 Shot/Loop> to select 1 Shot.

6. Press [REF/PHASE] Press [START/CONT]

Press <Rotate 90 deg.> a few times during the scan to generate some changes in the data.

Display the Trace and Scan menu. Highlight the scan length. Set the scan length to 100 seconds. At the default

sample rate of 1 Hz, this represents 100 points in the scan.

Take one scan and then stop.

Display the Reference and Phase menu. Start the scan. The quantity X is sampled and

stored at a rate of 1 Hz. The trace buffer is graphed on the chart display as the data is taken.

Each time the phase is shifted by 90°, the value of X changes from (plus or minus) the signal amplitude to zero and back.

After 100 seconds, the scan will finish and we can save the graph on disk.

7. Put a blank double-sided, double density (DS/DD)3.5" disk into the drive.

Use a blank if disk if possible, otherwise any disk that you don't mind formatting will do. Make sure the write protect tab is off.

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The Disk Drive

8. Press [DISK]

Press <Disk Utils> Press <Disk Format>

Press <Return> Press <Data Save> Press <File Name> Press [ALT]

Press [D] [A] [T] [A] [1] [ALT]

Press <Data Save>

Display the Disk menu. Choose Disk Utilities. Make sure that the disk does not contain any infor-

mation that you want. Formatting the disk takes about a minute.

Go back to the main Store and Recall menu. Display the Data Save menu. Now we need a file name. [ALT] lets you enter the letter characters printed

below each key. The numbers function as normal. Type a file name such as DATA1 (or any legal

DOS file name) and turn off the ALT mode. This saves the trace data which is displayed on

the active display to disk using the file name specified above. If the entered file name has no extension, then the extension .85T is appended to the file name.

9. Press [DISPLAY/SCALE]

Press <Type/Trace> twice to highlight the trace number.

Use the knob to change the trace number to 2.

10. Press [DISK]

Press <Data Save> Press <File Name>

All stored data points in the selected trace are saved. Only the trace in the active display is saved. In this case, only trace 1 (X) is saved, even though the other traces have data stored.

In addition to the data, the instrument state (most lock-in parameters, scan parameters, and the active trace definition) is stored.

Let's change the display to show another trace. The other traces are stored in the buffer and can

be displayed at any time. This displays trace 2 (Y) on the chart so we can

save it also.

Display the Disk menu. Choose the Data Save menu. Save trace 2 (Y) using a new file name. This way

you can have multiple files in the disk catalog.

Press [ALT] [D] [A] [T] [A] [2] [ALT]

Use the file name DATA2 (or any legal DOS file name) and turn off the ALT mode.

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Press <Data Save>

11.

Press <Catalog> to select On.

Press <Return>

12.

Press [PAUSE RESET]

13.

Press <Data Recall> Press <Catalog> to select On.

Use the knob to select the first file.

Press <Data Recall>

14.

Press [DISPLAY/SCALE] Press <Format> to select Up/Down Press<Type>

Save Trace 2.

Display the disk catalog. This display lists all of the files on the disk. The files which you just saved should appear in the catalog. Each file has a name, extension, and type. The file type for binary trace data is TRC.

Go back to the main Store and Recall menu.

Reset the scan. This clears the data buffers within the lock-in.

Display the Data Recall menu. Display the disk catalog. The 2 files which you just

saved should be listed. The knob chooses a file in the catalog display.

Let's recall the X data (the file made by saving Trace 1).

This recalls the data file from disk and stores it in the active display trace. The active display trace is redefined to agree with the recalled data trace definition. In this case, the data is recalled into Trace 2 (since it is currently being shown on the active display). Trace 2 becomes defined as X since that is the trace definition of the recalled data.

Data acquisition is paused so no new data will be taken.

If the active display is not a chart, the data is still recalled into the trace which is shown by the active display. For example, if the active display is a bar graph showing Trace 2, then the recalled data fills Trace 2. The trace is redefined to agree with the recalled data and the bar graph will show the present value of the redefined trace.

Data files may not be recalled into traces which are not presently being stored.

Show the Display and Scale menu. Choose the dual display format. Highlight the Top display type.

The Disk Drive

2-26

The Disk Drive

Use the knob to select the Chart display. Press <Full, Top or Bottom> to select Bottom.

Use the knob to select the Chart display for the bottom display.

Press [AUTO SCALE]

Display two charts. Select the bottom display. The bottom display type

should be highlighted. Both displays should be charts.

Auto scale the bottom display. The [AUTO SCALE] will scale the active display. In this case, the bottom display is active since we just changed it. The active display shows its trace number in inverse at the upper left of the display.

Note that both Trace 1 (top) and Trace 2 (bottom) are defined as X. Trace 2 is the recalled X data. Trace 1, which was empty before the data was recalled, has been filled with zeroes so that its length agrees with the recalled trace.

All stored traces must have the same length. If the recalled data trace has less points than existing traces in memory, then the recalled trace is padded with zeroes until it is the same length. If the recalled data has more points than the existing traces in memory (as was the case here), the existing traces are padded with zeroes until they are the same length as the recalled trace. Data is never destroyed in the recall process.

Press [ACTIVE DISPLAY]

15. Press [DISK]

Press <Data Recall> Press <Catalog> to select On. Use the knob to select the second file.

If the recalled trace has more points than the existing trace buffer allocation (16k points for 4 stored traces, 32k points for 2 stored traces, or 64k points for 1 stored trace), then as many points are recalled as will fit in the existing trace buffer. The other existing traces are either padded with zeroes or left alone, depending upon how many points are presently stored.

Make the top display active. The top display trace number should be highlighted at the upper left of the top display. This makes Trace 1 the active display trace.

Let's recall the stored Y trace into Trace 1. Display the Data Recall menu. Display the disk catalog. The knob chooses a file in the catalog display.

Let's recall the Y data (the file made by saving Trace 2).

2-27

Press <Data Recall>

The Disk Drive

This recalls the data file from disk and stores it in the active display trace. The active display trace is redefined to agree with the recalled data trace definition. In this case, the data is recalled into Trace 1 (since it is currently being shown on the active display). Trace 1 becomes defined as Y since that is the trace definition of the recalled data.

The existing data in Trace 2 (bottom display) is not changed.

Press [AUTO SCALE]

Auto Scale the top display. In general, the existing lock-in state may not agree

with the state stored in the recalled data file. In this case, the lock-in state is also recalled along with the data. Existing data in other traces is not destroyed but may lose their meaning given the new lock-in state. For example, if the existing data sample rate is 1 Hz and data is stored in the traces, recalling a data file whose data was stored at 2 Hz will change the sample rate to 2 Hz. The existing data is not destroyed but will be displayed as if the data was sampled at 2 Hz. If the state was not recalled with the data, then the recalled data would have no meaning. This way, the recalled data is meaningful. Existing data is presumably more easily recaptured and can also be saved if important.

2-28

STORING AND RECALLING SETTINGS

The Disk Drive

1. Turn the lock-in on while holding down the [←]

(backspace) key. Wait until the power-on tests are completed. Disconnect any cables from the lock-in.

2. Press [GAIN/TC]

Press <Sensitivity> Use the knob to change the sensitivity to

100 mV. Press <Time Constant> Use the knob to select 1 S.

3. Press [DISK]

Press <Settings Save> Press <File Name>

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

Change the lock-in setup so that we have a nondefault setup to save.

Show the Gain and Time Constant menu. Highlight the full scale sensitivity. Select 100 mV.

Highlight the time constant. Select 1 second.

Display the Disk menu. Choose the Settings Save menu. Now we need a file name.

Press [ALT]

Press [T] [E] [S] [T] [1] [ALT]

Press <Settings Save>

4. Turn the lock-in off and on while holding down

the [←] (backspace) key. Wait until the poweron tests are complete.

Press [GAIN/TC]

5. Press [DISK]

Press <Settings Recall>

[ALT] lets you enter the letters printed below each key. The numbers function as normal.

Type a file name such as TEST1 (or any legal DOS file name) and turn off the ALT mode.

This saves the setup to disk using the file name specified above. If the entered file name has no extension, then the extension .85S is appended to the file name.

Change the lock-in setup back to the default setup. Now let's recall the lock-in setup that we just saved.

Check that the sensitivity and time constant are 1V and 100 ms (default values).

Display the Disk menu. Choose the Settings Recall menu.

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Press <Catalog>

The Disk Drive

Display the disk catalog listing. Note that settings files have the file type SET.

Use the knob to select the settings file which you just saved.

6. Press <Settings Recall>

Press [GAIN/TC]

When the disk catalog is displayed, the knob highlights a file. Use the knob to choose the file TEST1 to recall.

This recalls the settings from the file TEST1. The lock-in settings are changed to those stored in TEST1.

The sensitivity and time constant should be the same as those in effect when you created the file.

Settings files store the lock-in state (sensitivity, time constant, reference, etc.), the display setup (display format, type, trace parameters, etc.) as well as the system setup (plotter, printer, interface settings, etc.).

2-30

Aux Outputs and Inputs

AUX OUTPUTS and INPUTS

This measurement is designed to illustrate the use of the Aux Outputs and Inputs on the rear panel. You will need BNC cables and a digital voltmeter (DVM).

Specifically, you will set the Aux Output voltages and measure them with the DVM. These outputs will then be connected to the Aux Inputs to simulate external DC voltages which the lock-in can measure.

1. Disconnect all cables from the lock-in. Turn

the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

2. Connect Aux Out 1 on the rear panel to the

DVM. Set the DVM to read DC volts.

3. Press [AUX OUTPUTS]

Press <Voltage> Press [1] [0] [ENTER]

Press [-] [5] [ENTER]

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

The 4 Aux Outputs can provide programmable voltages between -10 and +10 volts. The outputs can be a fixed voltage or they can sweep with the scan.

Display the Aux Output menu. Highlight the output voltage of Aux Out 1. Change the output to 10V. The DVM should dis-

play 10.0 V. The knob can also be used to adjust the voltages.

Change the output to -5V. The DVM should display -5.0 V.

The 4 outputs are useful for controlling other parameters in an experiment, such as pressure, temperature, wavelength, etc.

4. Press [DISPLAY/SCALE]

Press <Monitor> to select Input/Output.

Show the Display and Scale menu. Change the monitor display at the top of the

screen to show the Aux Inputs (A1, A2, A3 and A4).

The Aux Inputs can read 4 analog voltages. These inputs are useful for monitoring and measuring other parameters in an experiment, such as pressure, temperature, position, etc.

We'll use Aux Out 1 to provide an analog voltage to measure.

2-31

5. Disconnect the DVM from Aux Out 1. Connect

Aux Outputs and Inputs

Aux Out 1 to Aux In 1 on the rear panel.

The A1 monitor should now display -5 V. The monitor display shows all 4 Aux Inputs. To display and save the Aux Input values, a trace needs to be defined to measure an Aux Input.

6. Press [TRACE/SCAN] Press the second softkey, next to the trace

definition, to highlight the X. Use the knob to change the A parameter from

X to AI1.

Press [AUTO SCALE]

7. Press <Scan Length> Press [1] [0] [0] [ENTER]

Display the Trace and Scan menu. Trace 1 is defined as X. Let's change it to Aux

Input 1. The Aux Inputs are abbreviated AI1, AI2, AI3 and

AI4. Trace 1 is now defined as AI1. The top graph shows trace 1 and should display -5.0 V.

The traces can measure Aux Inputs directly. In addition, these inputs can be used to multiply or divide other quantities (such as X, Y or R) for ratio normalization or gain modulation.

Auto Scale the top bar graph. Now let's setup a voltage sweep on Aux Output 1.

Highlight the scan length. Set the scan time to 100 seconds. The sample

rate is 1 Hz so the scan is 100 samples long.

8. Press [AUX OUTPUTS] Press <Fixed / Log / Linear> twice to select

Linear.

Press <Start> Press [1] [ENTER]

Press <Stop> Press [5] [ENTER]

9. Press [START/CONT]

Display the Aux Output menu again. Choose a linear sweep for Aux Output 1. Each

Aux Output may be swept in voltage in either log or linear fashion.

Highlight the start voltage. Enter 1 V for the start voltage. The Aux 1 output

changes to 1 V since data acquisition is stopped right now. All swept parameters return to their start values when a scan is stopped.

Highlight the stop voltage. Enter 5 V for the stop voltage. The offset voltage is used to offset the sweep with-

out changing the start and stop. For log (exponential) sweeps, the offset allows much more flexibility in defining the range and acceleration of a sweep.

Start the scan. Aux Out 1 will linearly ramp from

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Aux Outputs and Inputs

1 V to 5 V in 100 seconds updating every second. The output voltage is measured on Aux In 1, recorded in Trace 1 and displayed on the top graph.

10. Press [DISPLAY/SCALE]

Press <Type / Trace> to highlight the type of the top display.

Use the knob to change the display type to Chart.

Show the Display and Scale menu. The top display is a bar graph. Let's change it to a

chart to show the history of Aux In 1. The chart display shows the history of the sweep. The SR850 can be used as a general purpose 4

channel digital chart recorder. The displays can be scaled vertically and horizontally with full cursor readouts. Data can be stored on disk and output to a printer or plotter.

2-33

Aux Outputs and Inputs

2-34

BNC cables and a 50Ω terminator.

Connect a 50Ω terminator to the A input.

The input impedance of the lock-in is 10 MΩ. The

Trace Math

TRACE MATH

This example is designed to familiarize the user with the trace math functions in the lock-in. You will need

Specifically, you will record the input noise in a trace and perform various calculations with the trace. The internal oscillator will also be used to provide signal data for curve fits.

There are a few points to remember about the trace math functions.

Math functions may only be performed on trace data which is stored in a trace buffer and displayed in the active chart display. Data which are not within the time window of the chart are not operated upon. Use

the horizontal chart scale to select the size of the time window and move the cursor to pan the window to the desired portion of the trace buffer. Data which exceeds the upper or lower display range of the graph are, of course, operated upon.

The amount of time a math function takes to complete depends upon its complexity and the number of data points which are operated on. For example, 25-point smoothing takes longer than 5-point smoothing while each type of smoothing takes longer the more points there are. Do not operate on more points than necessary.

Math functions can only be performed while data acquisition is stopped, either by pausing or finishing a scan. Some math operations change the stored trace data. Resuming a scan after smoothing, for example, will result in a trace where a region of the trace is smoothed and other regions are not.

1. Disconnect all cables from the lock-in. Turn

the power on while holding down the [←] (backspace) key. Wait until the power-on tests are completed.

When the power is turned on with the backspace key depressed, the lock-in returns to its default settings. See the Default Settings list in the Menu section for a complete listing of the settings.

terminator effectively provides a short at the input so that the input noise is predominantly the voltage noise of the input transistors.

The lock-in defaults to the internal oscillator reference set at 1.000 kHz. All measurements will be made at 1 kHz in this example.

3. Press [GAIN/TC]

Press <Sensitivity>

Display the Gain and Time Constant menu. Highlight the sensitivity.

2-35

Use the knob to select 50 nV.

Trace Math

To measure the input noise, we need to use an appropriate sensitivity.

4. Press [TRACE/SCAN] Press <Sample Rate>

Use the knob to change the sample rate to 16 Hz.

5. Press [DISPLAY/SCALE] Press <Format> to select Single. Press <Type> Use the knob to select Chart. Press <± Range> Press [5] [0] [EXP] [-] [9] [ENTER] Press <sec/Div> (the last softkey).

Display the Trace and Scan menu. Since the time constant is 100 ms, we need a

sample rate greater than 1 Hz to record the output. Choose 16 Hz as the sample rate. Leave the scan mode on Loop. Data will be

recorded indefinitely with the trace buffer storing the last 16k (1000 seconds) of data.

Show the Display and Scale menu. Use a full screen display. Highlight the display type. Math functions require a chart display. Highlight the chart range. Enter 50 nV for the chart range. Highlight the horizontal time scale.

Use the knob to select 5.0 S/Div.

6. Press [START/CONT]

Wait until the data fills the graph (50 sec) and data starts scrolling past the left edge.

Press [PAUSE/CONT]

7. Press [MATH] Press <Stats> Press <Do Stats>

Change the scale to 5.0 S/Div so 50 seconds of data will fill the graph.

Start the scan. The X output is recorded on the chart display. The chart shows the last 50 seconds of data. The graph should be a noisy trace about 2 divisions peak to peak.

Pause the data acquisition. No new data is recorded and the graph stops scrolling to the left.

Display the Math menu. Choose the Statistics menu. The mean, standard deviation, total and time

span are calculated for the data between the left and right limits. The limits are shown as vertical heavy dashed lines. The limits default to the left

2-36

Press <Return> twice.

Use the knob to select √.

√Hz) is thus the standard deviation divided by the

The lock-in can measure noise directly in V/√Hz,

Trace Math

and right edge of the graph display. In this case, 50 seconds of data (800 data points at 16 Hz sample rate).

The results are displayed at the bottom of the screen. The standard deviation (σ)should be about 6 nV or so. This is the rms noise of the input in a noise equivalent bandwidth of 1.2 Hz (100 ms, 12 dB/oct time constant). The input noise (in Volts/

square root of 1.2 Hz.

this measurement is meant to illustrate the statistical functions.

Return to the main Math menu.

8. Press <Smooth>

Press <17 point>

Press [CURSOR] Use the knob to move the cursor past the left

edge of the graph. The data will scroll to the right to display unsmoothed portions of the trace.

Press <Return>

8. Press <Calc>

Press <Operation> Use the knob to select x2.

Choose the Smoothing menu. Perform 17 point smoothing on the noisy data. The

data should become less noisy and smoother. Smoothing reduces narrow variations in the data.

Let the knob move the cursor. The smoothing operation changed the data within

the time window of the graph. Data which was not displayed was not smoothed. This trace now contains a region which has been smoothed and a region which is untouched.

Smoothing changes the data in the buffer and the original unsmoothed points are lost.

Return to the main Math menu.

Choose the Calculator menu. Highlight the operation. Let's square the data.

Press <Do Calc.>

Press [AUTO SCALE]

Calculations are performed on all of the data within the time window of the graph. Let the calculation finish.

X squared is a positive quantity. The magnitude of the data is now 10 view the data.

Select square root.

-18

so auto scale is required to

2-37

Press <Do Calc.>

Trace Math

The net effect is to take the absolute value of X.

Let the calculation finish. Press [AUTO SCALE] Use the knob to select log10. Press <Do Calc.> Use the knob to select Press <Argument Type> to select Constant. Press <Constant Value> Press [2] [0] [ENTER] Press <Do Calc.>

Press [AUTO SCALE] Press [CURSOR] Use the knob to read points from the graph.

❊.

The magnitude of the data is back to 10-9.

Take the log of |X|.

Let the calculation finish.

Let's multiply the data by something.

Multiply the data by a constant.

Highlight the constant value.

Enter 20.

The final data is 20log|X| which results in a graph

of X scaled in dBV. Let the calculation finish.

Auto scale the graph.

Activate the cursor.

The values of the data should be in the range

below -160 dBV and below.

9. Press [PAUSE/RESET]

10. Press [DISPLAY/SCALE] Press <Format> to select Up/Down.

11. Press [GAIN/TC] Press <Sensitivity> Use the knob to change the sensitivity to 1V. Press <Time Constant> Use the knob to change the time constant to

3S. Press <Filter db/oct.> until 6 db is selected.

12. Press [TRACE/SCAN] Press <Scan Length>

Clear the data buffers for the next measurement.

Show the Display and Scale menu. Display the bar graphs.

Display the Gain and Time Constant menu. Highlight the sensitivity. Change the sensitivity to measure the Sine Out. Highlight the time constant. Use a long time constant.

Choose the simplest filter response. Show the Trace and Scan menu. Highlight the scan length.

Press [5] [0] [ENTER]

Enter a scan length of 50 seconds.

2-38

Trace Math

Press <1 Shot/Loop> to select 1 Shot.

13.

Connect the Sine Out to the A input using a BNC cable.

Wait until the value of X reaches 1 V.

14.

Press [DISPLAY/SCALE] Press <Format> to select Single. Press the <± Range> softkey. This is the fifth

softkey from the top. Press [1] [ENTER] Press the <± Range> softkey again to high-

light the center (@) value. Press [0] [ENTER]

15.

Press [START/CONT] and after about 10 seconds, remove the cable from the A input.

16.

Press [MATH] Press <Fit> Press <Fit Type> to select Exp. Press [CURSOR] Use the knob to position the cursor at the point

where the signal starts to decay.

Stop data acquisition after the scan is complete.

Show the Display and Scale menu. Display the full screen chart again. Set the chart scale.

Set the range to ±1 V. Set the chart center.

Set the chart center to zero.

Start the scan. When the cable is removed, the value of X should decrease to zero over the next 15 seconds or so.

Wait until the scan finishes. When the scan is finished, the DONE indictor at the bottom left of the screen will switch on.

The graph should be an exponential decay starting when the cable was removed from the input. Let's fit a curve to this data.

Display the Math menu. Choose the Fit menu. Choose exponential fit. Activate the cursor. Use the cursor to determine the graph region over

which the curve fit will be calculated.

2-39

Press <Left Limit>

Use the knob to position the cursor 3 divisions to the right of the left limit.

Press <Right Limit> Move the cursor farther to the right.

Press <Do Fit>

17.

Press any key to continue.

18. Press <Fit Type> twice to select Line. Press <Do Fit> Press any key to continue.

Press any key to continue.

19.

Press [DISPLAY/SCALE] Press <S/Div> Use the knob to change the horizontal time

scale to 1 S/Div. Press [CURSOR]

Set the left limit of the region at the start of the signal decay.

Select the smallest region which covers the signal decay.

Set the right limit. The fit region is between the two limit marks (verti-

cal heavy dashed lines). Only the data between the limits is used to calculate the fit.

Curve fit calculations can take a long time if the fit region encompasses a lot of data points. Try to use the smallest region possible when performing fits.

The curve fit uses a multi-iteration chi-squared minimization technique. After each iteration, the value of chi2 is displayed at the bottom of the screen. Pressing the last softkey during the fit will terminate the calculation after the current iteration.

The fit parameters are displayed in a window in the center of the screen. The decay parameter b should be 3 seconds (6 db time constant).

The first time a key is pressed, the parameter window is removed. The curve fit is plotted over the data on the graph.

The next key removes the curve fit from the graph.

Try fitting a line to this region. Fit a line to this region. Remove the parameter window. The calculated fit

is terrible of course. Remove the curve fit.

Show the Display and Scale menu. Highlight the horizontal scale. Zoom in on the graph.

Activate the cursor.

Trace Math

2-40

Trace Math

Move the cursor past the left edge of the graph to pan the data window until the signal decay becomes visible again.

20.

Press [MATH] Press <Fit> Press <View Params>

Press any key to continue.

Scroll the data to show the signal decay region.

Go back to the Math menu. Choose the Fit menu. View the most recent fit. The most recent fit is

stored in memory and can be viewed again. Remove the parameter window so that the plotted

fit can be seen. The fit is now being displayed at a different graph scale than before. Details on the quality of the fit can be examined up close.

Remove the fit from the graph. The math functions are very powerful data analy-

sis tools. Together with the flexible trace definitions, the SR850 can perform complex data acquisition and analysis tasks.

2-41

Trace Math

2-42

Lock-in amplifiers are used to detect and measure very small AC signals - all the way down to a few nanovolts! Accurate measurements may be made even when the small signal is obscured by noise sources many thousands of times larger.

Lock-in amplifiers use a technique known as phase-sensitive detection to single out the component of the signal at a specific reference frequency AND phase. Noise signals at frequencies other than the reference frequency are rejected and do not affect the measurement.

Why use a lock-in?

Let's consider an example. Suppose the signal is a 10 nV sine wave at 10 kHz. Clearly some amplification is required. A good low noise amplifier will have about 5 nV/√Hz of input noise. If the amplifier bandwidth is 100 kHz and the gain is 1000, then we can expect our output to be 10 µV of signal (10 nV x 1000) and 1.6 mV of broadband noise (5 nV/√Hz x √100 kHz x 1000). We won't have much luck measuring the output signal unless we single out the frequency of interest.

If we follow the amplifier with a band pass filter with a Q=100 (a VERY good filter) centered at 10 kHz, any signal in a 100 Hz bandwidth will be detected (10 kHz/Q). The noise in the filter pass band will be 50 µV (5 nV/√Hz x √100 Hz x 1000) and the signal will still be 10 µV. The output noise is much greater than the signal and an accurate measurement can not be made. Further gain will not help the signal to noise problem.

Now try following the amplifier with a phasesensitive detector (PSD). The PSD can detect the signal at 10 kHz with a bandwidth as narrow as

0.01 Hz! In this case, the noise in the detection bandwidth will be only 0.5 µV (5 nV/√Hz x √.01 Hz x 1000) while the signal is still 10 µV. The signal to noise ratio is now 20 and an accurate measurement of the signal is possible.

What is phase-sensitive detection?

Lock-in measurements require a frequency reference. Typically an experiment is excited at a fixed frequency (from an oscillator or function generator) and the lock-in detects the response from the

experiment at the reference frequency. In the diagram below, the reference signal is a square wave at frequency

ωr. This might be the sync output

from a function generator. If the sine output from the function generator is used to excite the experiment, the response might be the signal waveform shown below. The signal is

sig

sin(

ωrt +

sig

)

where V

sig

is the signal amplitude.

The SR850 generates its own sine wave, shown as the lock-in reference below. The lock-in reference is VLsin(

ωLt +

ref

The SR850 amplifies the signal and then multiplies it by the lock-in reference using a phase-sensitive detector or multiplier. The output of the PSD is simply the product of two sine waves.

psd

sigVL

sin(

ωrt +

sig

)

sin(

ωLt +

ref

)

1/2 V

sigVL

cos([ωr -

ωL]t +

sig

ref

) -

1/2 V

sigVL

cos([ωr +

ωL]t +

sig

ref

)

The PSD output is two AC signals, one at the difference frequency (

ωr -

ωL) and the other at the

sum frequency (

ωr +

ωL).

If the PSD output is passed through a low pass filter, the AC signals are removed. What will be left? In the general case, nothing. However, if

equals

ωL, the difference frequency component

will be a DC signal. In this case, the filtered PSD output will be

psd

1/2 V

sigVL

cos(θ

sig

ref

)

WHAT IS A LOCK-IN AMPLIFIER?

3-1

Reference

Signal

Lock-in Reference

sig

SR850 BASICS

ref

SR850 Basics

This is a very nice signal - it is a DC signal proportional to the signal amplitude.

Narrow band detection

Now suppose the input is made up of signal plus noise. The PSD and low pass filter only detect signals whose frequencies are very close to the lockin reference frequency. Noise signals at frequencies far from the reference are attenuated at the PSD output by the low pass filter (neither

noise

ref

nor

noise

ref

are close to DC). Noise at frequencies very close to the reference frequency will result in very low frequency AC outputs from the PSD (|

noise

ref

| is small). Their attenuation depends upon the low pass filter bandwidth and roll-off. A narrower bandwidth will remove noise sources very close to the reference frequency, a wider bandwidth allows these signals to pass. The low pass filter bandwidth determines the bandwidth of detection. Only the signal at the reference frequency will result in a true DC output and be unaffected by the low pass filter. This is the signal we want to measure.

Where does the lock-in reference come from?

We need to make the lock-in reference the same as the signal frequency, i.e.

ωr =

ωL. Not only do

the frequencies have to be the same, the phase between the signals can not change with time, otherwise cos(θ

sig

ref

)

will change and V

psd

will not be a DC signal. In other words, the lock-in reference needs to be phase-locked to the signal reference.

Lock-in amplifiers use a phase-locked-loop (PLL) to generate the reference signal. An external reference signal (in this case, the reference square wave) is provided to the lock-in. The PLL in the lock-in locks the internal reference oscillator to this external reference, resulting in a reference sine wave at

ωr with a fixed phase shift of

ref

. Since the PLL actively tracks the external reference, changes in the external reference frequency do not affect the measurement.

All lock-in measurements require a reference signal.

In this case, the reference is provided by the excitation source (the function generator). This is called an external reference source. In many situations, the SR850's internal oscillator may be used instead. The internal oscillator is just like a function generator (with variable sine output and a TTL

sync) which is always phase-locked to the reference oscillator.

Magnitude and phase

Remember that the PSD output is proportional to V

sig

cosθ where θ = (

sig

ref

). θ is the phase difference between the signal and the lock-in reference oscillator. By adjusting

ref

we can make

equal to zero, in which case we can measure V

sig

(cosθ=1). Conversely, if θ is 90°, there will be no output at all. A lock-in with a single PSD is called a single-phase lock-in and its output is V

sig

cosθ.

This phase dependency can be eliminated by adding a second PSD. If the second PSD multiplies the signal with the reference oscillator shifted by 90°, i.e. VLsin(

ωLt +

ref

+ 90°), its low pass fil-

tered output will be V

psd2

1/2 V

sigVL

sin(θ

sig

ref

)

psd2

sig

sin

Now we have two outputs, one proportional to cosθ and the other proportional to sinθ. If we call the first output X and the second Y,

X = V

sig

cos

Y =

sig

sin

these two quantities represent the signal as a vector relative to the lock-in reference oscillator. X is called the 'in-phase' component and Y the 'quadrature' component. This is because when

=0, X measures the signal while Y is zero.

By computing the magnitude (R) of the signal vector, the phase dependency is removed.

R = (X2 + Y2)

1/2

= V

sig

R measures the signal amplitude and does not depend upon the phase between the signal and lock-in reference.

A dual-phase lock-in, such as the SR850, has two PSD's, with reference oscillators 90° apart, and can measure X, Y and R directly. In addition, the phase θ between the signal and lock-in reference, can be measured according to

= tan-1 (Y/X)

3-2

So what exactly does the SR850 measure?Fourier's theorem basically states that any input signal can be represented as the sum of many, many sine waves of differing amplitudes, frequencies and phases. This is generally considered as representing the signal in the "frequency domain". Normal oscilloscopes display the signal in the "time domain". Except in the case of clean sine waves, the time domain representation does not convey very much information about the various frequencies which make up the signal.

What does the SR850 measure?

The SR850 multiplies the signal by a pure sine wave at the reference frequency. All components of the input signal are multiplied by the reference simultaneously. Mathematically speaking, sine waves of differing frequencies are orthogonal, i.e. the average of the product of two sine waves is zero unless the frequencies are EXACTLY the same. In the SR850, the product of this multiplication yields a DC output signal proportional to the component of the signal whose frequency is exactly locked to the reference frequency. The low pass filter which follows the multiplier provides the averaging which removes the products of the reference with components at all other frequencies.

The SR850, because it multiplies the signal with a pure sine wave, measures the single Fourier (sine) component of the signal at the reference frequency. Let's take a look at an example. Suppose the input signal is a simple square wave at frequency f. The square wave is actually composed of many sine waves at multiples of f with carefully related amplitudes and phases. A 2V pk-pk square wave can be expressed as

S(t) =

1.273sin(ωt) + 0.4244sin(3ωt) +

0.2546sin(5ωt) + ...

where ω = 2πf. The SR850, locked to f will single out the first component. The measured signal will be 1.273sin(ωt), not the 2V pk-pk that you'd measure on a scope.

In the general case, the input consists of signal plus noise. Noise is represented as varying signals at all frequencies. The ideal lock-in only responds to noise at the reference frequency. Noise at other

WHAT DOES A LOCK-IN MEASURE?

frequencies is removed by the low pass filter following the multiplier. This "bandwidth narrowing" is the primary advantage that a lock-in amplifier provides. Only inputs at frequencies at the reference frequency result in an output.

RMS or Peak?

Lock-in amplifiers as a general rule display the input signal in Volts RMS. When the SR850 displays a magnitude of 1V (rms), the component of the input signal at the reference frequency is a sine wave with an amplitude of 1 Vrms or

2.8 V pk-pk. Thus, in the previous example with a2 V pk-pk

square wave input, the SR850 would detect the first sine component, 1.273sin(ωt). The measured and displayed magnitude would be 0.90 V (rms) (1/√2 x 1.273).

Degrees or Radians?

In this discussion, frequencies have been referred to as f (Hz) and ω (2πf radians/sec). This is because people measure frequencies in cycles per second and math works best in radians. For purposes of measurement, frequencies as measured in a lock-in amplifier are in Hz. The equations used to explain the actual calculations are sometimes written using ω to simplify the expressions.

Phase is always reported in degrees. Once again, this is more by custom than by choice. Equations written as

sin(ωt + θ) are written as if θ is in radians mostly for simplicity. Lock-in amplifiers always manipulate and measure phase in degrees.

SR850 Basics

3-3

SR850 Basics

3-4

The functional block diagram of the SR850 DSP Lock-In Amplifier is shown below. The functions in the gray area are handled by the digital signal processor (DSP). We'll discuss the DSP aspects of the SR850 as they come up in each functional block description.

THE FUNCTIONAL SR850

Phase

Sensitive

Detector

PLL

Low Noise

Differential

Amp

Voltage

Current

50/60 Hz

Notch

Filter

Reference In Sine or TTL

Phase

Shifter

DC Gain

Offset

Expand

Gain

X Out

Y Out

Discriminator

100/120 Hz

Notch

Filter

Phase

Shift

Phase

Locked

Loop

Internal

Oscillator

Low Pass Filter

DC Gain

Offset

Expand

Low Pass Filter

Sine Out

Discriminator

TTL Out

R and

Ø Calc

Phase

Sensitive

Detector

A B

SR850 Basics

R Ø

SR850 FUNCTIONAL BLOCK DIAGRAM

3-5

SR850 Basics

3-6

A lock-in amplifier requires a reference oscillator phase-locked to the signal frequency. In general, this is accomplished by phase-locking an internal oscillator to an externally provided reference signal. This reference signal usually comes from the signal source which is providing the excitation to the experiment.

Reference Input

The SR850 reference input can accept an analog signal (like a sine wave) or a TTL logic signal. The first case is called External Sine. The input is AC coupled (above 1 Hz) and the input impedance is 1 MΩ. A sine wave input greater than 200 mV pk will trigger the input discriminator. Positive zero crossings are detected and considered to be the zero for the reference phase shift.

TTL reference signals can be used at all frequencies up to 102 kHz.

For frequencies below 1 Hz,

a TTL reference signal is required.

Many function generators provide a TTL SYNC output which can be used as the reference. This is convenient since the generator's sine output might be smaller than 200 mV or be varied in amplitude. The SYNC signal will provide a stable reference regardless of the sine amplitude.

When using a TTL reference, the reference input can be set to External Rising (detect rising edges) or External Falling (detect falling edges). In each case, the internal oscillator is locked (at zero phase) to the detected edge.

Internal Oscillator

The internal oscillator in the SR850 is basically a 100 kHz function generator with sine and TTL sync outputs. The oscillator can be phase-locked to the external reference.

The oscillator generates a digitally synthesized sine wave. The digital signal processor, or DSP, sends computed sine values to a 16 bit digital-toanalog converter every 4 µs (256 kHz). An antialiasing filter converts this sampled signal into a low distortion sine wave. The internal oscillator sine wave is output at the SINE OUT BNC on the front panel. The amplitude of this output may be set from 4 mV to 5 V.

REFERENCE CHANNEL

When an external reference is used, this internal oscillator sine wave is phase-locked to the reference. The rising zero crossing is locked to the detected reference zero crossing or edge. In this mode, the SINE OUT provides a sine wave phaselocked to the external reference. At low frequencies (below 10 Hz), the phase locking is accomplished digitally by the DSP. At higher frequencies, a discrete phase comparator is used.

The internal oscillator may be used without an external reference. In the Internal Reference mode, the SINE OUT provides the excitation for the experiment. The phase-locked-loop is not used in this mode since the lock-in reference is providing the excitation signal.

The TTL OUT on the rear panel provides a TTL sync output. The internal oscillator's rising zero crossings are detected and translated to TTL levels. This output is a square wave.

Reference Oscillators and Phase

The internal oscillator sine wave is not the reference signal to the phase sensitive detectors. The DSP computes a second sine wave, phase shifted by

ref

from the internal oscillator (and thus from an external reference), as the reference input to the X phase sensitive detector. This waveform is sin(

ωrt + θ

ref

). The reference phase shift is adjust-

able in .001° increments. The input to the Y PSD is a third sine wave, com-

puted by the DSP, shifted by 90° from the second sine wave. This waveform is sin(

ωrt + θ

ref

+ 90°).

Both reference sine waves are calculated to 20 bits of accuracy and a new point is calculated every 4 µs (256 kHz). The phase shifts (

ref

and the 90° shift) are also exact numbers and accurate to better than .001°. Neither waveform is actually output in analog form since the phase sensitive detectors are actually multiply instructions inside the DSP.

Phase Jitter

When an external reference is used, the phaselocked loop adds a little phase jitter. The internal oscillator is supposed to be locked with zero phase shift relative the external reference. Phase

SR850 Basics

3-7

SR850 Basics

jitter means that the average phase shift is zero but the instantaneous phase shift has a few millidegrees of noise. This shows up at the output as noise in phase or quadrature measurements.

Phase noise can also cause noise to appear at the X and Y outputs. This is because a reference oscillator with a lot of phase noise is the same as a reference whose frequency spectrum is spread out. That is, the reference is not a single frequency, but a distribution of frequencies about the true reference frequency. These spurious frequencies are attenuated quite a bit but still cause problems. The spurious reference frequencies result in signals close to the reference being detected. Noise at nearby frequencies now appears near DC and affects the lock-in output.

Phase noise in the SR850 is very low and generally causes no problems. In applications requiring no phase jitter, the internal reference mode should be used. Since there is no PLL, the internal oscillator and the reference sine waves are directly linked and there is no jitter in the measured phase. (Actually, the phase jitter is the phase noise of a

crystal oscillator and is very, very small).

Harmonic Detection

It is possible to compute the two PSD reference sine waves at a multiple of the internal oscillator frequency. In this case, the lock-in detects signals at Nxf

ref

which are synchronous with the reference. The SINE OUT frequency is not affected. The SR850 can detect at any harmonic up to N=32767 as long as Nxf

ref

does not exceed

102 kHz.

3-8

SR850 Basics

The SR850 multiplies the signal with the reference sine waves digitally. The amplified signal is converted to digital form using a 16 bit A/D converter sampling at 256 kHz. The A/D converter is preceded by a 102 kHz anti-aliasing filter to prevent higher frequency inputs from aliasing below 102 kHz. The signal amplifier and filters will be discussed later.

This input data stream is multiplied, a point at a time, with the computed reference sine waves described previously. Every 4 µs, the input signal is sampled and the result is multiplied by the two reference sine waves (90° apart).

Digital PSD vs Analog PSD

The phase sensitive detectors (PSD's) in the SR850 act as linear multipliers, that is, they multiply the signal with a reference sine wave. Analog PSD's (both square wave and linear) have many problems associated with them. The main problems are harmonic rejection, output offsets, limited dynamic reserve and gain error.

The digital PSD multiplies the digitized signal with a digitally computed reference sine wave. Because the reference sine waves are computed to 20 bits of accuracy, they have very low harmonic content. In fact, the harmonics are at the

-120

dB level! This means that the signal is multiplied by a single reference sine wave (instead of a reference and its many harmonics) and only the signal at this single reference frequency is detected. The SR850 is completely insensitive to signals at harmonics of the reference. In contrast, a square wave multiplying lock-in will detect at all of the odd harmonics of the reference (a square wave contains many large odd harmonics).

Output offset is a problem because the signal of interest is a DC output from the PSD and an output offset contributes to error and zero drift. The offset problems of analog PSD's are eliminated using the digital multiplier. There are no erroneous DC output offsets from the digital multiplication of the signal and reference. In fact, the actual multiplication is totally free from errors.

The dynamic reserve of an analog PSD is limited to about 60 dB. When there is a large noise signal

present, 1000 times or 60 dB greater than the full scale signal, the analog PSD measures the signal with an error. The error is caused by non-linearity in the multiplication (the error at the output depends upon the amplitude of the input). This error can be quite large (10% of full scale) and depends upon the noise amplitude, frequency, and waveform. Since noise generally varies quite a bit in these parameters, the PSD error causes quite a bit of output uncertainty.

In the digital lock-in, the dynamic reserve is limited by the quality of the A/D conversion. Once the input signal is digitized, no further errors are introduced. Certainly the accuracy of the multiplication does not depend on the size of the numbers. The A/D converter used in the SR850 is extremely linear, meaning that the presence of large noise signals does not impair its ability to correctly digitize a small signal. In fact, the dynamic reserve of the SR850 can exceed 100 dB without any problems. We'll talk more about dynamic reserve a little later.

An analog linear PSD multiplies the signal by an analog reference sine wave. Any amplitude variation in the reference amplitude shows up directly as a variation in the overall gain. Analog sine wave generators are susceptible to amplitude drift, especially as a function of temperature. The digital reference sine wave has a precise amplitude and never changes. This eliminates a major source of gain error in a linear analog lock-in.

The overall performance of a lock-in amplifier is largely determined by the performance of its phase sensitive detectors. In virtually all respects, the digital PSD outperforms its analog counterparts.

We've discussed how the digital signal processor in the SR850 computes the internal oscillator and two reference sine waves and handles both phase sensitive detectors. In the next section, we'll see the same DSP perform the low pass filtering and DC amplification required at the output of the PSD's. Here again, the digital technique eliminates many of the problems associated with analog lockin amplifiers.

THE PHASE SENSITIVE DETECTORS (PSD's)

3-9

SR850 Basics

3-10

Remember, the output of the PSD contains many signals. Most of the output signals have frequencies which are either the sum or difference between an input signal frequency and the reference frequency. Only the component of the input signal whose frequency is exactly equal to the reference frequency will result in a DC output.

The low pass filter at the PSD output removes all of the unwanted AC signals, both the 2F (sum of the signal and the reference) and the noise components. This filter is what makes the lock-in such a narrow band detector.

Time Constants

Lock-in amplifiers have traditionally set the low pass filter bandwidth by setting the time constant. The time constant is simply 1/2πf where f is the

-3 dB frequency of the filter. The low pass filters are simple 6 dB/oct roll off, RC type filters. A 1 second time constant referred to a filter whose

-3 dB point occurred at 0.16 Hz and rolled off at 6 dB/oct beyond 0.16 Hz. Typically, there are two successive filters so that the overall filter can roll off at either 6 dB or 12 dB per octave. The time constant referred to the -3 dB point of each filter alone (not the combined filter).

The notion of time constant arises from the fact that the actual output is supposed to be a DC signal. In fact, when there is noise at the input, there is noise on the output. By increasing the time constant, the output becomes more steady and easier to measure reliably. The trade off comes when real changes in the input signal take many time constants to be reflected at the output. This is because a single RC filter requires about 5 time constants to settle to its final value. The time constant reflects how slowly the output responds, and thus the degree of output smoothing.

Note that the SR850 displays the time constant and the equivalent noise bandwidth (ENBW) in the time constant menu. The ENBW is NOT the filter

-3 dB pole, it is the effective bandwidth for Gaussian noise. More about this later.

Digital Filters vs Analog Filters

The SR850 improves on analog filters in many ways. First, analog lock-ins provide at most, two

TIME CONSTANTS and DC GAIN

stages of filtering with a maximum roll off of 12 dB/oct

. This limitation is usually due to space and expense. Each filter needs to have many different time constant settings. The different settings require different components and switches to select them, all of which is costly and space consuming.

The digital signal processor in the SR850 handles all of the low pass filtering. Each PSD can be followed by up to four filter stages for up to

24 dB/oct of roll off. Since the filters are digital, the SR850 is not limited to just two stages of filtering.

Why is the increased roll off desirable? Consider an example where the reference is at 1 kHz and a large noise signal is at 1.05 kHz. The PSD noise outputs are at 50 Hz (difference) and 2.05 kHz (sum). Clearly the 50 Hz component is the more difficult to low pass filter. If the noise signal is 80 dB above the full scale signal and we would like to measure the signal to 1% (-40 dB), then the 50 Hz component needs to be reduced by 120 dB. To do this in two stages would require a time constant of at least 3 seconds. To accomplish the same attenuation in four stages only requires 100 ms of time constant. In the second case, the output will respond 30 times faster and the experiment will take less time.

Synchronous Filters

Another advantage of digital filtering is the ability to do synchronous filtering. Even if the input signal has no noise, the PSD output always contains a component at 2F (sum frequency of signal and reference) whose amplitude equals or exceeds the desired DC output depending upon the phase. At low frequencies, the time constant required to attenuate the 2F component can be quite long. For example, at 1 Hz, the 2F output is at 2 Hz and to attenuate the 2 Hz by 60 dB in two stages requires a time constant of 3 seconds.

A synchronous filter, on the other hand, operates totally differently. The PSD output is averaged over a complete cycle of the reference frequency. The result is that all components at multiples of the reference (2F included) are notched out completely. In the case of a clean signal, almost no additional filtering would be required. This is

SR850 Basics

3-11

SR850 Basics

increasingly useful the lower the reference frequency. Imagine what the time constant would need to be at 0.001 Hz!

In the SR850, synchronous filters are available at detection frequencies below 200 Hz. At higher frequencies, the filters are not required (2F is easily removed without using long time constants). Below 200 Hz, the synchronous filter follows either one or two stages of normal filters. The output of the synchronous filter is followed by two more stages of normal filters. This combination of filters notches all multiples of the reference frequency and provides overall noise attenuation as well.

Long Time Constants

Time constants above 100 seconds are difficult to accomplish using analog filters. This is simply because the capacitor required for the RC filter is prohibitively large (in value and in size!). Why would you use such a long time constant? Sometimes you have no choice. If the reference is well below 1 Hz and there is a lot of low frequency noise, then the PSD output contains many very low frequency components. The synchronous filter only notches multiples of the reference frequency, the noise is filtered by the normal filters.

The SR850 can provide time constants as long as 30000 seconds at reference frequencies below 200 Hz. Obviously you don't use long time constants unless absolutely necessary, but they're available.

DC Output Gain

How big is the DC output from the PSD? It depends on the dynamic reserve. With 60 dB of dynamic reserve, a noise signal can be 1000 times (60 dB) greater than a full scale signal. At the PSD, the noise can not exceed the PSD's input range. In an analog lock-in, the PSD input range might be 5V. With 60 dB of dynamic reserve, the signal will be only 5 mV at the PSD input. The PSD typically has no gain so the DC output from the PSD will only be a few millivolts! Even if the PSD had no DC output errors, amplifying this millivolt signal up to 10 V is error prone. The DC output gain needs to be about the same as the dynamic reserve (1000 in this case) to provide a 10 V output for a full scale input signal. An offset as small as 1 mV will appear as 1 V at the output! In fact, the PSD output offset plus the input offset of the DC amplifier needs to be on the order of 10 µV in order to not affect the measurement. If

the dynamic reserve is increased to 80dB, then this offset needs to be 10 times smaller still. This is one of the reasons why analog lock-ins do not perform well at very high dynamic reserve.

The digital lock-in does not have an analog DC amplifier. The output gain is yet another function handled by the digital signal processor. We already know that the digital PSD has no DC output offset. Likewise, the digital DC amplifier has no input offset. Amplification is simply taking input numbers and multiplying by the gain. This allows the SR850 to operate with 100 dB of dynamic reserve without any output offset or zero drift.

What about resolution?

Just like the analog lock-in where the noise can not exceed the input range of the PSD, in the digital lock-in, the noise can not exceed the input range of the A/D converter. With a 16 bit A/D converter, a dynamic reserve of 60 dB means that while the noise has a range of the full 16 bits, the full scale signal only uses 6 bits. With a dynamic reserve of 80 dB, the full scale signal uses only

2.5 bits. And with 100 dB dynamic reserve, the signal is below a single bit! Clearly multiplying these numbers by a large gain is not going to result in a sensible output. Where does the output resolution come from?

The answer is filtering. The low pass filters effectively combine many data samples together. For example, at a 1 second time constant, the output is the result of averaging data over the previous 4 or 5 seconds. At a sample rate of 256 kHz, this means each output point is the exponential average of over a million data points. (A new output point is computed every 4 µs and is a moving exponential average). What happens when you average a million points? To first order, the resulting average has more resolution than the incoming data points by a factor of million . This represents a gain of 20 bits in resolution over the raw data. A 1 bit input data stream is converted to 20 bits of output resolution from 1 out of a million all the way up to a million out of a million or 1.

The compromise here is that with high dynamic reserve (large DC gains), some filtering is required. The shortest time constants are not available when the dynamic reserve is very high. This is not really a limitation since presumably there is noise which is requiring the high dynamic reserve and thus substantial output filtering will also be required.

3-12

The SR850 has X and Y outputs on the rear panel and Channel 1 and 2 (CH1 and CH2) outputs on the front panel.

X and Y

The X and Y rear panel outputs are the outputs from the two phase sensitive detectors with low pass filtering, offset and expand. These outputs are the traditional outputs of an analog lock-in. The X and Y outputs have an output bandwidth of 100 kHz.

CH1 and CH2

The two front panel outputs can be configured to output voltages proportional to X, Y, R, θ, or Traces 1-4.

If the outputs are set to X or Y, these outputs duplicate the rear panel outputs.

If they are set to R or θ the output voltages are proportional to the calculated values of R and θ. These calculations are performed at a rate of 512 Hz and the R and θ outputs are updated at the 512 Hz rate.

If the outputs are proportional to a data trace, then the output is also updated at 512 Hz. The traces are defined in the TRACE menu as A•B/C where A,B,C can be X, Y, R, θ, Xnoise, Ynoise, Rnoise, Frequency, Aux Inputs 1-4, or unity (C may also be any quantity squared). If a trace is defined as simply X, this trace, when output through CH1 or CH2, will only update at 512 Hz. It is better in this case to set CH1 to output X directly, rather than the trace defined as X. The output scale of a data trace is discussed later in this section.

X, Y, R and θ Output scales

The sensitivity of the lock-in is the rms amplitude of an input sine (at the reference frequency) which results in a full scale DC output. Traditionally, full scale means 10 VDC at the X, Y or R BNC output. The overall gain (input to output) of the amplifier is then 10 V/sensitivity. This gain is distributed between AC gain before the PSD and DC gain following the PSD. Changing the dynamic reserve at a given sensitivity changes the gain distribution while keeping the overall gain constant.

The SR850 considers 10 V to be full scale for any output proportional to simply X, Y or R. This is the output scale for the X and Y rear panel outputs as well as the CH1 and CH2 outputs when configured to output X, Y or R. When the CH1 or CH2 outputs are proportional to a data trace which is simply defined as X, Y or R, the output scale is also 10 V full scale.

Lock-in amplifiers are designed to measure the RMS value of the AC input signal. All sensitivities and X, Y and R outputs and displays are RMS values.

Phase is a quantity which ranges from -180° to +180° regardless of the sensitivity. When the CH1 or CH2 outputs a voltage proportional to θ, the output scale is 18°/Volt or 180°=10V.

X, Y and R Output Offset and Expand

The SR850 has the ability to offset the X, Y and R outputs. This is useful when measuring deviations in the signal around some nominal value. The offset can be set so that the output is offset to zero. Changes in the output can then be read directly from the display or output voltages. The offset is specified as a percentage of full scale and the percentage does not change when the sensitivity is changed. Offsets up to ±105% can be programmed.

The X, Y and R outputs may also be expanded. This simply takes the output (minus its offset) and multiplies by an expansion factor. Thus, a signal which is only 10% of full scale can be expanded to provide 10 V of output rather than only 1 V. The normal use for expand is to expand the measurement resolution around some value which is not zero. For example, suppose a signal has a nominal value of 0.9 mV and we want to measure small deviations, say 10 µV or so, in the signal. The sensitivity of the lock-in needs to be 1 mV to accommodate the nominal signal. If the offset is set so to 90% of full scale, then the nominal 0.9 mV signal will result in a zero output. The 10 µV deviations in the signal only provide 100 mV of DC output. If the output is expanded by 10, these small deviations are magnified by 10 and provide outputs of 1 VDC.

The SR850 can expand the output by a factor from

DC OUTPUTS and SCALING

SR850 Basics

3-13

SR850 Basics

1 to 256 provided the expanded output does not exceed full scale. In the above example, the 10 µV deviations can be expanded up to 100 times before they exceed full scale (at 1 mV sensitivity).

The analog output with offset and expand is Output = (signal/sensitivity - offset) x Expand x10V where offset is a fraction of 1 (50%=0.5), expand

is an integer from 1 to 256 and the output can not exceed 10 V. In the above example,

Output = (0.91mV/1mV - 0.9) x 10 x 10V = 1V for a signal which is 10 µV greater than the 0.9 mV

nominal. (Offset = 0.9 and expand =10). The X and Y offset and expand functions in the

SR850 are output functions, they do NOT affect the calculation of R or θ. R has its own output offset and expand.

Trace displays

Only data traces may be displayed on the screen. In order to display the quantity X, it is necessary to define a trace to be X and then choose to display that trace.

Output offsets ARE reflected in data trace displays which depend upon X, Y or R. For example, a trace which is defined as X is affected by the X offset. When the X output is offset to zero, the displayed trace value on the screen will drop to zero also. Any display which is showing a trace which is affected by a non-zero offset will display a highlighted

Offst

indicator at the lower left of the

display. Output expands do NOT increase the displayed

values of X, Y or R in data traces. Expand increases the resolution of the X, Y or R value used to calculate the trace value. For example, a trace which is defined as X does not increase its displayed value when X is expanded. This is because the expand function increases the resolution with which the signal is measured, not the size of the input signal. The displayed value will show an increased resolution but will continue to display the original

value

of X minus the X offset. Any display which is showing a trace which is affected by a non-unity expand will display a highlighted

Expd

indicator at the lower left of the display.

Complex data traces are displayed and stored in the actual units of the computed quantity. For example, if a trace is defined as X•θ/Aux 1 and X=1 mV, θ=37°, and Aux 1= 2.34 V, then the trace value is 0.001 x 37/2.34 Volt•degrees per Volt or 0.01581 Vdeg/V. This value is not changed by the sensitivity (X is the input signal, not the output voltage) or by X expand. An X offset will, however, change the value of this trace.

Trace output scaling

What about CH1 or CH2 outputs proportional to data traces which are not simply X, Y, R or θ? If a trace is defined as A•B/C, then the trace output voltage depends upon the values of each parameter. Trace output voltages are calculated by determining the output voltages for the individual quantities, A, B and C. The individual output voltages (-10 V to +10 V) are then combined using the trace definition to determine the trace output voltage.

For example, suppose a trace is defined as X/R. The parameters X and R scale as 10 V for a full scale input signal. If the sensitivity is 1 V and the measured values are X=500 mV and R=1 V, the X output would be 5 V and the R output would be 10 V. The trace output voltage is simply (X=5 V)/(R=10 V)=0.5 V.

Output voltages for traces which are defined as A, B, A/C, B/C or A•B/C are calculated using the output voltages for A, B and C. Traces defined as A•B (A,B≠1, C=1) have output voltages which are the product of the A and B output voltages divided by 10.

For example, suppose a trace is defined as X•θ. The parameter X scales as 10 V for a full scale input signal and θ scales as 10 V for 180° of phase shift. If the measured X is 1 V on the 1 V sensitivity, X would be 100% of full scale or 10 V. If the phase is 180°, then θ is also 10 V. The trace output voltage is thus, (X=10 V)•(θ=10 V)/10=10 V. The extra factor of 10 allows products of two full scale quantities to be output.

X, Y and R output offsets ARE reflected in trace outputs which depend upon X, Y or R. For example, a trace which is defined as X and output through CH1 or CH2 is affected by the X offset. When the X output is offset to zero, the trace output voltage will drop to zero also.

3-14

Output expands DO increase the output voltage of X, Y or R in trace outputs. Expand increases the output voltages of X, Y or R in trace output calculations. For example, a trace which is defined as X and output through CH1 or CH2 increases its output voltage by the expand factor when X is expanded. This is because the output voltage of X is expanded.

The output voltage scales for the individual quantities are listed below.

X,Y,R

(signal/sensitivity-offset)xExpandx10V

10V/180°

Xn,Yn,Rn

(noise signal/sensitivity)xExpandx10V

Aux In 1-4

output voltage = Aux input voltage

5V - 10V for each octave in frequency. For example,

1000 Hz = 5V 1200 Hz = 6V 1600 Hz = 8V 1800 Hz = 9V 1990 Hz = 9.95V

2000 Hz = 5V (next octave) The octaves are defined as follows, ...

62.5 Hz - 125 Hz 125 Hz - 250 Hz 250 Hz - 500 Hz 500 Hz - 1000 Hz 1 kHz - 2 kHz 4 kHz - 8 kHz 8 kHz - 16 kHz ...

SR850 Basics

3-15

SR850 Basics

3-16

We've mentioned dynamic reserve quite a bit in the preceding discussions. It's time to clarify dynamic reserve a bit.

What is dynamic reserve really?

Suppose the lock-in input consists of a full scale signal at f

ref

plus noise at some other frequency. The traditional definition of dynamic reserve is the ratio of the largest tolerable noise signal to the full scale signal, expressed in dB. For example, if full scale is 1 µV, then a dynamic reserve of 60 dB means noise as large as 1 mV (60 dB greater than full scale) can be tolerated at the input without overload.

The problem with this definition is the word 'tolerable'. Clearly the noise at the dynamic reserve limit should not cause an overload anywhere in the instrument - not in the input signal amplifier, PSD, low pass filter or DC amplifier. This is accomplished by adjusting the distribution of the gain. To achieve high reserve, the input signal gain is set very low so the noise is not likely to overload. This means that the signal at the PSD is also very small. The low pass filter then removes the large noise components from the PSD output which allows the remaining DC component to be amplified (a lot) to reach 10 V full scale. There is no problem running the input amplifier at low gain. However, as we have discussed previously, analog lock-ins have a problem with high reserve because of the linearity of the PSD and the DC offsets of the PSD and DC amplifier. In an analog lock-in, large noise signals almost always disturb the measurement in some way.

The most common problem is a DC output error caused by the noise signal. This can appear as an offset or as a gain error. Since both effects are dependent upon the noise amplitude and frequency, they can not be offset to zero in all cases and will limit the measurement accuracy. Because the errors are DC in nature, increasing the time constant does not help. Most lock-ins define tolerable noise as noise levels which do not affect the output more than a few percent of full scale. This is more severe than simply not overloading.

Another effect of high dynamic reserve is to generate noise and drift at the output. This comes about

because the DC output amplifier is running at very high gain and low frequency noise and offset drift at the PSD output or the DC amplifier input will be amplified and appear large at the output. The noise is more tolerable than the DC drift errors since increasing the time constant will attenuate the noise. The DC drift in an analog lock-in is usually on the order of 1000ppm/°C when using 60 dB of dynamic reserve. This means that the zero point moves 1% of full scale over 10°C temperature change. This is generally considered the limit of tolerable.

Lastly, dynamic reserve depends on the noise frequency. Clearly noise at the reference frequency will make its way to the output without attenuation. So the dynamic reserve at f

ref

is 0dB. As the noise frequency moves away from the reference frequency, the dynamic reserve increases. Why? Because the low pass filter after the PSD attenuates the noise components. Remember, the PSD outputs are at a frequency of |f

noise-fref

|. The rate at which the reserve increases depends upon the low pass filter time constant and roll off. The reserve increases at the rate at which the filter rolls off. This is why 24 dB/oct filters are better than 6 or 12 dB/oct filters. When the noise frequency is far away, the reserve is limited by the gain distribution and overload level of each gain element. This reserve level is the dynamic reserve

referred to in the specifications. The above graph shows the actual reserve vs the

frequency of the noise. In some instruments, the

DYNAMIC RESERVE

ref

60 dB

40 dB

20 dB

0 dB

noise

actual reserve

low pass filter bandwidth

60 dB specified reserve

SR850 Basics

3-17

SR850 Basics

signal input attenuates frequencies far outside the lock-in's operating range (f

noise

>>100 kHz). In these cases, the reserve can be higher at these frequencies than within the operating range. While this may be a nice specification, removing noise at frequencies very far from the reference does not require a lock-in amplifier. Lock-ins are used when there is noise at frequencies near the signal. Thus, the dynamic reserve for noise within the operating range is more important.

Dynamic reserve in the SR850

The SR850, with its digital phase sensitive detectors, does not suffer from DC output errors caused by large noise signals. The dynamic reserve can be increased to above 100 dB without measurement error. Large noise signals do not cause output errors from the PSD. The large DC gain does not result in increased output drift.

In fact, the only drawback to using ultra high dynamic reserves (>60 dB) is the increased output noise due to the noise of the A/D converter. This increase in output noise is only present when the dynamic reserve is increased above 60 dB AND above the minimum reserve. (If the minimum reserve is 80 dB, then increasing to 90 dB may increase the noise. As we'll discuss next, the minimum reserve does not have increased output noise no matter how large it is.)

To set a scale, the SR850's output noise at 100 dB dynamic reserve is only measurable when the signal input is grounded. Let's do a simple experiment. If the lock-in reference is at 1 kHz and a large signal is applied at 9.5 kHz, what will the lock-in output be? If the signal is increased to the dynamic reserve limit (100 dB greater than full scale), the output will reflect the noise of the signal at 1 kHz. The spectrum of any pure sine generator always has a noise floor, i.e. there is some noise at all frequencies. So even though the applied signal is at 9.5 kHz, there will be noise at all other frequencies, including the 1 kHz lock-in reference. This noise will be detected by the lock-in and appear as noise at the output. This output noise will typically be greater than the SR850's own output noise. In fact, virtually all signal sources will have a noise floor which will dominate the lock-in output noise. Of course, noise signals are generally much noisier than pure sine generators and will have much higher broadband noise floors.

If the noise does not reach the reserve limit, the SR850's own output noise may become detectable

at ultra high reserves. In this case, simply lower the dynamic reserve and the DC gain will decrease and the output noise will decrease also. In general, do not run with more reserve than necessary. Certainly don't use ultra high reserve when there is virtually no noise at all.

The frequency dependence of dynamic reserve is inherent in the lock-in detection technique. The SR850, by providing more low pass filter stages, can increase the dynamic reserve close to the reference frequency. The specified reserve applies to noise signals within the operating range of the lock-in, i.e. frequencies below 100 kHz. The reserve at higher frequencies is actually higher but is generally not that useful.

Minimum dynamic reserve

The SR850 always has a minimum amount of dynamic reserve. This minimum reserve changes with the sensitivity (gain) of the instrument. At high gains (full scale sensitivity of 50 µV and below), the minimum dynamic reserve increases from 37 dB at the same rate as the sensitivity increases. For example, the minimum reserve at 5 µV sensitivity is 57 dB. In many analog lock-ins, the reserve can be lower. Why can't the SR850 run with lower reserve at this sensitivity?

The answer to this question is - Why would you want lower reserve? In an analog lock-in, lower reserve means less output error and drift. In the SR850, more reserve does not increase the output error or drift. More reserve can increase the output noise though. However, if the analog signal gain before the A/D converter is high enough, the 5 nV/√Hz

noise of the signal input will be amplified to a level greater than the input noise of the A/D converter. At this point, the detected noise will reflect the actual noise at the signal input and not the A/D converter's noise. Increasing the analog gain (decreasing the reserve) will not decrease the output noise. Thus, there is no reason to decrease the reserve. At a sensitivity of 5 µV, the analog gain is sufficiently high so that A/D converter noise is not a problem. Sensitivities below 5 µV do not require any more gain since the signal to noise ratio will not be improved (the front end noise dominates). The SR850 does not increase the gain below the 5 µV sensitivity, instead, the minimum reserve increases. Of course, the input gain can be decreased and the reserve increased, in which case the A/D converter noise might be detected in the absence of any signal input.

3-18

A lock-in can measure signals as small as a few nanovolts. A low noise signal amplifier is required to boost the signal to a level where the A/D converter can digitize the signal without degrading the signal to noise. The analog gain in the SR850 ranges from roughly 7 to 1000. As discussed previously, higher gains do not improve signal to noise and are not necessary.

The overall gain (AC plus DC) is determined by the sensitivity. The distribution of the gain (AC versus DC) is set by the dynamic reserve.

Input noise

The input noise of the SR850 signal amplifier is about 5 nVrms/√Hz. What does this noise figure mean? Let's set up an experiment. If an amplifier has 5 nVrms/√Hz of input noise and a gain of 1000, then the output will have 5 µVrms/√Hz of noise. Suppose the amplifier output is low pass filtered with a single RC filter (6 dB/oct roll off) with a time constant of 100 ms. What will be the noise at the filter output?

Amplifier input noise and Johnson noise of resistors are Gaussian in nature. That is, the amount of noise is proportional to the square root of the bandwidth in which the noise is measured. A single stage RC filter has an equivalent noise bandwidth (ENBW) of 1/4T where T is the time constant (RxC). This means that Gaussian noise at the filter input is filtered with an effective bandwidth equal to the ENBW. In this example, the filter sees 5 µVrms/√Hz of noise at its input. It has an ENBW of 1/(4x100ms) or 2.5 Hz. The voltage noise at the filter output will be 5 µVrms/√Hz

x √2.5Hz or 7.9 µVrms. For Gaussian noise, the peak to peak noise is about 5 times the rms noise. Thus, the output will have about 40 µV pk-pk of noise.

Input noise for a lock-in works the same way. For sensitivities below about 5 µV full scale, the input noise will determine the output noise (at minimum reserve). The amount of noise at the output is determined by the ENBW of the low pass filter. The SR850 displays the ENBW in the Time Constant menu. The ENBW depends upon the time constant and filter roll off. For example, suppose the SR850 is set to 5 µV full scale with a 100

SIGNAL INPUT AMPLIFIER and FILTERS

ms time constant and 6 dB/oct of filter roll off. The lock-in will measure the input noise with an ENBW of 2.5 Hz. This translates to 7.9 nVrms at the input. At the output, this represents about 0.16% of full scale (7.9 nV/5 µV). The peak to peak noise will be about 0.8% of full scale.

All of this assumes that the signal input is being driven from a low impedance source. Remember resistors have Johnson noise equal to

0.13x√R nVrms/√Hz

. Even a 50Ω resistor has almost 1 nVrms/√Hz of noise! A signal source impedance of 2kΩ will have a Johnson noise greater than the SR850's input noise. To determine the overall noise of multiple noise sources, take the square root of the sum of the squares of the individual noise figures. For example, if a 2kΩ source impedance is used, the Johnson noise will be 5.8 nVrms/√Hz. The overall noise at the SR850 input will be [52 + 5.82]

1/2

or 7.7 nVrms/√Hz.

We'll talk more about noise sources later in this section.

At lower gains (sensitivities above 50 µV), there is not enough gain at high reserve to amplify the input noise to a level greater than the noise of the A/D converter. In these cases, the output noise is determined by the A/D noise. Fortunately, at these sensitivities, the DC gain is low and the noise at the output is negligible.

Notch filters

The SR850 has two notch filters in the signal amplifier chain. These are pre-tuned to the line frequency (50 or 60 Hz) and twice the line frequency (100 or 120 Hz). In circumstances where the largest noise signals are at the power line frequencies, these filters can be engaged to remove noise signals at these frequencies. Removing the largest noise signals before the final gain stage can reduce the amount of dynamic reserve required to perform a measurement. To the extent that these filters reduce the required reserve to either 60 dB or the minimum reserve (whichever is higher), then some improvement might be gained. If the required reserve without these notch filters is below 60 dB or if the minimum reserve is sufficient, then these filters do not significantly improve the measurement.

SR850 Basics

3-19

SR850 Basics

Using either of these filters precludes making measurements in the vicinity of the notch frequencies. These filters have a finite range of attenuation, generally 10 Hz or so. Thus, if the lock-in is making measurements at 70 Hz, do not use the 60 Hz notch filter! The signal will be attenuated and the measurement will be in error. When measuring phase shifts, these filters can affect phase measurements up to an octave away.

Anti-aliasing filter

After all of the signal filtering and amplification, there is an anti-aliasing filter. This filter is required by the signal digitization process. According to the Nyquist criterion, signals must be sampled at a frequency at least twice the highest signal frequency. In this case, the highest signal frequency is 100 kHz and the sampling frequency is 256 kHz so things are ok. However, no signals above 128 kHz can be allowed to reach the A/D converter. These signals would violate the Nyquist criterion and be undersampled. The result of this undersampling is to make these higher frequency signals appear as lower frequencies in the digital data stream. Thus a signal at 175 kHz would appear below 100 kHz in the digital data stream and be detectable by the digital PSD. This would be a problem.

To avoid this undersampling, the analog signal is filtered to remove any signals above 154 kHz (when sampling at 256 kHz, signals above 154 kHz will appear below 102 kHz). This filter has a flat pass band from DC to 102 kHz so as not to affect measurements in the operating range of the lock-in. The filter rolls off from 102 kHz to 154 kHz and achieves an attenuation above 154 kHz of at least 100 dB. Amplitude variations and phase shifts due to this filter are calibrated out at the factory and do not affect measurements. This filter is transparent to the user.

Input Impedance

The input impedance of the SR850 is 10 MΩ. If a higher input impedance is desired, then the SR550 remote preamplifier must be used. The SR550 has an input impedance of 100 MΩ and is AC coupled from 1 Hz to 100 kHz.

3-20

In order to achieve the best accuracy for a given measurement, care must be taken to minimize the various noise sources which can be found in the laboratory. With intrinsic noise (Johnson noise, 1/f noise or input noise), the experiment or detector must be designed with these noise sources in mind. These noise sources are present regardless of the input connections. The effect of noise sources in the laboratory (such as motors, signal generators, etc.) and the problem of differential grounds between the detector and the lock-in can be minimized by careful input connections.

There are two basic methods for connecting a voltage signal to the lock-in - the single-ended connection is more convenient while the differential connection eliminates spurious pick-up more effectively.

Single-Ended Voltage Connection (A)

In the first method, the lock-in uses the A input in a single-ended mode. The lock-in detects the signal as the voltage between the center and outer conductors of the A input only. The lock-in does not force the shield of the A cable to ground, rather it is internally connected to the lock-in's ground via a resistor. The value of this resistor is chosen in the INPUT menu. Float uses 1 kΩ and Ground uses 10Ω. This avoids ground loop problems between the experiment and the lock-in due to differing ground potentials. The lock-in lets the shield 'quasi-float' in order to sense the experiment ground. However, noise pickup on the shield will appear as noise to the lock-in. This is bad since the lock-in cannot reject this noise. Common mode noise, which appears on both the center and shield, is rejected by the 100 dB CMRR of the lock-in input, but noise on only the shield is not rejected at all.

Differential Voltage Connection (A-B)

The second method of connection is the differential mode. The lock-in measures the voltage difference between the center conductors of the A and B inputs. Both of the signal connections are shielded from spurious pick-up. Noise pickup on the shields does not translate into signal noise since the shields are ignored.

When using two cables, it is important that both cables travel the same path between the experiment and the lock-in. Specifically, there should not be a large loop area enclosed by the two cables. Large loop areas are susceptible to magnetic pickup.

Common Mode Signals

Common mode signals are those signals which appear equally on both center and shield (A) or both A and B (A-B). With either connection scheme, it is important to minimize both the common mode noise and the common mode signal. Notice that the signal source is held near ground potential in both illustrations above. If the signal source floats at a nonzero potential, the signal which appears on both the A and B inputs will not be perfectly cancelled. The common mode rejection ratio (CMRR) specifies the degree of cancellation. For low frequencies, the CMRR of 100 dB indicates that the common mode signal is canceled to 1 part in 105. Even with a CMRR of 100 dB, a 100 mV common mode signal behaves like a 1 µV differential signal! This is especially bad if the common mode signal is at the reference frequency (this happens a lot due to ground loops). The CMRR decreases by about 6 dB/ octave (20 dB/decade) starting at around 1 kHz.

INPUT CONNECTIONS

Experiment

Signal Source

A +-

Grounds may be at different potentials

Loop

Area

Experiment

Signal Source

SR850 Lock-In

A +-

Grounds may be at different potentials

SR850 Basics

SR850 Lock-In

3-21

SR850 Basics

Current Input (I)

The current input on the SR850 uses the A input BNC. Voltage or current input is chosen in the INPUT menu. The current input has a 1 kΩ input impedance and a current gain of either 106 or 108 Volts/Amp

. Currents from 1 µA down to 2 fA

full scale can be measured. The impedance of the signal source is the most

important factor to consider in deciding between voltage and current measurements.

For high source impedances, greater than 1 MΩ (106 gain) or 100 MΩ (108 gain), and small currents, use the current input. Its relatively low impedance greatly reduces the amplitude and phase errors caused by the cable capacitance-source impedance time constant. The cable capacitance should still be kept small to minimize the high frequency noise gain of the current preamplifier.

For moderate to low source impedances, or larger currents, the voltage input is preferred. A small value resistor may be used to shunt the signal current and generate a voltage signal. The lock-in then measures the voltage across the shunt resistor. Select the resistor value to keep the shunt voltage small (so it does not affect the source current) while providing enough signal for the lock-in to measure.

Which current gain should you use? The current gain determines the input current noise of the lockin as well as its measurement bandwidth. Signals far above the input bandwidth are attenuated by 6 dB/oct. The noise and bandwidth are listed below.

Gain

Noise

Bandwidth

130 fA/√Hz

70 kHz

13 fA/√Hz

700 Hz

The current gain is selected in the INPUT menu when the I input is in use.

AC vs DC Coupling

The signal input can be either AC or DC coupled. The AC coupling high pass filter passes signals above 160 mHz (0.16 Hz) and attenuates signals at lower frequencies. AC coupling should be used at frequencies above 50 mHz whenever possible. At lower frequencies, DC coupling is required.

A DC signal, if not removed by the AC coupling filter, will multiply with the reference sine wave and produce an output at the reference frequency. This signal is not normally present and needs to be removed by the low pass filter. If the DC component of the signal is large, then this output will be large and require a long time constant to remove. AC coupling removes the DC component of the signal without any sacrifice in signal as long as the frequency is above 160 mHz.

The current input current to voltage preamplifier is always DC coupled. AC coupling can be selected following the current preamplifier to remove any DC current signal.

3-22

Random noise finds its way into experiments in a variety of ways. Good experimental design can reduce these noise sources and improve the measurement stability and accuracy.

There are a variety of intrinsic noise sources which are present in all electronic signals. These sources are physical in origin.

Johnson noise

Every resistor generates a noise voltage across its terminals due to thermal fluctuations in the electron density within the resistor itself. These fluctuations give rise to an open-circuit noise voltage,

where k=Boltzmann's constant (1.38x10

-23

J/°K), T is the temperature in °Kelvin (typically 300°K), R is the resistance in Ohms, and ∆f is the bandwidth in Hz. ∆f is the bandwidth of the measurement.

Since the input signal amplifier in the SR850 has a bandwidth of approximately 300 kHz, the effective noise at the amplifier input is V

noise

= 70√R nVrms or 350√R nV pk-pk. This noise is broadband and if the source impedance of the signal is large, can determine the amount of dynamic reserve required.

The amount of noise measured by the lock-in is determined by the measurement bandwidth. Remember, the lock-in does not narrow its detection bandwidth until after the phase sensitive detectors. In a lock-in, the equivalent noise bandwidth (ENBW) of the low pass filter (time constant) sets the detection bandwidth. In this case, the measured noise of a resistor at the lock-in input, typically the source impedance of the signal, is simply

The SR850 displays the ENBW in the TIME CONSTANT menu. This is the correct noise bandwidth for the time constant and the number of poles and should be used to calculate the detected Johnson noise. The displayed ENBW does not take the synchronous filter into account.

The signal amplifier bandwidth determines the amount of broadband noise that will be amplified. This affects the dynamic reserve. The time constant sets the amount of noise which will be measured at the reference frequency. See the SIGNAL INPUT AMPLIFIER discussion for more information about Johnson noise.

Shot noise

Electric current has noise due to the finite nature of the charge carriers. There is always some nonuniformity in the electron flow which generates noise in the current. This noise is called shot noise. This can appear as voltage noise when current is passed through a resistor, or as noise in a current measurement. The shot noise or current

noise is given by where q is the electron charge (1.6x10

-19

Coulomb), I is the RMS AC current or DC current depending upon the circuit, and ∆f is the bandwidth.

When the current input of a lock-in is used to measure an AC signal current, the bandwidth is typically so small that shot noise is not important.

1/f noise

Every 10 Ω resistor, no matter what it is made of, has the same Johnson noise. However, there is excess noise in addition to Johnson noise which arises from fluctuations in resistance due to the current flowing through the resistor. For carbon composition resistors, this is typically 0.1 µV-3 µV of rms noise per Volt of applied across the resistor. Metal film and wire-wound resistors have about 10 times less noise. This noise has a 1/f spectrum and makes measurements at low frequencies more difficult.

Other sources of 1/f noise include noise found in vacuum tubes and semiconductors.

Total noise

All of these noise sources are incoherent. The total random noise is the square root of the sum of the squares of all the incoherent noise sources.

INTRINSIC (RANDOM) NOISE SOURCES

ENBW nV

SR850 Basics

noise

(rms)= 0.13 R

noise

(rms)= 4kTR∆f

( )

1/2

(rms)= 2qI∆f( )

noise

1/2

3-23

SR850 Basics

3-24

In addition to the intrinsic noise sources discussed in the previously, there are a variety of external noise sources within the laboratory.

Most of these noise sources are asynchronous, i.e. they are not related to the reference and do not occur at the reference frequency or its harmonics. Examples include lighting fixtures, motors, cooling units, radios, computer screens, etc. These noise sources affect the measurement by increasing the required dynamic reserve or lengthening the time constant.

Some noise sources, however, are related to the reference and, if picked up in the signal, will add or subtract from the actual signal and cause errors in the measurement. Typical sources of synchronous noise are ground loops between the experiment, detector and lock-in, and electronic pick up from the reference oscillator or experimental apparatus.

Many of these noise sources can be minimized with good laboratory practice and experiment design. There are several ways in which noise sources are coupled into the signal path.

Capacitive coupling

An AC voltage from a nearby piece of apparatus can couple to a detector via a stray capacitance. Although C

stray

may be very small, the coupled noise may still be larger than a weak experimental signal. This is especially damaging if the coupled noise is synchronous (at the reference frequency).

We can estimate the noise current caused by a stray capacitance by,

where ω is 2π times the noise frequency, V

noise

the noise amplitude, and C

stray

is the stray

capacitance.

For example, if the noise source is a power circuit, then f = 60 Hz and V

noise

= 120 V. C

stray

can be estimated using a parallel plate equivalent capacitor. If the capacitance is roughly an area of 1 cm

at a separated by 10 cm, then C

stray

is 0.009 pF. The resulting noise current will be 400 pA (at 60 Hz). This small noise current can be thousands of times larger than the signal current. If the noise source is at a higher frequency, the coupled noise will be even greater.

If the noise source is at the reference frequency, then the problem is much worse. The lock-in rejects noise at other frequencies, but pick-up at the reference frequency appears as signal!

Cures for capacitive noise coupling include:

Removing or turning off the noise source.

Keeping the noise source far from the experiment (reducing C

stray

). Do not bring the signal cables close to the noise source.

Designing the experiment to measure voltages with low impedance (noise current generates very little voltage).

Installing capacitive shielding by placing both the experiment and detector in a metal box.

Inductive coupling

An AC current in a nearby piece of apparatus can couple to the experiment via a magnetic field. A changing current in a nearby circuit gives rise to a changing magnetic field which induces an emf (dØB/dt) in the loop connecting the detector to the experiment. This is like a transformer with the experiment-detector loop as the secondary winding.

EXTERNAL NOISE SOURCES

= ωC

strayVnoise

Detector

Stray Capacitance

Noise

Source

Experiment

Detector

Noise

Source

Experiment

B(t)

SR850 Basics

i= C

stray

3-25

SR850 Basics

Cures for inductively coupled noise include:

Removing or turning off the interfering noise source.

Reduce the area of the pick-up loop by using twisted pairs or coaxial cables, or even twisting the 2 coaxial cables used in differential connections.

Using magnetic shielding to prevent the magnetic field from crossing the area of the experiment.

Measuring currents, not voltages, from high impedance detectors.

Resistive coupling or ground loops

Currents flowing through the ground connections can give rise to noise voltages. This is especially a

problem with reference frequency ground currents. In this illustration, the detector is measuring the signal relative to a ground far from the rest of the experiment. The experiment senses the detector signal plus the voltage due to the noise source's ground return current passing through the finite resistance of the ground between the experiment and the detector. The detector and the experiment are grounded at different places which, in this case, are at different potentials.

Cures for ground loop problems include:

Grounding everything to the same physical point.

Using a heavy ground bus to reduce the resistance of ground connections.

Removing sources of large ground currents from the ground bus used for small signals.

Detector

Noise Source

Experiment

I(t)

+ V

= i

Microphonics

Not all sources of noise are electrical in origin. Mechanical noise can be translated into electrical noise by microphonic effects. Physical changes in the experiment or cables (due to vibrations for example) can result in electrical noise over the entire frequency range of the lock-in.

For example, consider a coaxial cable connecting a detector to a lock-in. The capacitance of the cable is a function of its geometry. Mechanical vibrations in the cable translate into a capacitance that varies in time, typically at the vibration frequency. Since the cable is governed by Q=CV, taking the derivative, we have

Mechanical vibrations in the cable which cause a dC/ dt will give rise to a current in the cable. This current affects the detector and the measured signal.

Some ways to minimize microphonic signals are:

1) Eliminate mechanical vibrations near the experiment.

2) Tie down cables carrying sensitive signals so they do not move.

3) Use a low noise cable that is designed to reduce microphonic effects.

Thermocouple effects

The emf created by junctions between dissimilar metals can give rise to many microvolts of slowly varying potentials. This source of noise is typically at very low frequency since the temperature of the detector and experiment generally changes slowly. This effect is large on the scale of many detector outputs and can be a problem for low frequency measurements, especially in the mHz range.

Some ways to minimize thermocouple effects are:

1) Hold the temperature of the experiment or detector constant.

2) Use a compensation junction, i.e. a second junction in reverse polarity which generates an emf to cancel the thermal potential of the first junction. This second junction should be held at the same temperature as the first junction.

3-26

Lock-in amplifiers can be used to measure noise. Noise measurements are generally used to characterize components and detectors.

The SR850 measures input signal noise AT the reference frequency. Many noise sources have a frequency dependence which the lock-in can measure.

How does a lock-in measure noise?

Remember that the lock-in detects signals close to the reference frequency. How close? Input signals within the detection bandwidth set by the low pass filter time constant and roll-off appear at the output at a frequency f=f

sig-fref

. Input noise near f

ref

appears as noise at the output with a bandwidth of DC to the detection bandwidth.

The noise is simply the standard deviation (root of the mean of the squared deviations)of the measured X, Y or R . The SR850 can measure this noise exactly by recording the output quantity on a chart display and then calculating the standard deviation using the trace math functions. The noise, in Volts/√Hz, is simply the standard deviation divided by the square root of the equivalent noise bandwidth of the time constant.

For Gaussian noise, the equivalent noise bandwidth (ENBW) of a low pass filter is the bandwidth of the perfect rectangular filter which passes the same amount of noise as the real filter. The ENBW is displayed along with the time constant in the GAIN/TC menu.

Noise estimation

The above technique, while mathematically sound, can not provide a real time output or an analog output proportional to the measured noise. For these measurements, the SR850 can estimate the X, Y or R noise directly.

To display or record the noise of X, for example, simply define a trace as Xn (in the Trace/Scan menu). The quantity Xn is computed in real time and is an estimate of the noise of X. The quantities Yn and Rn are estimations of the Y noise and R noise.

The quantity Xn is computed from the measured values of X using the following algorithm. The

NOISE MEASUREMENTS

moving average of X is computed. This is the mean value of X over some past history. The present mean value of X is subtracted from the present value of X to find the deviation of X from the mean. Finally, the moving average of the absolute value of the deviations is calculated. This calculation is called the mean average deviation or MAD. This is not the same as an RMS calculation. However, if the noise is Gaussian in nature, then the RMS noise and the MAD noise are related by a constant factor.

The SR850 uses the MAD method to estimate the RMS noise quantities Xn, Yn and Rn. The advantage of this technique is its numerical simplicity and speed.

The noise calculations for X, Y and R occur at 512 Hz. At each sample, the mean and moving average of the absolute value of the deviations is calculated. The averaging time (for the mean and average deviation) depends upon the time constant. The averaging time is selected by the SR850 and ranges from 10 to 80 times the time constant. Shorter averaging times yield a very poor estimate of the noise (the mean varies rapidly and the deviations are not averaged well). Longer averaging times, while yielding better results, take a long time to settle to a steady answer.

To change the settling time, change the time constant. Remember, shorter settling times use smaller time constants (higher noise bandwidths) and yield noisier noise estimates.

The quantities Xn, Yn and Rn are displayed in units of Volts/√Hz. The ENBW of the time constant is already factored into the calculation. Thus, the mean value of Xn should not depend upon the time constant.

The SR850 performs the noise calculations all of the time, whether or not Xn, Yn or Rn are being recorded or displayed. Thus, as soon as Xn is displayed, the value shown is up to date and no settling time is required. If the sensitivity is changed, then the noise estimate will need to settle to the correct value.

For most applications, noise estimation and standard deviation calculations yield the same answer.

SR850 Basics

3-27

SR850 Basics

Which method you use depends upon the requirements of the experiment.

R noise

The quantity Rn can be somewhat hard to understand. For example, suppose X and Y are equally noisy and centered about zero. The values of R are always positive (magnitude) and thus average to a nonzero value. In this case, X and Y noise result in an average R which can be interpreted as the minimum detectable value of R. Increasing the time constant reduces the X and Y output noise and reduces this average value of R. The calculation of R noise by either method will typically yield a value smaller than either Xn or Yn. This is because X and Y have both positive and negative values with a zero center yielding large deviations while R is always positive with a non zero mean and has smaller deviations. In this case, R noise is mathematically defined but not indicative of the Gaussian noise typically measured.

If there is a nonzero steady state value of R such that the noise excursions of R are small compared with the mean R, then R noise is meaningful. This is the case when measuring noise in the presence of real detectable signal. In this case, the value Rn approaches Xn and Yn.

3-28

POWER BUTTON

The SR850 is turned on by pushing in the power button. The video display may take a few seconds to warm up and become visible. Adjust the brightness until the screen is easily readable.The model, firmware version and serial number of the unit are displayed when the power is turned on.

A series of internal tests are performed at this point. Each test is displayed as it is performed and the results are represented graphically as OK or NOT OK. The tests are described below.

RAM

This test performs a read/write test to the processor RAM. In addition, the nonvolatile backup memory is tested. All instrument settings are stored in nonvolatile memory and are retained when the power is turned off. If the memory check passes, then the instrument returns to the settings in effect when the power was last turned off. If there is a memory error, then the stored settings are lost and the default settings are used.

ROM

This test checks the processor ROM.

CLR

This test indicates whether the unit is being reset. To reset the unit, hold down the

backspace [←] key while the power is turned on. The unit will use the default settings. The default setup is listed in a later chapter.

CLK

This test checks the CMOS clock and calendar for a valid date and time. If the there is an error, the time will be reset to a default time. Change the clock settings using the SYSTEM SETUP menu.

DSP

This test checks the digital signal processor (DSP).

VIDEO DISPLAY

The monochrome video display is the user interface for data display and front panel programming operations. The resolution of the display is 640H by 480V. The brightness is adjusted using the brightness control knob located at the upper left corner. As with most video displays, do not set the brightness higher than necessary. The display may be adjusted left/right and up/down in the Screen Settings function in the SYSTEM SETUP menu.

Power Button

Brightness Control

Soft Keys

Spin Knob

Key Pad

Disk Drive

Front Panel BNC Connectors

Video Display

FRONT PANEL

4-1

R S T

M N O

G H I

B C A D E F

Y Z

P U Q

V X

K L

AUTO RESERVE

AUTO GAIN

AUTO PHASE

AUTO SCALE

ALT EXP ENTER

CURSOR MAX/MIN

1 3

CURSOR SETUP

4 6

EDIT MARK

7 9

MARK

START CONT

CURSOR ACTIVE

DISPLAY

PAUSE RESET

DISK

AUX OUTPUTS

TRACE SCAN

GAIN TC

REF PHASE

SYSTEM SETUP

MATH

DISPLAY SCALE

OUTPUT OFFSET

INPUT FILTERS

HELP

MODEL SR850 DSP LOCK-IN AMPLIFIER

STANFORD RESEARCH SYSTEMS

SRS

AUTO

SYSTEM

ENTRY

CONTROL

100M /15pF

REFERENCE IN

SIGNAL IN

SINE OUT

OUTPUT

<20mA

CH1 A-ICH2 B

Ω Ω

Ω

LOCAL

is 1 MΩ AC coupled (>1 Hz) for the sine input. For

The internal oscillator output has a 50Ω output

low impedance, such as 50Ω, the amplitude will be 50Ω load).

Front Panel

The main area of the display is occupied by the output display(s). Both single and dual trace displays are available. In addition, each display can be formatted as a large numeric readout with bar graph, a polar graph, or a strip chart.

A complete description of the screen display options follows in the next section.

play zooming and scrolling use the knob as well. In these cases, the knob function is selected by the soft keys. The [CURSOR] key, which can be pressed at any time, will set the knob function to scrolling the cursor if there is a strip chart displayed.

DISK DRIVE

SOFT KEYS

The SR850 has a menu driven user interface. The 6 soft keys to the right of the video display have different functions depending upon the information displayed in the menu boxes at the right of the screen. In general, the soft keys have two uses. The first is to toggle a feature on and off or to choose between various options. The second is to highlight a parameter which is then changed using the spin knob or numeric keypad. In both cases, the soft keys select the parameters which are displayed adjacent to them.

KEYPAD

The keypad consists of five groups of keys. The ENTRY keys are used to enter numeric parameters which have been highlighted by a soft key. The MENU keys select a menu of soft keys. Pressing a menu key will change the menu boxes which are displayed next to the soft keys. Each menu presents a group of related parameters and functions. The CONTROL keys start and stop actual data acquisition, select the cursor and toggle the active display. These keys are not in a menu since they are used frequently and while displaying any menu. The SYSTEM keys print the screen to a printer and display help messages. Once again, these keys can be accessed from any menu. The AUTO keys perform auto functions and are accessible from any menu.

A complete description of the keys follows in the next section.

SPIN KNOB

The spin knob is used to adjust parameters which have been highlighted using the soft keys. Most numeric entry fields may be adjusted using the knob. Some parameters with many options, sensitivity for example, use the knob to select the desired option. In addition, functions such as dis-

The 3.5" disk drive is used to store data and instrument settings. Double sided, double density disks should be used. The disk capacity is 720k bytes formatted. The disk format is DOS compatible. Disks written by the SR850 may be read by PC compatible computers equipped with a 3.5" drive and DOS 3.0 or higher.

Only use double sided double density (DS/DD) disks. Do not use high density (DS/HD) disks.

FRONT PANEL BNC CONNECTORS

Refer to the previous section, SR850 Basics, for detailed information about each input or output.

Reference Input

The reference input can be a sine wave (rising zero crossing detected) or a TTL pulse or square wave (rising or falling edge). The input impedance

low frequencies (<1 Hz), it is necessary to use a TTL reference signal. The TTL input provides the best overall performance and should be used whenever possible.

Sine Out

impedance and varies in amplitude from 4 mVrms to 5 Vrms. The output level is specified into a high impedance load. If the output is terminated in a

less than the programmed amplitude (half for a

This output is active even when an external reference is used. In this case, the sine wave is phase locked to the reference and its amplitude is programmable.

A TTL sync output is provided on the rear panel. This output is useful for triggering scopes and other equipment at the reference frequency. The TTL sync output is a square wave derived from the

4-2

zero crossings of the sine output.

Ch1 & Ch2 Outputs

The Channel 1 and Channel 2 outputs can be configured to output a voltage from -10 V to +10 V proportional to X, Y, R, θ, or Traces 1 through 4. ±10 V is full scale. The outputs can source 10 mA maximum.

Signal Inputs

The input mode may be single-ended, A, or differential, A-B. The A and B inputs are voltage inputs with 10 MΩ, 25 pF input impedance. Their connector shields are isolated from the chassis by 10 Ω (Ground) or 1 kΩ (Float). Do not apply more than 50 V to either input. The shields should never exceed 1 V. The I (current) input is 1 kΩ to a virtual ground.

Front Panel

4-3

Front Panel

4-4

Lock-in Parameters

Trace 1

Stop

Soft Keys

Sensitivity and

Dynamic Reserve

Time Constant

and Slope

Input configuration

and signal filters

Bottom Display

SCREEN DISPLAY

DEFAULT DISPLAY

The SR850's default display is shown above. This is the display format in effect when the unit is turned on.

This screen resembles a "normal" lock-in front panel. The lock-in setup is displayed across the top of the screen. The sensitivity, reserve, time constant, prefilters and input configuration are all easily visible. The upper numeric readout and bar graph show the value of X (Rcosθ) and the lower graph shows the value of Y (Rsinθ).

The bar graphs are normally scaled so that plus full scale is at the right end, minus full scale is at

the left end, and zero is in the middle. Whenever the sensitivity is changed, the bar graphs are scaled to the full scale sensitivity. The [AUTO SCALE] key will scale the active display to the actual measured signal (the center remains zero). The range and center of a bar graph may be manually adjusted to expand a portion of the scale.

Status indicators are displayed across the bottom of the screen. These include the reference mode, unlock alert, reference frequency, harmonic detect, overloads, and GPIB/RS232 activity, error and remote status.

Soft Key Definitions.

Pressing the corresponding

soft key will either highlight a

field or select an option.

Top

Display

Full Scale = 10 mV Dyn Reserve = 0 dB

100 mS

12 dB/oct Line 2xLin AC A

X = 9.7284 mV

± 10.000 e-3 0.0 V

Trace 2

Y =-1.2050 mV

± 10.000 e-3 0.0 V

Intrnl

Fr= 100.00 Hz Harmonic= 1 LOCLOCK

Syncro

Sensitivity

10 mV f.s.

60 dB gain

Reserve

Max

Time Constant

Filter dB/oct.

6 12

18 24

Synchronous

Off

< 200Hz

Min

Manual

100 mS

1.2 Hz

Status and

activity

indicators

4-5

Screen Display

DATA TRACES

The SR850 collects and displays data in the form of traces. There are four data traces which may be defined. Each trace is defined as A•B/C where the parameters A, B, and C are chosen from X, Y, R,

, Xnoise, Ynoise, Rnoise, Aux Inputs 1-4, Frequency, and unity (1). C can also be any quantity squared. The traces are defined in the TRACE/ SCAN menu.

Only data traces may be displayed.

In order to display the quantity X, it is necessary to define a trace to be X and then choose to display that trace.

When the unit is reset, the traces are defined as follows:

Trace 1

Trace 2

Trace 3

Trace 4

where B and C are set to unity in each case.

In most cases, the default trace definitions will suffice. For specialized situations, the traces may be redefined to fit the experiment. Some examples:

Trace 3

R/AI1

Magnitude/Aux Input 1. This normalizes the magnitude to an external slowly varying signal. (detector output normalized to laser power for instance.)

Trace 4

Xnoise. The SR850 calculates the rms noise of X in the bandwidth determined by the time constant.

Trace 3

AI3

Aux Input 3. Store and display the value of Aux Input 3. The SR850 can monitor an external voltage while recording normal lock-in quantities such as X, Y, R or θ.

Trace 4

Frequency. Store the reference frequency along with the X, Y, R or θ.

4-6

Trace 2

Stop

SINGLE and DUAL TRACE DISPLAYS

The screen can be formatted as a single trace (Single) display or a dual trace (Up/Down) display. The screen format is selected in the DISPLAY/ SCALE menu. There are three displays which may be configured, the Single screen display and the Top and Bottom displays for the split screen. Each display can show a different trace using a separate display type.

There are three different display types - Bar (with large numbers), Polar, and Chart (of stored traces only). The Bar graph resembles a "normal" lock-in display. The Polar graph plots X and Y on a circular graph to illustrate the signal as a vector relative to the reference. The Chart displays stored data in a strip chart form, complete with zooming, panning and cursor. In order to use the analysis functions such as curve fitting, the data must be stored in the buffer and displayed in a strip chart.

The default screen (pg. 4-5) is a dual trace display where the top display shows Trace 1 (X) and the bottom display shows Trace 2 (Y). Both displays are bar graphs.

Remember, only data traces may be displayed.

The traces are defined in the TRACE/SCAN menu. The choices of which traces are displayed, and in which formats, are selected in the DISPLAY/SCALE menu.

A dual trace screen showing both Bar and Chart displays is shown below. Each display is labelled with a trace identifier indicating which trace is being displayed. The trace definition is also shown. In the screen below, the top display is showing Trace 1 which is defined to be X.

One of the displays is the active display. The active display is denoted by displaying the trace identifier in inverse video (bottom display below). Certain functions, such Auto Scale and cursor movement, affect the active display only. The [ACTIVE DISPLAY] key is used to switch the active display between the top and bottom displays. A full screen display is always the active display.

Screen Display

Top display trace

identifier and trace

definition.

Bottom display trace

identifier and trace

definition. Shown in

inverse to indicate the

active display.

Full Scale = 10 mV Dyn Reserve = 0 dB

Trace 1

100 mS

12 dB/oct Line 2xLin AC A

Syncro

X = 9.7284 mV

± 10.000 e-3 0.0 V

10 S /div 0.000 S

center = 0.0 ± 50.00 e-3 V

Fr= 100.00 HzIntrnl Harmonic= 1 LOCLOCK

36.000 S 58.332 e-3

Format

Single Up/Down

Monitor

Settings

Input/Output

Display Scale

Full Top

Bottom

Type: Chart Trace: 2

50.0 e-3

@ 0.0

10 S /div

4-7

Screen Display

4-8

ExpdOffst

Screen Display

BAR GRAPHS

The most commonly used display type is the Bar graph with large numeric readout. This display most closely resembles a "normal" lock-in. The bar graph display is shown below. The bar graph only occupies half of the screen, even when the screen format is full height. Thus, it generally makes sense to use the bar graph in split screen mode and show two bar graphs.

Trace Identifier Trace Definition

Trace 1

X = 9.7284 mV

Full scale range

Trace Identifier and Active Display

The bar graph is labelled with a trace identifier above it. This indicates which trace is being displayed. The trace definition is shown next to the identifier. If this display is the active display, the trace identifier will be in inverse. When a bar graph is the active display, the [AUTO SCALE] key will scale the bar graph. There is no cursor function for this display. Pressing the [CURSOR] key will not activate a cursor.

± 10.000 e-3 0.0 V

Trace Offset and Expand Indicators

Center value and Trace Units

graph to expand a portion of the full scale range around a nominal value. The bar will always be drawn from the center (nominal value).

For the simple traces, X, Y, and R, changing the sensitivity will automatically scale the bar graphs so the range is equal to the sensitivity and zero is at the center. For other trace definitions, the bar scaling is not changed when the sensitivity is changed.

When the trace definition is simple (X, Y, R, θ or F) the trace definition is displayed in the large numeric readout (X=). If the trace is defined as Xn, Yn, Rn, AI1, AI2, AI3 or AI4, or involves a product or ratio (A•B/C where either B or C or both are nonunity), then the large readout simply shows 'T1=' (for Trace 1) instead of the actual parameter(s) being monitored. The trace definition above the readout is always displayed fully however.

Bar Range and Center

The graph range and center value are displayed below the graph. These values are in the units of the displayed trace.

Bar Scaling

The bar graph scaling can be changed in the DISPLAY/SCALE menu. Both the center value and the range can be changed. This allows the bar

Using [AUTO SCALE] will adjust the range to make the measured output greater than 40% of the new range. [AUTO SCALE] always returns the center to zero.

Rate

The bar graph is updated at a rate of about 7 Hz while the numeric readout changes at about 2 Hz. When the data is noisy, the bar graph more accurately shows the "noisiness" while with steady readings, the numeric display is an accurate measure of the signal.

Offset and Expand

If the trace being shown is affected by a non-zero offset or a non-unity expand, then the Offst and Expd alert indicators are turned on.

4-9

ExpdOffst

and the resultant vector exceed full scale by √2 (at

Screen Display

POLAR GRAPHS

The polar graph is a convenient way to view magnitude and phase. The signal is represented as a vector on an X-Y coordinate axes. The full screen polar display is shown below. The split screen polar graph is half as big.

Y Axis (90°)

Signal Vector

X Axis (0°)

Trace Offset and Expand Indicators

Plot of X and Y

The polar graph is not labelled - there is no trace identifier above it. This is because the polar graph always plots X and Y as a vector. This display cannot be changed to display any other traces. Changes made to X and Y, such as offsets, will change the vector on the polar graph. Changes made to R, such as offset, will not.

The [ACTIVE DISPLAY] key will not select this display since there is no cursor associated with it and it cannot be autoscaled.

Scale

The graph is oriented like a normal X-Y axes. Positive X is to the right and positive Y is up, and zero is in the center. The four circles indicate 25%, 50%, 75% and 100% of full scale. The polar graph is always scaled to the full scale sensitivity. Note that X and Y can both be full scale in amplitude

Signal Vector

Coherent signals have a steady phase and the signal vector will have a steady direction. Signals which are noisy will move around in direction as well as magnitude. The polar display can quickly give a feeling for whether a signal is coherent or not. Signals whose frequencies are close to, but not synchronous with the reference frequency will to rotate at the difference frequency between the signal and reference.

Offset and Expand

If the either X or Y has a non-zero offset or a nonunity expand, then the Offst and Expd alert indicators are turned on. The vector is plots the offset and expanded quantities X and Y. If X and Y have unequal expands (differing gains), the signal vector is generally not meaningful.

45°).

4-10

Trace 2

ExpdOffst

Screen Display

STRIP CHARTS

Chart displays are used to view stored traces. Only stored traces have a time history, thus, only stored traces may be displayed on a chart. The full screen chart display is shown below. If the split screen format is used, the chart will display half as many vertical divisions but will be the same as the full size display in all other aspects.

Trace Identifier Trace Definition Cursor Readout

Y 36.000 S 58.332 e-3

Trace Offset and Expand Indicators

Trace Identifier and Active Display

The chart is labelled with a trace identifier at the upper left. This indicates which trace is being displayed. The trace definition is shown next to the identifier. If this display is the active display, the trace identifier will be in inverse. When a chart is the active display, the [AUTO SCALE] key will scale the chart so all of the displayed data is on the graph. In addition, when a chart is the active display, pressing the [CURSOR] key will activate the cursor.

Chart Scaling

The graph vertical range is the center value plus and minus the range. The center value is the value of a data point located at the vertical midpoint of the graph. The horizontal scale is the number of seconds per division across the graph. The time value of the right most point is shown at the bottom right. When the most recent point is at the right, the time shown will be 0.000 S.

center = 0.0 ± 50.00 e-3 V

center value

10 S /div

Vertical rangeVertical

Cursor region is

defined by heavy

dashed lines

Cursor is located at

the Min, Max, or

Mean of the data

within the cursor

region

0.000 S

Horizontal scale

The chart scaling can be changed in the DISPLAY/SCALE menu. Both the vertical scale (center value and range) and horizontal scale can be changed. [AUTO SCALE] will automatically adjust the vertical center and range to display all of the data within the graph. [AUTO SCALE] will not change the horizontal scale.

By changing the horizontal scale, the entire trace buffer can be displayed at once or a small portion may be expanded. If only a portion of the buffer is being displayed, use the cursor to pan right and left within the buffer.

Offset and Expand

If the trace being shown is affected by a non-zero offset or a non-unity expand, then the Offst and Expd alert indicators are turned on.

Time value of

right most point

4-11

Screen Display

Data Scrolling

The chart display acts like a strip chart recorder where the pen is drawing the most recent data. For example, if the sample rate is 1 Hz (1 point taken per second) and the horizontal scale is 10 S/div, then the graph displays 100 data points (10 divisions x 10 points per division). As new data is taken, the old data scrolls to the left at the rate of 10 S/div. This is because new points are added at a fixed location (right edge of the graph) just like a strip recorder. In this case, the time value of the right most point is 0.000 S meaning the most recent data point.

The chart displays a fixed window in time which is 10 divisions wide (100 seconds in this case) starting Tright seconds ago (where Tright is the time value of the right most point). Since the data is always getting older, it scrolls left continuously (whenever data is being taken).

Cursor

The cursor region is the graph region between the two heavy vertical dashed lines. The cursor region may be set to 1 division (wide), 1/2 division (norm), or a single vertical line (spot). The cursor region does not change with horizontal scaling. The cursor is the small square which seeks the minimum, maximum, or mean of the data within the cursor region. When seeking min or max, the cursor is located at the position of the data point which is the min or max. This allows peaks and valleys in the data to be easily specified. When seeking the mean, the X position of the cursor is at the center of the cursor region and the Y position is the mean of the data within the region. The cursor type is defined in the CURSOR SETUP menu.

play. Use the [ACTIVE DISPLAY] key to select the desired display (top or bottom). When the cursor readout is surrounded by this box, the knob adjusts the position of the cursor region. Moving the cursor beyond the edge of the graph pans the display left (showing older data points) and right (showing more recent data points). Remember, the time window shown in the graph does not change with time. As the data points get older, the data will scroll to the left as new points are taken.

Cursor Display

The cursor readout displays the horizontal position and the trace data at the cursor. The horizontal position is displayed as time (from the beginning of the trace), delay (time from the most recent point), bin (number of data points since the start), and frequency (if the reference is internally swept). In this illustration, the cursor point was taken 36 seconds before the most recent point.

Marks

While data is being added to the data buffer, events may be marked using the [MARK] key. Pressing [MARK] will tag the next trace buffer location. A mark will appear on the chart and will scroll with the data. This is analogous to marking a real strip chart while it is recording. Marks are useful for marking when an external event occurred or when the experimental conditions changed.

A maximum of eight marks may be placed in the data buffer. A mark will appear on ALL stored traces at the same buffer location. The different

Often the display is scaled such that there are many more data points than can be resolved on the display. The chart display is 496 pixels wide. If more than that number of data points are being displayed, then each horizontal position represents multiple data points. In this case, a vertical line is drawn between the minimum and maximum data points represented by a single horizontal location. In this case, even the spot cursor region represents multiple data points. The cursor will seek the max, min or mean of these data points.

Pressing the [CURSOR] key will draw a box around the cursor readout of the active chart dis-

mark symbols are shown below. A mark is always placed at the buffer start to mark the oldest (first) data point at the start of a scan.

The [EDIT MARK] key allows the mark data to be viewed. The value of each stored trace and the time the mark was placed is displayed. The user can add comments to the mark data to label a specific event.

When trace data is saved to disk, the marks are saved as well. When a trace is recalled from disk, the marks are recalled as well. Existing marks are replaced with the recalled marks.

4-12

TRACE SCANS, SWEEPS & ALIASING

Trace and Scan parameters are selected in the TRACE/SCAN menu.

Trace Storage

Having defined up to four data traces for an experiment, the issue of data storage needs to be addressed.

Only traces that are stored may be

displayed in strip chart form.

If a graph or record of a trace over time is desired, then that trace's data must be stored. The SR850 can record up to 64000 data points in memory. The data buffer can store 64000 points of a single trace, 32000 points of two traces, or 16000 points of all four traces. When defining the traces, the Store or Do Not Store option needs to be decided. The default is all four traces stored.

Data Points and Bins

Data points stored in a trace are sometimes referred to by their bin position within the trace buffer. The oldest data point is bin0, the next point is bin1, etc. A trace with N points numbers them from 0 to N-1.

Sample Rate

The Sample Rate can be varied from 512 Hz down to 62.5 mHz (1 point every 16 sec). The sample rate sets how often points are added to the storage buffers. All stored traces are sampled at the same rate (and at the same times).

In addition to the internal sample rates, samples can be triggered by an external TTL trigger. This mode is selected by increasing the sample rate past 512 Hz. In this mode, a sample is recorded within 2 ms of a rising edge trigger on the rear panel Trigger input. Triggers which occur faster than 512 Hz are ignored. When viewing an externally triggered data trace on a chart graph, set the cursor readout to Bin (in the CURSOR SETUP menu). This displays the horizontal position of the cursor as bin or data point number rather than time (for scaling purposes, the time scale of the graph is based upon a 1 Hz sample rate - bins and seconds are equivalent).

Scan Length

The Scan Length is the time duration of a single scan expressed in seconds. The maximum scan length is determined by the number of stored traces (maximum storage buffer length) and the

sample rate. When storing a single trace, the maximum scan length is 125 seconds at 512 Hz or 12 days at 62.5 mHz (64000 points). Changing the sample rate will only change the scan length if the maximum number of data points is already being used. Otherwise, the number of data points in the scan is changed to keep the scan length constant. The number of points in the buffer can vary from 1 to a maximum of 16000, 32000, or 64000 depending upon the number of traces being stored.

There is only one Scan Length, i.e. the number of points stored will be the same for all traces being stored.

Sweep Time

The scan length is the sweep time for frequency sweeps and Aux Output sweeps. Swept parameters are synchronized with the data acquisition. For example, if the internal reference is programmed to sweep from 1 kHz to 2 kHz, the sweep will take a scan length to finish. The frequency will change once per stored point. Thus, if the sample rate is 1 Hz and the scan length is 100 seconds, the frequency will change 100 times and move from 1 kHz to 2 kHz in 100 seconds. At each sample, the trace data is stored before the swept parameter is changed. The next data point is taken after one sample interval to allow the outputs to settle as long as possible.

End of Scan

When the scan is complete, data storage can stop or continue.

The first case is called 1 Shot (data points are stored for a single Scan Length). At the end of the scan, data acquisition stops and swept parameters are held at their final stop values.

The second case is called Loop. In this case, a new scan is started at the end of each scan. Scans repeat indefinitely until halted by the user. The data buffer will store as many points as possible (16000, 32000 or 64000 depending upon the number of stored traces). The buffer will start filling at the start and will hold as many scans as will fit. The buffer always holds at least one complete scan. If the scan is short, then the buffer will hold multiple scans of data. When the buffer end is reached, the buffer starts filling at the beginning

Screen Display

4-13

again. The oldest data will be overwritten and lost. This looping continues indefinitely. In this mode, the scan length is only meaningful is parameters are being swept. Once the trace buffer has looped around, the oldest point (at any time) is at bin#0 and the most recent point is at bin#k where k is the buffer length (minus 1).

The default mode is Loop.

Default Scan

Upon reset, all four traces are stored for a maximum of 16000 points. The sample rate is 1 Hz, the scan length is 16000 seconds and the scan mode is Loop. The trace definitions are X, Y, R and θ for Traces 1-4.

Starting and Stopping a Scan

The [START/CONT] and [PAUSE/RESET] keys are used to control data acquisition. Basically, the [START/CONT] key starts a scan or continues a paused scan and the [PAUSE/RESET] key pauses a scan or resets a finished scan. See the discussion of keypad operation later in this section for details. Scans can also be controlled via the computer interfaces. See the programming section for an explanation.

In addition, the rear panel Trigger input can be used to start a scan. To select this mode, set the Trigger Starts option in the AUX menu. In this mode, a rising TTL trigger will act the same as the [START/CONT] key. The sample rate can be either internal or Triggered. In the first case, the trigger starts the scan and data is sampled at the programmed sample rate (up to 512 Hz). In the latter case, the first trigger will start the scan and data will be sampled at every subsequent trigger.

Aliasing Effects

In any sampled data stream, it is possible to sample a high frequency signal such that it will appear to be a much lower frequency. This is called aliasing.

For example, suppose the lock-in is detecting a signal near 1 Hz with a relatively short time constant. The X output will have a DC component and a 2 Hz component (2xf). If the sample rate is 2 Hz,

then the samples may be taken as illustrated below.

The samples represent a sine wave much slower than 2 Hz that isn't actually present in the output! The chart display of this trace will show a sine wave at a very low frequency and will be rather misleading. In this case, a much higher sampling rate will solve the problem.

Aliasing occurs whenever the output signal being sampled contains signals at frequencies greater than 1/2 the sample rate.

The effect is most noticeable when trying to sample an output frequency at an integer multiple of the sample rate (as above). The above aliasing problem will be the same for a 1 kHz output (500 times the sample rate) as for the 2 Hz output.

Generally, the highest possible sample rate should be used given the desired scan length and number of stored traces. The lock-in time constant and filter slope should be chosen to attenuate signals at frequencies higher than 1/2 the sample rate as much as possible.

Aliasing can occur with the polar and bar graph displays as well. These displays sample the output signal at a fixed rate.

Screen Display

1 second

4-14

SETTINGS & INPUT/OUTPUT MONITOR

Syncro DigPll

Band Pass 100.0 Hz

X= 135.23 mV Y= 22.78 mV

R= 137.14 mV A1= 0.000 V

A2= 0.000 V

A3= 0.000 V A4= 0.000 V

= 9.56 °θ

The upper two lines of the screen are the monitor display (see the screen on pg. 4-5). The lock-in settings (sensitivity, time constant, etc.) or the lock-in signal measurements (X, Y, R, θ, and the Aux Inputs) may be monitored. Use the DISPLAY menu to select the type of monitor (Settings or Input/Output).

Screen Display

MENU DISPLAY

The Soft Key menu boxes define the functions of the 6 soft keys to the right of the screen. The menu boxes are grouped into menus. Pressing each of the ten Menu keys will display a different menu of boxes. Related functions are grouped into a single menu.

Full Scale = 10 mV Dyn Reserve = 40 dB

100 mS

12 dB/oct Line 2xLin AC A

The Settings Monitor is shown above. The sensitivity, dynamic reserve, time constant and roll-off are always displayed. When the synchronous output filter is selected AND the detection frequency is below 200 Hz, then Syncro will be displayed. If the detection frequency is above 200 Hz, synchronous filtering is not active and Syncro is not displayed. When the external reference is below 10 Hz, the digital phase lock loop is active and DigPll is displayed.

The input filters are shown when they are in, their display boxes are empty when the corresponding filter is out. The input coupling and type (A, A-B, or I) are always shown.

The Input/Output Monitor is shown above. The values of X, Y, R and θ are shown, regardless of the trace definitions or displays chosen. In addition, the readings of the rear panel Aux Inputs are displayed. These readings are updated a few times a second.

In general, pressing a soft key does one of two things. One is to toggle between 2 or 3 specific options. An example is the Filter Slope box illustrated on page 4-5. Pressing the fourth soft key toggles the slope from 6 to 12 to 18 to 24 and back to 6 dB/oct.

The second soft key mode is to highlight an entry field and knob function. An example would be the Phase Adjust. Pressing this soft key will highlight the phase setting. The phase may then be adjusted with the knob or entered as a value using the numeric entry keys. Each menu is described at length in a following section.

4-15

(1MΩ gain) or 100 nA DC or 14 nA AC (100MΩ

ALT

UNLOCK

OUTPT

FILTR

Run

RESRV

SRQ

Harmonic= 1

LOC

TRIG

ERR

Screen Display

STATUS INDICATORS

Fr= 100.00 HzExt S

GPIB

There are a number of status indicators which are displayed at the bottom of the screen. These include the scan, unlock, and overload indicators, the reference frequency and source, and interface status.

Stop • Run 1 • Run • Pause • Done

When the data buffers are reset (pressing [PAUSE RESET] while paused or done), then Stop will be indicated.

When a scan is in progress in the 1 Shot mode, Run 1 is indicated. The storage of trace data in the buffer continues until the scan is complete at which time Done is displayed.

If a Loop scan is in progress, Run is displayed. The storage of trace data in the buffer may continues indefinitely. When the buffer fills, the oldest data is written over.

If the scan is paused (with the [PAUSE/RESET] key for instance), then the Pause indicator will be on. Pressing [START/CONT] will continue the scan from a paused state.

RESRV • INPUT

If the analog signal amplifier overloads before the phase sensitive detector, then RESRV or INPUT is displayed.

RESRV indicates that the signal amplifier is overloaded. Change the sensitivity or increase the dynamic reserve.

INPUT indicates that the actual signal input is overloaded. This occurs for voltage inputs greater than 1.4Vpk (unless removed by AC coupling) or current inputs greater than 10 µA DC or 1.4 µA AC

gain). Reduce the input signal level.

FILTR

If an overload occurs in the low pass filters after the PSD's, then FILTR is displayed. Increase the time constant or filter roll-off or decrease the dynamic reserve.

OUTPT

If the output (either X, Y, R or a trace output voltage) is greater than 1.09 times full scale, then OUTPT is displayed. This can occur if the sensitivity is too low or if the output is expanded such that the output voltage exceeds 10 V. Note that a trace output can overload even if it is not being displayed on the screen or output to CH1 or CH2.

Intrnl • Sweep • Ext S • Ext + • Ext -

If the internal reference is being used, then Intrnl is displayed. If the internal reference frequency is being swept, then Sweep is displayed. When using an external reference source, the reference mode may be set to Sine (Ext S), Rising TTL edge (Ext +), or Falling TTL edge (Ext -).

LOCK • UNLOCK

The UNLOCK indicator turns on if the SR850 can not lock to the external reference. LOCK is displayed when the SR850 is successfully locked to the reference. LOCK is always on when in internal reference mode.

Fr= XX.YYY Hz

The reference frequency (internal or external) is displayed continuously.

Harmonic = N

The SR850 can detect synchronous signals at N times the reference frequency. Generally, N is equal to 1.

GPIB • RS232

Flashes when there is activity on the computer interfaces. This does not flash for printer or plotter activity.

ERR

Flashes whenever there is a computer interface error such as an illegal command or out of range parameter is received. This does not flash for a printer or plotter error.

LOC • REM

REM is on when the front panel is locked out by a computer interface. No front panel adjustments may be made. To return the unit to local control (if

4-16

allowed), press the [HELP] key. LOC is on whenever local front panel control is allowed (usually on).

SRQ

This indicator is on whenever a GPIB Service Request is generated by the SR850. SRQ stays on until a serial poll is completed.

ALT

Indicates that the ALTERNATE keypad is in use. The ALTERNATE keypad uses the alphabetic legends printed below each key. To enter the ALT mode, press the [ALT] key once. Pressing the keys will now enter letters into the active entry field. The [0]...[9], [.], [-], [←] and [ALT] have the same function in the ALTERNATE keypad. To return to the normal keypad, press the [ALT] key again.

Screen Display

4-17

Screen Display

4-18

R S T

M N O

G H I

B C A D E F

Y Z

V X

K L

AUTO RESERVE

AUTO GAIN

AUTO PHASE

AUTO SCALE

ALT EXP ENTER

CURSOR MAX/MIN

1 3

CURSOR SETUP

4 6

EDIT MARK

7 9

MARK

START CONT

CURSOR ACTIVE

DISPLAY

PAUSE RESET

DISK

AUX OUTPUTS

TRACE SCAN

GAIN TC

REF PHASE

SYSTEM SETUP

MATH

DISPLAY SCALE

OUTPUT OFFSET

INPUT FILTERS

HELP

AUTO

SYSTEM

ENTRY

CONTROL

LOCAL

KEYPAD

NORMAL AND ALTERNATE KEYS

The normal key definitions are printed on each key. In addition, each key also has an alternate definition printed below it. The [ALT] key toggles the keypad between the two definitions. The ALT screen indicator is on when the alternate definitions are in use. The [0]...[9], [.], [-], [←] and [ALT] keys have the same definition in both modes. The alternate keys should only be used when accessing files on the disk drive or entering labels.

MENU KEYS

All operating parameters of the SR850 are grouped into function menus. The ten menu keys select which menu of parameters is displayed next to the six soft keys. The soft keys then either toggle a parameter, highlight a parameter entry field (for numeric entry or knob adjustment), or display a submenu. These menus are listed below.

[REF/PHASE]

Sets the reference source and phase shift. Also sets the internal oscillator frequency, sweep limits and output level.

[INPUT/FILTERS]

Configures the signal inputs and selects the notch prefilters.

[GAIN/TC]

Select the full scale sensitivity, dynamic reserve,

4-19

time constant and roll-off.

[OUTPUT/OFFSET]

Configures the Channel 1 and 2 front panel outputs and sets the X, Y and R output offsets and output expands.

[TRACE/SCAN]

Define the four data traces, the scan length and sample rate.

Stanford Research Systems SR850 User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual