LINEAR TECHNOLOGY LTC1966, LTC1967, LTC1968 Technical data

Application Note 106

February 2007

Instrumentation Circuitry Using RMS-to-DC Converters

RMS Converters Rectify Average Results

Jim Williams

INTRODUCTION

It is widely acknowledged that RMS (Root of the Mean
of the Square) measurement of waveforms furnishes

1

the most accurate amplitude information.

Rectify-and­average schemes, usually calibrated to a sine wave, are
only accurate for one waveshape. Departures from this
waveshape result in pronounced errors. Although accurate,
RMS conversion often entails limited bandwidth, restricted
range, complexity and diffi cult to characterize dynamic
and static errors. Recent developments address these
issues while simultaneously improving accuracy. Figure 1

®

shows the LTC

1966/LTC1967/LTC1968 device family. Low
frequency accuracy, including linearity and gain error, is
inside 0.5% with 1% error at bandwidths extending to
500kHz. These converters employ a sigma-delta based
computational scheme to achieve their performance.

2

Figure 2’s pinout descriptions and basic circuits reveal an
easily applied device. An output fi lter capacitor is all that is
required to form a functional RMS-to-DC converter. Split
and single supply powered variants are shown. Such ease
of implementation invites a broad range of application;
examples begin with Figure 3.

Isolated Power Line Monitor

BEFORE PROCEEDING ANY FURTHER, THE READER
IS WARNED THAT CAUTION MUST BE USED IN THE
CONSTRUCTION, TESTING AND USE OF THIS CIRCUIT.
HIGH VOLTAGE, LETHAL POTENTIALS ARE PRESENT IN
THIS CIRCUIT. EXTREME CAUTION MUST BE USED IN
WORKING WITH, AND MAKING CONNECTIONS TO, THIS
CIRCUIT. REPEAT: THIS CIRCUIT CONTAINS DANGER­OUS, HIGH VOLTAGE POTENTIALS. USE CAUTION.

Figure 3’s AC power line monitor has 0.5% accuracy over
a sensed 90VAC to 130VAC input and provides a safe, fully
isolated output. RMS conversion provides accurate report­ing of AC line voltage regardless of waveform distortion,
which is common.

, LT, LTC and LTM are registered trademarks of Linear Technology Corporation.
All other trademarks are the property of their respective owners.

1

See Appendix A, “RMS-to-DC Conversion” for complete discussion of

RMS measurement.

2

Appendix A details sigma-delta based RMS-to-DC converter operation.

LINEARITY

PART NUMBER

LTC1966 0.02/0.15 0.1/0.3 6 800 2.7 ±5 170
LTC1967 0.02/0.15 0.1/0.3 200 4MHz 4.5 5.5 390
LTC1968 0.02/0.15 0.1/0.3 500 15MHz 4.5 5.5 2.3mA

Figure 1. Primary Differences in RMS to DC Converter Family are Bandwidth and Supply Requirements.
All Devices Have Rail-to-Rail Differential Inputs and Output

ERROR

TYP/MAX (%)

CONVERSION

GAIN ERROR

TYP/MAX (%)

1% ERROR

BANDWIDTH

(kHz)

3dB ERROR

BANDWIDTH

(kHz)

SUPPLY VOLTAGE I

MIN(V) MAX(V)

AN106-1

SUPPLY

MAX (µA)

an106f

Application Note 106

POSITIVE SUPPLY

2.7V TO 5.5V

DEPENDING ON DEVICE CHOICE

DIFFERENTIAL

MAX COMMON MODE

INPUTS.

RANGE = ±V SUPPLY.

MAX DIFFERENTIAL = 1V.

MINIMUM INPUT = 5mV

INPUT 1

INPUT 2

±5V Supplies, Differential, DC-Coupled

RMS-to-DC Converter

5V

V

DD

DC + AC

INPUTS

(1V

DIFFERENTIAL)

PEAK

LTC1966

IN1

IN2

SS

–5V

V

OUT RTN

GND ENV

OUT

Figure 2. RMS Converter Pin Functions (Top) and Basic Circuits (Bottom).
Pin Descriptions are Common to All Devices, with Minor Differences

SET HIGH TO
SHUT DOWN

C

AVE

1µF

LTC1966
LTC1967
LTC1968

LTC1966 ONLY.

0V TO –5V

SUPPLY

DC OUTPUT

= 85kΩ

Z

O

+V

–V*ENABLE

DIFFERENTIAL)

OUTPUT OUTPUT

OUTPUT RETURN

GND

POWER

GROUND

OUTPUT TO FILTER CAPACITOR

OUTPUT REFERRED
TO THIS PIN.
NORMALLY GROUNDED

*NO –V PIN ON THE LTC1967/LTC1968

5V Single Supply, Differential, AC-Coupled

RMS-to-DC Converter

5V

V

DD

AC INPUTS

(1V

PEAK

0.1µF

LTC1966

V

IN1

IN2

C

C

SS

OUT RTN

GND ENV

OUT

AN106 F02

C
1µF

AVE

DC OUTPUT

= 85kΩ

Z

O

LINE INPUT

90VAC

TO 140VAC

T1

145

BIAS SUPPLY

100Ω

A

1W

6

ISOLATED LINE SENSE

7

B

1k

8

120VAC

TRIM

T1 = TAMURA-PAN MAG 3FS-212

*1% METAL FILM RESISTOR
1µF = WIMA MKS-2

1k

100µF

+

1k

+

100µF

100Ω
1W

0.25%

100Ω

10Ω

0.25%

= 1N4148

= 1N4689 5.1V

–5V

5V

DANGER! Lethal Potentials Present—See Text

5V –5V

+V –V

IN1 OUT

IN2

EN GND

C1

LTC1966

OUT RTN

RMS CONVERTER

1µF

+

A1

®

1006

LT

–

RMS OUT

0.9V TO 1.4V =
90VAC TO 140VAC

100k*

100k*

AN106 F03

Figure 3. Isolated Power Line Monitor Senses Via Transformer with 0.5% Accuracy Over 90VAC to 130VAC Input.
Secondary Loading Optimizes Transformer Voltage Conversion Linearity

AN106-2

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Application Note 106

The AC line voltage is divided down by T1’s ratio. An isolated
and reduced potential appears across T1’s secondary B,
where it is resistively scaled and presented to C1’s input.
Power for C1 comes from T1’s secondary A, which is
rectifi ed, fi ltered and zener regulated to DC. A1 takes gain
and provides a numerically convenient output. Accuracy
is increased by biasing T1 to an optimal loading point,
facilitated by the relatively low resistance divider values.
Similarly, although C1 and A1 are capable of single supply
operation, split supplies maintain symmetrical T1 loading.
The circuit is calibrated by adjusting the 1k trim for 1.20V
output with the AC line set at 120VAC. This adjustment is
made using a variable AC line transformer and a well fl oated
(use a line isolation transformer) RMS voltmeter.

F

igure 4’s error plot shows 0.5% accuracy from 90VAC

3

to 130VAC, degrading to 1.4% at 140VAC. The benefi cial
effect of trimming at 120VAC is clearly evident; trim­ming at full scale would result in larger overall error,
primarily due to non-ideal transformer behavior. Note
that the data is specifi c to the transformer specifi ed.
Substitution for T1 necessitates circuit value changes
and recharacterization.

2.0

1.5

1.0

0.5
120VAC TRIM POINT

0

–0.5

–1.0

RMS OUTPUT READING ERROR (%)

–1.5

–2.0

90 100 120

Figure 4. Error Plot for Isolated Line Monitor Shows 0.5%
Accuracy from 90VAC to 130VAC, Degrading to 1.4% at 140VAC.
Transformer Parasitics Account for Almost All Error

110

RMS INPUT VOLTAGE (V)

130 140

AN106 F04

Fully Isolated 2500V Breakdown,
Wideband RMS-to-DC Converter

NOTE: BEFORE PROCEEDING ANY FURTHER, THE
READER IS WARNED THAT CAUTION MUST BE USED
IN THE CONSTRUCTION, TESTING AND USE OF THIS
CIRCUIT. HIGH VOLTAGE, LETHAL POTENTIALS ARE
PRESENT IN THIS CIRCUIT. EXTREME CAUTION MUST
BE USED IN WORKING WITH, AND MAKING CON­NECTIONS TO, THIS CIRCUIT. REPEAT: THIS CIRCUIT
CONTAINS DANGEROUS, HIGH VOLTAGE POTENTIALS.
USE CAUTION.

Accurate RMS amplitude measurement of SCR chopped
AC line related waveforms is a common requirement. This
measurement is complicated by the SCR’s fast switching
of a sine wave, introducing odd waveshapes with high
frequency harmonic content. Figure 5’s conceptual SCR­based AC/DC converter is typical. The SCRs alternately
chop the 220VAC line, responding to a loop enforced,
phase modulated trigger to maintain a DC output. Figure
6’s waveforms are representative of operation. Trace A is
one AC line phase, trace B the SCR cathodes. The SCR’s
irregularly shaped waveform contains DC and high fre­quency harmonic, requiring wideband RMS conversion
for measurement. Additionally, for safety and system
interface considerations, the measurement must be fully
isolated.

3

See Appendix B, “AC Measurement and Signal Handling Practice,” for
recommendations on RMS voltmeters and other AC measurement related
gossip.

DANGER! Lethal Potentials Present—See Text

220VAC

INPUT

NEUTRAL

220VAC

AC LINE SYNC

AND PHASE

MODULATION

TRIGGER

DC

OUTPUT

AN106 F05

REF

Figure 5. Conceptual AC/DC Converter is Typical of SCR-Based
Confi gurations. Feedback Directed, AC Line Synchronized
Trigger Phase Modulates SCR Turn-On, Controlling DC Output

an106f

AN106-3

Application Note 106

A = 100V/DIV

B = 50V/DIV

ON 170 VDC

LEVEL

1ms/DIV

Figure 6. Typical SCR-Based Converter Waveforms Taken at AC
Line (Trace A) and SCR Cathodes (Trace B). SCR’s Irregularly
Shaped Waveform Contains DC and High Frequency Harmonic,
Requiring Wideband RMS Converter for Measurement

AN106 F06

Figure 7 provides isolated power and data output paths to
an RMS-to-DC converter, permitting safe, wideband, digital
output RMS measurement. A pulse generator confi gured
comparator combines with Q1 and Q2 to drive T1, resulting
in isolated 5V power at T1’s rectifi ed, fi ltered and zener
regulated output. The RMS-to-DC converter senses either
135VAC or 270VAC full-scale inputs via a resistive divider.
The converter’s DC output feeds a self-clocked, serially
interfaced A/D converter; optocouplers convey output data
across the isolation barrier. The LTC6650 provides a 1V
reference to the A/D and biases the RMS-to-DC converter’s
inputs to accommodate the voltage divider’s AC swing.
Calibration is accomplished by adjusting the 20k trim while
noting output data agreement with the input AC voltage.
Circuit accuracy is within 1% in a 200kHz bandwidth.

0.001µF

PULSE GENERATOR

1N4148

1k

220k

–

LT1671

+

DRIVER

1k

750k

750k

750k

DATA

ISOLATORS

SCK

DATA

OUTPUTS

SDO

5VPOWER

1k

100Ω

Q1
2N2369

5V

ISOLATION/POWER

Q2
ZTX-749

2Ω

3

1

6

4

T1

TRANSFORMER

2500V BREAKDOWN
ISOLATION BARRIER

5V

5V

ISOLATED POWER SUPPLY

1N5817

1N4148

4.7k

4.7k

1N4689

5.1V

5V ISO

A/D RMS CONVERTER

5V ISO

+V

SCK V

LTC2400

SDO

FOGND CS

5V ISO

+

5V ISO

+

100µF

DANGER! Lethal Potentials Present—See Text

5V ISO

–

IN

REF

10µF

5V ISO

LT1006

+

1µF

†

5V ISO

+V

OUT IN1

LTC1967

OUT RTN IN2

GND

EN

CALIBRATE

20k

0.1µF

182k*

182k*

1k*

INPUT

135VAC

OR

270VAC

FULL SCALE

ISOLATORS = AGILENT-HCPL-2300-010
T1 = BI TECHNOLOGIES HM-41-11510
* = 1% METAL FILM RESISTOR

† = WIMA MKS-2

= CIRCUIT COMMON

= AC LINE GROUND

1µF

400mV

REFERENCE

LT6650

+

OUT

–

15k*

FB

10k*

1µF

1VDC

AN106 F07

Figure 7. Isolated RMS Converter Permits Safe, Digital Output, Wideband RMS Measurement. T1-Based Circuitry Supplies Isolated
Power. RMS-to-DC Converter Senses High Voltage Input via Resistive Divider. A/D Converter Provides Digital Output Through
Optoisolators. Accuracy is 1% in 200kHz Bandwidth

AN106-4

an106f

Application Note 106

Low Distortion AC Line RMS Voltage Regulator

NOTE: BEFORE PROCEEDING ANY FURTHER, THE
READER IS WARNED THAT CAUTION MUST BE USED
IN THE CONSTRUCTION, TESTING AND USE OF THIS
CIRCUIT. HIGH VOLTAGE, LETHAL POTENTIALS ARE
PRESENT IN THIS CIRCUIT. EXTREME CAUTION MUST
BE USED IN WORKING WITH, AND MAKING CON­NECTIONS TO, THIS CIRCUIT. REPEAT: THIS CIRCUIT
CONTAINS DANGEROUS, HIGH VOLTAGE POTENTIALS.
USE CAUTION.

DANGER! Lethal Potentials Present—See Text

1.5A

AC

SB

HIGH

UNREGULATED

AC LINE

INPUT

0.22µF

AC

LOW

+V REGULATORS

470k

0.47µF

1N5281B
200V

200k

200k

HEAT SINK IRF-840
*1% METAL FILM RESISTOR
OPTODRIVER = TOSHIBA TLP190B

= 1N4005

Q3
2N5210

100k

1N4690

5.6V

BAT85

OVERVOLTAGE
PROTECTION

170V

Q4
MPSA42

5V

0.1µF

2N3440

10k
2W

ISOLATED
GATE BIAS

5.6k

Q1

REFERENCE

0.4V OUT5V IN

LT6650

GND

1M

Almost all AC line voltage regulators rely on some form of
waveform chopping, clipping or interruption to function.
This is effi cient, but introduces waveform distortion, which
is unacceptable in some applications. Figure 8 regulates
the AC line’s RMS value within 0.25% over wide input
swings and does not introduce distortion. It does this by
continuously controlling the conductivity of a series pass
MOSFET in the AC lines path. Enclosing the MOSFET in
a diode bridge permits it to operate during both AC line
polarities.

AC SERIES PASS

AND CURRENT LIMIT

0.03µF

FB

170V

1µF

0.22µF

0.1µF

5V

LT1077

430k

0.7Ω

A1

100k

Q2
IRF-840

10k

CONTROL

AMPLIFIER

22k

–

+

330k

1µF

10k

Q5
2N4393

Q6
2N3904

2.2µF
MYLAR

RMS-TO-DC CONVERTER

C1

OUT

1µF

OUT RTN

1N4689

5.1V

5V

+V

LTC1966

–VEN

GND

FEEDBACK

IN1

IN2

SENSE

AC HIGH

1k

AC LOW

2.2M*

REGULATED

105VAC
TO 120VAC
ADJUST

7.32k*

OUTPUT

VAC

AN106 F08

SOFT-START/–V

BIAS

Figure 8. Adjustable AC Line Voltage Regulator Introduces No Waveform Distortion. Line Voltage RMS Value is Sensed and
Compared to a Reference by A1. A1 Biases Photovoltaic Optocoupler via Q1, Setting Q2-Diode Bridge Conductivity and Closing a
Control Loop. VIN Must be ≥2V Above V

to Maintain Regulation

OUT

an106f

AN106-5

Application Note 106

The AC line voltage is applied to the Q2-diode bridge. The
Q2-diode bridge output is sensed by a calibrated variable
voltage divider which feeds C1. C1’s output, representing
the regulated lines RMS value, is routed to control ampli­fi er A1 and compared to a reference. A1’s output biases
Q1, controlling drive to a photovoltaic optoisolator. The
optoisolator’s output voltage provides level-shifted bias
to diode bridge enclosed Q2, closing a control loop which
regulates the output’s RMS voltage against AC line and
load shifts. RC components in A1’s local feedback path
stabilize the control loop. The loop operates Q2 in its
linear region, much like a common low voltage DC linear
regulator. The result is absence of introduced distortion
at the expense of lost power. Available output power is
constrained by heat dissipation. For example, with the
output adjustment set to regulate 10V below the normal
input, Q2 dissipates about 10W at 100W output. This fi gure
can be improved upon. The circuit regulates for V
above V
dropout as V

, but operation in this region risks regulation

OUT

varies.

IN

≥ 2V

IN

Circuit details include JFET Q5 and associated components.
The passive components associated with Q5’s gate form
a slow turn-on negative supply for C1. They also provide
gate bias for Q5. Q5, a soft-start, prevents abrupt AC power
application to the output at start-up. When power is off,
Q5 conducts, holding A1’s “+” input low. When power
is applied, A1 initially has a zero volt reference, causing
the control loop to set the output at zero. As the 1MΩ

0.22µF combination charges, Q5’s gate moves negative,
causing its channel conductivity to gradually decay. Q5
ramps off, A1’s positive input moves smoothly towards
the LT6650’s 400mV reference, and the AC output similarly
ascends towards its regulation point. Current sensor Q6,
measuring across the 0.7Ω shunt, limits output current
to about 1A. At normal line inputs (90VAC to 135VAC) Q4
supplies 5V operating bias to the circuit. If line voltage
rises beyond this point, Q3 comes on, turning off Q4 and
shutting down the circuit.

X1000 DC Stabilized Millivolt Preamplifi er

The preceding circuits furnish high level inputs to the RMS
converter. Many applications lack this advantage and some
form of preamplifi er is required. High gain pre-amplifi cation
for the RMS converter requires more attention than might
be supposed. The preamplifi er must have low offset error
because the RMS converter (desirably) processes DC as

legitimate input. More subtly, the preamplifi er must have
far more bandwidth than is immediately apparent. The
amplifi ers –3db bandwidth is of interest, but its closed
loop 1% amplitude error bandwidth must be high enough
to maintain accuracy over the RMS converter’s 1% error
passband. This is not trivial, as very high open-loop gain
at the maximum frequency of interest is required to avoid
inaccurate closed-loop gain.

Figure 9 shows an x1000 preamplifi er which preserves the
LTC1966’s DC-6kHz 1% accuracy. The amplifi er may be
either AC or DC coupled to the RMS converter. The 1mV
full-scale input is split into high and low frequency paths.
AC coupled A1 and A2 take a cascaded, high frequency
gain of 1000. DC coupled, chopper stabilized A3 also has
X1000 gain, but is restricted to DC and low frequency by
its RC input fi lter. Assuming the switch is set to “DC + AC,”
high and low frequency path information recombine at the
RMS converter. The high frequency paths 650kHz –3db
response combines with the low frequency sections micro­volt level offset to preserve the RMS converters DC-6kHz
1% error. If only AC response is desired, the switch is set
to the appropriate position. The minimum processable
input, set by the circuits noise fl oor, is 15µV.

Wideband Decade Ranged X1000 Preamplifi er

The LTC1968, with a 500kHz, 1% error bandwidth, poses
a signifi cant challenge for an accurate preamplifi er, but
Figure 10 meets the requirement. This design features
decade ranged gain to X1000 with a 1% error bandwidth
beyond 500kHz, preserving the RMS converters 1% er­ror bandwidth. Its 20µV noise fl oor maintains wideband
performance at microvolt level inputs.

Q1A and Q1B form a low noise buffer, permitting high
impedance inputs. A1 and A2, both gain switchable, take
cascaded gain in accordance with the fi gure’s table. The
gains are settable via reed relays controlled by a 2-bit code.
A2’s output feeds the RMS converter and the converter’s
output is smoothed by a Sallen-Keys active fi lter. The
circuit maintains 1% error over a 10Hz to 500kHz band­width at all gains due to the preamplifi ers –3db, 10MHz
bandwidth. The 10Hz low frequency restriction could be
eliminated with a DC stabilization path similar to Figure
9’s but its gain would have to be switched in concert with
the A1-A2 path.

an106f

AN106-6