Campbell Scientific TDR100 User Manual
TDR100
Revision: 2/10
Copyright © 2000-2010
Campbell Scientific, Inc.
Warranty and Assistance
The TDR100 is warranted by CAMPBELL SCIENTIFIC, INC. to be free from
defects in materials and workmanship under normal use and service for twelve
(12) months from date of shipment unless specified otherwise. Batteries have
no warranty. CAMPBELL SCIENTIFIC, INC.'s obligation under this
warranty is limited to repairing or replacing (at CAMPBELL SCIENTIFIC,
INC.'s option) defective products. The customer shall assume all costs of
removing, reinstalling, and shipping defective products to CAMPBELL
SCIENTIFIC, INC. CAMPBELL SCIENTIFIC, INC. will return such
products by surface carrier prepaid. This warranty shall not apply to any
CAMPBELL SCIENTIFIC, INC. products which have been subjected to
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warranties of merchantability or fitness for a particular purpose. CAMPBELL
SCIENTIFIC, INC. is not liable for special, indirect, incidental, or
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Products may not be returned without prior authorization. The following
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repairs for customers within their territories. Please visit
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completed form must be either emailed to repair@campbellsci.com
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www.campbellsci.com/repair
. A
or faxed to
TDR100 Table of Contents
PDF viewers note: These page numbers refer to the printed version of this document. Use
the Adobe Acrobat® bookmarks tab for links to specific sections.
1. Introduction..................................................................1
1.1 TDR100 Packing List...............................................................................1
1.2 ENCTDR100 Packing List.......................................................................1
2. System Specifications.................................................2
2.1 General......................................................................................................2
2.2 Power Consumption .................................................................................2
2.2.1 TDR100 ..........................................................................................2
2.2.2 SDMX50.........................................................................................2
2.3 TDR100 Performance Specifications .......................................................2
2.4. Electromagnetic Compatibility................................................................3
3. Getting Started with TDR100 using PCTDR ..............3
3.1 Discussion of Distances and Propagation Velocity (Vp) when using
TDR100................................................................................................4
3.2 PCTDR Help.............................................................................................6
4. PCTDR Software ..........................................................6
4.1 General......................................................................................................7
4.2 PCTDR Help.............................................................................................7
4.3 Menu Selections .......................................................................................8
4.3.1 File Menu........................................................................................8
4.3.2 Settings Menu .................................................................................8
4.3.3 Options Menu .................................................................................8
4.4 PCTDR Parameter Selection Boxes .........................................................8
4.4.1 Cable...............................................................................................8
4.4.2 Waveform .......................................................................................9
4.4.2.1 A Discussion of Start and Length Parameters.......................9
5. System Components: Datalogger Control .............11
5.1 General....................................................................................................11
5.2 Datalogger ..............................................................................................11
5.3 TDR100..................................................................................................12
5.4 SDMX50.................................................................................................12
5.5 Power Supply..........................................................................................13
5.5.1 Grounding.....................................................................................13
5.6 SDM Communication.............................................................................14
5.6.1 SDM Addressing for TDR100 System.........................................14
5.6.2 SDM Cable and Cable Length Considerations .............................16
5.7 ENCTDR100..........................................................................................16
5.7.1 Mounting Equipment in ENCTDR100.........................................16
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TDR100 Table of Contents
6. Datalogger Instructions for TDR Measurements ....18
5.8 Soil Probes............................................................................................. 17
5.8.1 Determining Probe Constant, Kp, using PCTDR......................... 18
6.1 CR800, CR850, CR1000, or CR3000 Datalogger Instruction “TDR100”18
6.2 CR10X and CR23X Datalogger Instruction 119 ................................... 20
6.3 Discussion of TDR Instruction Parameters (Instruction 119)................ 21
6.3.1 Parameter 1: SDM Address.......................................................... 21
6.3.2 Parameter 2: Output Option .........................................................21
6.3.2.1 Enter 0: Measure La/L........................................................ 21
6.3.2.2 Enter 1: Collect Waveform................................................. 22
6.3.2.3 Enter 2: Collect Waveform and First Derivative................ 22
6.3.2.4 Enter 3: Measure Bulk Electrical Conductivity.................. 22
6.3.3 Parameter 3: Multiplexer and Probe Selection............................. 22
6.3.4 Parameter 4: Waveform Averaging.............................................. 23
6.3.5 Parameter 5: Relative Propagation Velocity ................................23
6.3.6 Parameter 6: Points....................................................................... 23
6.3.7 Parameter 7: Cable Length (meters)............................................. 23
6.3.8 Parameter 8: Window Length (meters)........................................ 24
6.3.9 Parameter 9: Probe Length (meters)............................................. 24
6.3.10 Parameter 10: Probe Offset (meters).......................................... 24
6.3.11 Parameter 11: Input Location..................................................... 24
6.3.11.1 Reflection Waveform Values to Input Storage................. 24
6.3.12 Parameter 12: Multiplier ............................................................ 25
6.3.13 Parameter 13: Offset................................................................... 25
6.3.13.1 Probe Constant for Electrical Conductivity Measurement25
7. TDR Principles ...........................................................26
8. Cable Length and Soil Electrical Conductivity Effect
on Water Content Determination...........................28
8.1 Cable Length Effect on Water Content Measurement........................... 28
8.2 Soil Electrical Conductivity Effect on Water Content Measurement ....29
9. Algorithm Description and Parameter Adjustment ...30
9.1 Introduction............................................................................................ 30
9.2 Algorithm for Calculation of TDR Probe Rod Apparent Length........... 30
9.2.1 Algorithm Description.................................................................. 30
9.2.1.1 Waveform Evaluation......................................................... 31
9.2.2 Algorithm Parameter Adjustment for Special Conditions............ 32
9.2.2.1 Terminal Emulator Commands for Apparent Length
Algorithm ........................................................................ 32
9.3 Algorithm for Calculation of Bulk Electrical Conductivity................... 33
9.3.1 Algorithm Description.................................................................. 33
9.3.2 Algorithm Parameter Adjustment for Special Conditions............ 33
10. Programming Examples..........................................35
10.1 CR1000 Program Example..................................................................35
10.2 CR10X/CR23X Program Examples..................................................... 38
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TDR100 Table of Contents
11. References ...............................................................51
Figures
3-1 Waveform of a CS610 in water................................................................5
3-2 Waveform of CS610 in water after changing Start and Length parameters
to display relevant portion of reflected signal......................................6
4-1 PCTDR waveform for CS610 in water ..................................................10
5-1 TDR System Components......................................................................11
5-2 SDMX50 signal attenuation...................................................................12
5-3 Terminal Strip Adapters for Connections to Battery..............................13
5-4 Location of Address Jumpers on SDMX50 ...........................................15
8-1 Waveforms collected in a sandy loam using CS610 probe
with RG8 connecting cable. Volumetric water content is
24% and bulk electrical conductivity is 0.3 dS m
8-2 Waveforms collected in a sandy loam using CS610 probe
with RG8 connecting cable. Volumetric water content
values are 10, 16, 18, 21 and 25%. Solution electrical
conductivity is 1.0 dS m
8-3 Waveforms collected in a sandy loam using CS610 probe
with RG8 connecting cable. Volumetric water content
values are 10, 18, 26, 30 and 37%. Solution electrical
conductivity is 10.2 dS m
9-1. Typical TDR100 waveform showing key features with numbers
1, 2 and 3............................................................................................31
9-2. PCTDR terminal emulator screen showing TDR100 algorithm
parameter variables............................................................................32
9-3. Waveform and derivative values near TDR probe and locations of
index for point of maximum derivative and maximum derivative
value. The green band represents the results of the search using
the threshold value.............................................................................34
10-1 Twenty-nine CS605 or CS610 probes connected to 4ea SDMX50
multiplexers........................................................................................50
-1
...................................................................29
-1
.................................................................30
-1
............................28
Tables
4-1 Recommended Waveform Length values for range of TDR probe rod
lengths assuming soil porosity of 0.60...............................................10
5-1 SDM Addressing for Early SN SDMX50s and Edlog Dataloggers.......15
6-1 Reflection waveform array header elements..........................................25
6-2 Probe Constant Values for Campbell Scientific Probes.........................26
iii
TDR100 Table of Contents
iv
TDR100
1. Introduction
This document presents operating instructions for the TDR100 and associated
equipment and discusses time domain reflectometry (TDR) principles. Section
3 (Getting Started with TDR100 using PCTDR) describes a simple start-up
configuration to quickly and easily display TDR probe waveforms using
PCTDR. See the “TDR Probes” manual for detailed information about TDR
probes available from Campbell Scientific. Manuals can be downloaded from
our website: www.campbellsci.com/manuals.
The TDR100 can be controlled either by a computer using Windows software
PCTDR or by using TDR100 instruction with a CR800, CR850, CR1000, or
CR3000 datalogger or Instruction 119 with a CR10X or CR23X datalogger.
PCTDR is used when display of waveform information is needed for setup and
troubleshooting but does not support automated measurements at prescribed
time intervals. The TDR100 and SDMX50 multiplexers can be configured for
automatic control using the dataloggers.
A single TDR probe can be connected directly to the TDR100 or multiple
probes connected via coaxial multiplexer units (SDMX50).
Warning
The TDR100 is sensitive to electrostatic discharge
damage. Avoid touching the inner part of the panel
BNC connector or the center rod of TDR probes
connected to the TDR100.
1.1 TDR100 Packing List
The following are included with a TDR100.
1. PCTDR software and instruction manual on compact disk.
2. A 6 foot long, 9-conductor cable for connection between the serial port of
a computer and the RS-232 port of the TDR100.
3. Short 5-conductor cables for SDM connection between (a) datalogger and
TDR100 and between (b) TDR100 and an SDMX50 coaxial multiplexer.
1.2 ENCTDR100 Packing List
The following are included with an ENCTDR100.
1. Enclosure Supply Kit; desiccant packs, humidity indicator, cable ties,
putty and mounting hardware.
2. ENCTDR100 Enclosure Ground Wire Kit.
3. TDR100/SDMX50 Coaxial Interconnect Cable.
4. TDR100/SDMX50 and TDR100/Datalogger SDM 5-Conductor Cable.
5. Enclosure ENC16/18 with two 1.7 inch diameter cable penetration ports.
6. Terminals for external deep cycle battery.
1
TDR100
2. System Specifications
2.1 General
See the CR10X, CR23X, CR800/CR850, CR1000, or CR3000 datalogger
manuals for datalogger specifications.
2.2 Power Consumption
2.2.1 TDR100
• The current demand for the TDR100 during measurement is 270
milliamps.
• When the TDR100 is controlled by a datalogger, a 35 second timer puts
the device in sleep mode requiring about 20 milliamps. After 35 seconds
in sleep mode, a timer puts the TDR100 in standby mode requiring about
2 milliamps.
• When the TDR100 is controlled by PCTDR, a 60 second time-out puts
the device in low power mode requiring about 60 milliamps.
2.2.2 SDMX50
• The quiescent current demand for the SDMX50 multiplexer is less than 1
milliamp.
• Current demand during switching is approximately 90 milliamps.
• All multiplexers of the same level switch simultaneously (see Figure 5-1).
Switching takes less than 1 second.
2.3 TDR100 Performance Specifications
pulse generator output 250 mV into 50 ohms
output impedance
time response of combined pulse
generator and sampling circuit
pulse generator aberrations
pulse length 14 microseconds
timing resolution 12.2 picoseconds
waveform sampling
50 ohms ± 1%
≤ 300 picoseconds
±5% within first 10 nanoseconds
±0.5% after 10 nanoseconds
20 to 2048 waveform values over
chosen length
2
range
resolution
distance
-2 to 2100 meters 0 to 7 microseconds
1.8 millimeter 6.1 picoseconds
(Vp = 1) time (1 way travel)
TDR100
waveform averaging 1 to 128
electrostatic discharge protection internal clamping
power supply unregulated 12 volt (9.6 V to 16 V),
300 milliamps maximum
temperature range
dimensions 210mm x 110mm x 55 mm
weight 700 g
-40°C to 55°C
2.4. Electromagnetic Compatibility
The TDR100 is Πcompliant with performance criteria available upon request.
RF emissions are below EN55022 limit. The TDR100 meets EN61326
requirements for protection against electrostatic discharge and surge EXCEPT
for electrostatic discharge on the center conductor of the panel BNC connector.
Warning
The TDR100 is sensitive to electrostatic discharge
damage. Avoid touching the center conductor of the
panel BNC connector or the center rod of TDR probes
connected to the TDR100.
3. Getting Started with TDR100 using PCTDR
This section lists steps for a simple connection between a computer and the
TDR100 to monitor a single TDR probe using PCTDR software. A single
probe is connected directly to the TDR100, and no multiplexers are used.
TDR100 operation with SDMX50 multiplexers is described in Section 5.4.
1. Install PCTDR
The following instructions assume that drive D: is a CD-ROM drive. If
the drive letter is different, substitute the appropriate drive letter.
• Put the installatio n disk in the CD-ROM drive. The install application
should come up automatically. If the install does not start, use Start |
Run of the Windows system and type D:/Disk1/Setup.exe or use the
Browse button to access the CD-ROM drive and select the setup
executable file in the Disk1 folder
• The PCTDR Installation Utility is activated. Follow the prompts to
complete the installation.
2. Use the supplied 9 conductor cable to connect a computer to the
RS-232 connector on the TDR100
The RS-232 connector on the TDR100 is used for communication
between a serial communication port of a computer and the TDR100. A
9-conductor cable is supplied with the TDR100. Serial communication
3
TDR100
port 1 is the default setting and can be changed in PCTDR menu
Settings/Communications. The baud rate is factory set to 57600.
3. Connect 12 volt power to TDR100
12 volt power to the TDR100 is connected using terminals +12V and
GROUND on the panel 5-terminal connector. An external power supply
or the 12V terminals of a datalogger can be used for power. The C1, C2
and C3 terminals are for SDM (synchronous device for measurement
communication protocol) communications. The C1, C2 and C3 terminals
are not used for single probe monitoring with a computer using PCTDR.
4. Connect a TDR probe to the BNC connector of the TDR100
5. Start PCTDR by selecting PCTDR under Programs of the Windows
Start Menu or double-clicking the PCTDR icon.
6. View a waveform using Get Waveform
In the Waveform section of PCTDR, set Start to 0 or 1 m and Length to
the apparent length (see note below) of the attached probe cable plus 5
meters. Press Get Waveform.
3.1 Discussion of Distances and Propagation Velocity (Vp) when using TDR100
A TDR system is typically comprised of components with different signal
propagation properties. The V
transmission line characteristics such as the dielectric constant of interconductor insulating material. Setting V
simplifies system setup. The displayed position of a waveform is apparent
distance. The value chosen for V
conductivity measurement. The selected V
display.
The relationship between real and apparent distance is given as
apparent distance = (actual distance) x (selected V
For example, if the actual length of a cable having a V
the selected V
is 1.0, the apparent distance to the end of the cable is 5 x
p
(1.0/0.78) = 6.41 meters. Typical cable V
Scientific TDR probes use RG-58 with a Vp of 0.67 and RG-8 with a Vp of
0.78.
An example is presented in Figure 3-1. Displayed is the waveform for a
CS610 in water. The actual cable length is about 5 m. The apparent cable
length is about 6 m.
for a particular component depends on
p
= 1.0 and using apparent distances
p
does not affect water content or electrical
p
value does affect waveform
p
/actual Vp).
p
of 0.78 is 5 meters and
p
’s range from 0.67 to 0.9. Campbell
p
4
TDR100
FIGURE 3-1. Waveform of a CS610 in water.
Changing the Waveform Start value to 5.7 m and the Waveform Length to 5 m
gives the waveform displayed in Figure 3-2.
5
TDR100
FIGURE 3-2. Waveform of CS610 in water after changing Start and Length parameters to display
relevant portion of reflected signal.
3.2 PCTDR Help
Information on PCTDR is available from the HELP menu or by pressing F1.
Using F1 gives specific help associated with the position of the cursor or active
screen. See Section 4.2 for PCTDR HELP details.
4. PCTDR Software
A display for viewing waveforms is generally needed only for system setup
and troubleshooting, and the TDR100 does not have a built-in display.
Windows software PCTDR is used with a personal computer to configure the
TDR100 and multiplexers and display waveforms.
NOTE
Conflicts between commands simultaneously issued by a
datalogger and PCTDR will cause error messages in PCTDR .
To prevent these errors, halt the datalogger program while
controlling the TDR100 with PCTDR. Halting the program can
be accomplished by setting the datalogger table execution
interval to zero.
6
TDR100
r
Note for use of PCTDR
when TDR100 is
connected to CR23X
or CR1000 datalogge
When the TDR100 is connected to a CR23X or CR1000
datalogger using control ports 1-3 for SDM control and
SDMX50 multiplexers are also connected, an instruction must be
used in the datalogger program to properly configure the control
ports. If this is not done, PCTDR will not control the
multiplexers. This is required because the CR23X and CR1000
control ports present a low impedance to the SDM lines and this
will load the signal issued by TDR100 when PCTDR is used to
control multiplexers.
At the end of the CR23X datalogger program containing
TDR100 instruction (P119), use an instruction (P20) to
configure control ports 1, 2 and 3 as input.
Set Port(s) (P20)
1:9999 C8..C5 = nc/nc/nc/nc
2:9888 C4..C1 = nc/input/input/input
At the end of the CR1000 datalogger program containing
TDR100 instruction (TDR100), use an instruction (PortsConfig)
to configure control ports 1, 2 and 3 as input.
PortsConfig (&B00000111,&B00000000)
4.1 General
4.2 PCTDR Help
PCTDR requires a connection from a COM port of the computer to the RS-232
port of the TDR100. Choice of COM port and baud rate is made in PCTDR
menu Settings/Communications. The baud rate is set during TDR100
production to 57600.
There are several ways to access PCTDR's help system:
• The help file's Table of Contents can be opened by choosing Help |
Contents from the PCTDR menu.
• The help file's Index can be opened by choosing Help | Index from the
PCTDR menu.
• At any time you can press F1 for help that is relevant to cursor position.
• If the help file is opened, pressing the Contents button on the help system's
toolbar will open the Table of Contents.
• If the help file is opened, choosing the Index button from the help system's
toolbar will bring up the Index. Keywords can be typed in to search for a
topic. An in-depth search can be performed by pressing the Find button
and typing in a word.
If a highlighted link takes you to another topic, you can return to the original
topic by selecting the Back button from the help system's toolbar.
7
TDR100
4.3 Menu Selections
4.3.1 File Menu
Save Configuration/Load Configuration - save and reload configuration of
user-selectable parameters. Saves configuration as .wfd file.
Save ASCII Waveform - save displayed waveform as .dat file.
Save Mux Setup/Load Mux Setup - save and reload multiplexer setup. Saves as
.mux file.
Print Graph - send displayed graph to default printer
Exit - quit PCTDR
4.3.2 Settings Menu
Communication - select communication serial port and baud rate
Waveform Selection - select reflection waveform or reflection waveform plus
first derivative
Multiplexer - configure multiplexer switching
Calibration Function - select calibration functions for volumetric water content
and bulk electrical conductivity
Units - select meters or feet
4.3.3 Options Menu
Terminal Emulator - line command mode of PCTDR
Advanced - link for downloading TDR100 operating system
4.4 PCTDR Parameter Selection Boxes
4.4.1 Cable
The cable propagation velocity, Vp, depends on the dielectric constant of the
insulating material between the coaxial cable center conductor and outer
shield. The value entered in this parameter selection box is the ratio of the
actual propagation velocity for a selected medium to the propagation velocity
in a vacuum (3 x 10
available from manufacturer data books. It is only necessary to know the V
value if the TDR100 is used as a cable tester for finding cable lengths or faults.
See Section 3.1 for a discussion of propagation velocity.
Calculation of water content or electrical conductivity is independent of the
chosen value for V
value does affect waveform display.
8
m sec-1). Specific Vp values for each coaxial cable are
because Vp cancels in the calculation. However the Vp
p
p
8
For water content measurements, it is recommended that propagation velocity,
Vp, be set at 1.0.
4.4.2 Waveform
TDR100
Average - sets the number of measurements averaged at a given distance from
the TDR100. A value of 4 is recommended. Higher values can be used when
noise is present. Averaging is useful when noise from power sources or when
noise of random nature is superimposed on the reflection waveform.
Averaging is accomplished by collecting n values at a given distance before
collecting values at the next distance increment where n is the value entered in
Average.
Points - the number of points in the displayed or collected waveform (using
File/Save ASCII Waveform). For water content measurements, a value of 251
is recommended and will provide 250 waveform increments. A higher value
can provide better resolution when collecting waveforms.
Start - the apparent distance from the TDR100 to where the displayed
waveform will begin (using File/Save ASCII Waveform). For water content
measurements this value should be the apparent distance from the TDR100 to
the beginning of the probe minus approximately 0.5 meter. Figure 3-2 is an
example of the display when the correct start is chosen.
NOTE
4.4.2.1 A Discussion of Start and Length Parameters
The apparent distance is the (actual distance) x (selected
Vp/actual Vp). For example, if the actual length of a cable
having a Vp of 0.78 is 5 meters and the selected Vp is 1.0, the
apparent distance to the end of the cable is 5 x (1.0/0.78) = 6.41
meters.
Length - Beginning at distance Start, the length of the display window and
apparent length depicted by the number of data Points selected. For water
content measurements with the CS605 or CS610 TDR probes (30 cm rods) a
length of 4 meters is recommended. See Table 1.
Only the waveform reflection near the probe is used for water content
determination. The reflections for most of the cable between the TDR100 and
the TDR probe are not used for TDR100 measurements. The apparent probe
length algorithm begins analysis of the probe waveform at the distance set by
Waveform Start. The Waveform Start value must include a short section of
cable near the probe head to establish reference values. Subtracting 0.5 m
from the PCTDR x-axis value for the actual probe beginning is recommended.
The actual beginning of the probe displayed in Figure 4-1 is approximately 6.2
m. A Waveform Start value of 5.7 m will provide the complete data needed by
the algorithm to determine apparent probe length.
9
TDR100
FIGURE 4-1. PCTDR waveform for CS610 in water.
The algorithm will use the length of the waveform set by the Waveform
Length. After finding the probe beginning, the algorithm searches over the
remaining waveform for the end of the probe. The length must be large
enough to display a short distance past the end of the probe under the wettest
expected conditions.
TABLE 4-1. Recommended Waveform Length values for
range of TDR probe rod lengths assuming soil porosity of
0.60.
Probe rod length (m) Recommended Waveform Length
value (m)
0.10 to 0.20 3
0.21 to 0.30 4
0.31 to 0.40 5
0.41 to 0.6 6
0.61 to 0.75 7
0.76 to 1.00 9
Use the recommended values listed in Table 1 or use the following equation to
estimate the required window length, L
.
w
10
TDR100
(
L
⋅+
v
L
=
w
with L the actual probe rod length, and, θ
volumetric water content. Two m is added for the .5 m before the probe and
some distance after the probe end. For example, using a CS610 with 0.3 m
probe rod length in a soil with a porosity of 0.6 gives an estimated apparent
probe length of 4.04 m. Setting the Waveform Length to 4 m is recommended.
−θmax
0114
..0176
)
+
2
the maximum expected
v-max
5. System Components: Datalogger Control
5.1 General
Datalogger
5.2 Datalogger
FIGURE 5-1. TDR System Components
Campbell Scientific CR800, CR850, CR1000, and CR3000 dataloggers use
Instruction “TDR100” to control the TDR100 measurement sequence and store
the resulting data. PC400 or LoggerNet (version 3.0 or higher) are used to
create and send the CRBasic Program to the datalogger.
Campbell Scientific CR10X and CR23X dataloggers use Instruction 119 and
various other instructions to control the TDR100 measurement sequence and
store the resulting data. PC208W (version 3.1 or higher) or LoggerNet are
used to link the datalogger to a computer for data and program transfer.
11
TDR100
5.3 TDR100
The TDR100 contains the pulse generator for the signal applied to a TDR
probe. The TDR100 also digitizes the reflection and applies numerical
algorithms for measuring volumetric water content or electrical conductivity.
The TDR100 communicates with the datalogger using SDM protocol or with a
computer using PCTDR and serial communications.
5.4 SDMX50
The SDMX50 is a 50 ohm, eight-to-one, coaxial multiplexer. The same
multiplexer circuit is packaged as the SDMX50, the SDMX50LP or the
SDMX50SP. The SDMX50 is designed to minimize signal attenuation and all
channels have equal transmission line lengths. Spark gaps provide protection
from voltage surge damage. Figure 5-2 describes typical signal attenuation
from the common to one output channel for frequency range important for
TDR measurements.
0
0.2
0.4
0.6
0.8
1
SDMX50 attenuation (dBm)
1.2
1.4
100 1.10
Frequency (MHz)
FIGURE 5-2. SDMX50 signal attenuation.
Each of the eight ports can be connected to a probe or an other multiplexer (see
Figure 5-1).
3
12
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