Robert使得时域反射仪这一课题不再神秘，它能够帮助您检测，测量以及找出任何阻抗不匹配的输电线路。为了做到这一点，他解释了时域反射仪背后的理论，并提出了一些切实可行的实验。
Detect and Measure Impedance Mismatches
Robert demystifies the topic of time domain reflectometry, which
enables you to detect, measure, and locate any impedance mismatch
in a transmission line. To do so, he explains the theory behind it
and presents some practical experiments.
Welcome back to the Darker Side. We all have favorite topics. One
of mine is impedance matching. I know I have already brought it up
in previous columns while discussing antennas, filters, or
microstrips, but this month, I promise I will present it from
another angle: time domain. You may have read sentences such as,
“When matching is not perfect, a part of the signal is reflected
back to the source.” This may seem strange for engineers not used
to high-frequency effects. Imagine the worst case of an impedance
mismatch: a wire grounded at one of its ends. Do you think there
could be any signal, reflected or not, in such a wire? Of course,
and I will show it to you!
Signal reflection is in fact at the heart of an old but interesting
measurement technique: time domain reflectometry (TDR). TDR enables
you to detect, measure, and locate any impedance mismatch in a
transmission line. In this article, I’ll explain the theory. But
more importantly, I’ll present some practical experiments to
demystify these techniques. You will just need a good oscilloscope.
TDR BASICSNothing can go quicker than c = 3 × 108 m/s, the speed of light in
free space (except guys jumping from black hole to black hole, if
you trust some science fiction authors). The speed of an electrical
signal going through a wire is a little lower than c, due to the
velocity factor of the transmission line, which is always slightly
below unity.
Imagine that you have an infinite wire or a sufficiently long wire
terminated in its proper impedancematching load, which is
equivalent. Any signal will flow through the wire and will be
absorbed by its matched load. No problem, no reflection. Now
imagine you have a long, perfect cable that is grounded at its far
end. On the other end of the cable, connect a voltmeter and a
current-limited 10-V power supply, and switch on the power supply.
What will happen? If you don’t consider the cable length, then of
course the power supply will be short-circuited to ground through
the cable and the voltmeter will simply read 0 V. But there is no
way to immediately know that the other end is grounded. The
electrical signal will need to propagate through the cable up to
the end to “see” that it is grounded. Then some information will
need to return to give 0 V on the voltmeter. Practically speaking,
if you replace the voltmeter with a fast oscilloscope, you will
effectively see that the line voltage will at first be 10 V. It
will drop down to 0V only 2T later, with T being the time needed
for the electricity to travel through the wire!
You can also interpret this phenomenon as if the 10-V input signal
was reflected back from the grounded end as a–10-V signal, giving 0
V as soon as both signals are summed up, and this is effectively
the case. In more complex applications, there may be several
impedance changes through the wire, and each will reflect back a
signal. The shape of the reflected signal will be characteristic of
the mismatch. Its time position, relative to the initial pulse,
will be directly proportional to the distance from the source. This
is TDR, which is an invaluable technique for locating faults (e.g.,
in underwater communication lines and similar applications) and
pinpointing impedance-matching issues (e.g., on high-speed PCB
tracks).
Figure 1—A time-domain reflectometer (TDR) includes a fast pulse generator
and a way to display the reflected pulses, usually a high-speed
oscilloscope. Thanks to a signal coupler, the oscilloscope enables
you to display both the initial pulse and any reflected signals.
TDR can be performed with either a step signal as an excitation, as
in my previous example, or with a quick pulse. I will use the
latter in this article because the interpretation of the signals is
a little simpler. The basic setup for a pulse-based TDR system is
shown in Figure 1. A generator provides a sharp and short pulse,
which is sent to the transmission line to be tested through a
signal splitter, enabling you to connect a highspeed oscilloscope
while not perturbing the impedance of the wire. The oscilloscope
will then display both the initial pulse and any pulses reflected
by the wire. Note that the length of the cable between the splitter
and the oscilloscope doesn’t matter because both the initial pulse
and the reflected pulses have to support the same delay through
this cable.
Let me write a few words about 50-Ω signal splitters. Such a
splitter can be built with three 17-Ω resistors in a star
configuration. The 17-Ω value enables you to keep a 50-Ω impedance
on all branches. Why? Because each of the two output branches are
supposed to be connected to a 50-Ω load, so each will have a 67-Ω
impedance (i.e., 17 + 50) thanks to the 17-Ω serial resistance.
This gives 33.5 Ω as both branches are in parallel. Just add the
last 17-Ω resistor in series and you are back to 50 Ω. Magical,
isn’t it? So you could build a 50-Ω splitter just with three
resistors, but it is far easier to achieve good performances with
an off-the-shelf splitter, especially when manipulating
sub-nanosecond signals. The only disadvantage of such a resistive
splitter is that a 6-dB loss is incurred in each of the two
branches, but that’s life.
1-NS PULSE GENERATORUnfortunately, there is a problem with TDR techniques. If you need
a good distance resolution, then you must generate and detect quick
pulses. Consider a standard transmission line with a velocity
factor of, say, 0.8. The speed of light is 30 cm/ns in free space,
so it is 24 cm/ns (i.e., 0.8 × 30) in this wire. Because the signal
must go back and forth, you will need to be able to manage 1-ns
signals to get a 12-cm distance resolution.
There are two issues: oscilloscope and generator. As for the
oscilloscope, I can’t help you. Of course, if you just need to
locate a problem within tens of meters, a low-cost 50-MHz
oscilloscope will be fine. But, if you need to work with tens of
centimeters, you will need a high-end oscilloscope (500 MHz or even
1 GHz or more). If you have a tight budget, look for an old
Tektronix 7000 series on the Internet.
Figure 2—You can build a sub-nanosecond pulse generator for $5 or less using
an avalanche mode generator. A high-voltage generator, here built
using a CFL backlight power supply, drives an NPN bipolar
transistor in its avalanche region, which generates a fast pulse on
the output.
As for the generator, I can help you build a high-speed,
sub-nanosecond pulse generator for less than $5. As you can see in
Figure 2, it can’t be simpler, right? Well, I must admit that I had
to read it twice when I first saw this concept in an old National
Semiconductor application note. It is quite unusual to see a
transistor with a grounded base generating anything—and
ultra-high-speed pulses in particular. K1 is simply a DC/AC
high-voltage converter, the kind of converter used for CFL display
backlights. With D1 and C1, this is a convenient, inexpensive way
to generate a 300-VDC voltage. Yes, 300 V. This voltage is then
used to charge the small C2 capacitor (1.5 pF) through R1. And this
is where the magic happens. At a given point in time, the voltage
on C2 exceeds the avalanche breakdown voltage of Q1, usually around
60 to 80 V. Q1 then briefly conducts and discharges C2 through R3.
This generates a pulse on the output. The pulse’s duration will be
roughly proportional to C2. But more importantly, the pulse’s rise
time will be short, because the avalanche phenomenon is fast due to
the underlying physics. Intuitively, with such a high voltage, the
electrons will have a lot of energy and will be able to jump over
the transistor’s barrier very quickly. Some transistors are better
than others for this application. The old 2N2369s are fine, so I
have one. If you need longer pulses, just increase C2.
WHERE ARE YOUR MAGNIFYING GLASSES?Figure 2 is simple, but you need to be careful as you build it. Its
performance will depend on the parasitic component values. Any
useless wire in the critical section of the design (i.e., between
C2, Q1, R3, and the output connector) will inevitably introduce
parasitic inductances,which will drastically degrade the pulse
generator ’s performance. You need to build it as small as
possible.Surface-mount versions for C2 and R3 will at least yield
better results than classic packages; however, I don ’t know if
there are good SMT equivalents for the 2N2369. You may design a
custom SMT PCB for the generator.But on my side, I used an unusual
assembly technique,which I don ’t recommend for more complex
designs, or for trembling engineers. Let ’s call it the flying SMT
technique, or FST (see Photo 1). The idea is to use SMT components
for all passives and to solder them directly to the 2N2369 leads.
It works well, but it is a little annoying to build because these
nasty SMTs don ’t want to stay where you ’ve soldered them. It
worked for me after working patiently for 30 minutes, so it should
work for you too.
The flying SMT technique required some patience, but it enabled me
to build a compact pulse generator without any specific PCB
(thereby minimizing any parasitic inductance or capacitance).
Photo 2—I soldered the pulse generator transistor directly on the output
connector and added a reused CFL backlight DC/AC converter with a
1N4007 rectifying diode and a small 1,000-V ballast capacitor to
provide a 300-VDC supply. In fact, 100 V would be enough. I added a
small heatsink on the transistor just in case, but it seems
useless.
The power supply section of the design is not critical. The entire
assembly can fit in a small shielded box (see Photo 2). Just make
sure the output wire from Q1 to the output connector is as short as
possible.
FIRST EXPERIMENTSPhoto 3—This is the output of the avalanche generator, grabbed on a 1-GHz
digital
oscilloscope. The pulse rise time is measured at 244 ps, far below
the oscilloscope’s
specified rise time. The pulse width is less than 0.5 ns.
I am sure you want to know about the actual performance of this $5
avalanche generator. Photo 3 was taken with a high-end 1-GHz Lecroy
WaveRunner 6100 digital oscilloscope (which provides no less than
10-Gsps single-shot and 200-Gsps equivalent sampling speed for
repetitive signals), using 50-Ω input impedance. The pulse
rise time was measured at 244 ps,including the rise time of the
oscilloscope itself, which is specified at 400 ps, so the pulse
generator may be far quicker! The pulse width is around 0.5 ns,
which is not bad. Such a pulse has frequency components up to 1 GHz
or so, so it could be a helpful generator for numerous
experiments.Keep it on your bench just in case.
Photo 4—Check out my TDR setup. The custom pulse generator drives a
three-way 50-Ω splitter (an old Greenpar model in this case). One
output of the splitter (on the bottom) is connected to the
oscilloscope through a 50-Ω coaxial cable. The other drives the
system under test, which is a simple 1.5-m unterminated SMA cable.
It is time to show you my first actual TDR measurement. The test
setup is in Photo 4. The pulse generator is connected to an
off-the-shelf Greenpar three-way 50-Ω resistive splitter
(obsolete). One of the outputs of the splitter is connected to the
oscilloscope through a 50-Ω cable. The other is connected to a
1.5-m open-ended SMA cable (see Photo 4).
Photo 5—When a TDR is connected to an open-ended transmission line, there
is a positive reflected pulse. The amplitude of the reflected pulse
is equal to the incident pulse, but here the resistive three-way
splitter induces a 6-dB loss. Thus, the voltage is theoretically
divided by two (here a little more due to additional losses).
Switch on the oscilloscope, set the trigger voltage high enough to
synchronize only on the initial pulse, and you get Photo 5. As
expected, there is a reflected pulse 15.66 ns later than the
original signal. Assuming a velocity factor of 0.7, and keeping in
mind the factor of two for back and forth directions, this means
the discontinuity was 1.64 m away (i.e., 0.7 × 3 × 108 ×
15.66.10–9/2 m). Not too far from the actual 1.5-m cable length,
the difference is probably due to the delays in the splitter itself
or to a slightly different velocity factor. Moreover, the shape of
the reflection signal is useful.Remember my first example of a
shorted wire, which gave a negative reflected signal? The line is
openended,and in such a case, the reflected signal is positive. If
you have a step generator rather than a pulse generator,the
reflected signal will add to the incident signal and will double
its amplitude, as both have the same sign.This is normal because
the voltage on an open-ended 50-Ω generator is twice its
voltage when loaded with a matched 50-Ω load.
LET’S SIMULATE ITPhoto 6—QUCS makes it easy to simulate a TDR experiment. A pulse generator
drives an ideal three-way resistive signal splitter made with three
17-Ω resistors. One output drives a transmission line (here two 1-m
lines with a parasitic parallel capacitor in the middle). The other
drives a virtual voltage probe.
Before going on the test bench or even in the field with your basic
TDR system, it is nice to have a list of reflected pulse shapes for
the different “usual ” impedance mismatches:increase or decrease of
the resistive impedance, parallel or series parasitic capacitor or
inductance, and more. I could have built a dozen different test
benches and measured the actual behavior, but using simulation is a
wonderful time-saving tool. The only issue is that a classic analog
linear simulator like Spice can ’t easily handle line-length
effects, so it isn ’t appropriate to simulate TDR effects.
Fortunately, you can use the free Quite Universal Circuit Simulator
(QUCS), which I used in a previous column. The QUCS simulation of a
parasitic parallel capacitor in the middle of a transmission line
is shown in Photo 6. When a pulse is applied to a capacitor,this
component first behaves as a short circuit, giving a negative
reflected pulse similar to a short-circuited line. Then the
capacitor slowly loads and the reflected pulse is positive and
exponentially decreasing, with a time constant proportional to the
capacitance.
These are the results of the QUCS simulation of the reflected
shapes for the six elementary impedance mismatches: parallel and
serial R, C, and L.
Based on this simulation, it is easy to simulate all the other
classic disturbances. The results are provided in Figure 3. All
corresponding QUCS simulation files are posted on the Circuit
Cellar FTP site if you want to play with them. Figure 3 shows that
a parallel resistor gives a reflected pulse shape similar to a
short-circuited line: a negative pulse, but with a smaller
amplitude than a full short circuit. Similarly,a series resistor is
a small open circuit with a small positive reflected pulse. You can
also see that a series inductor gives a shape similar to a parallel
capacitor but with an opposite polarity. Parallel inductors and
series capacitors also have a dual behavior.
REAL LIFE VS. SIMULATIONPhoto 7—I reused the microstrip test board I presented in my Circuit Cellar
223 article. I added a parasitic serial or parallel 22-pF SMT 0805
capacitor in the middle of the line to compare the theoretical TDR
behavior and an actual one.
Let ’s compare simulation with real life. I ’ll begin with a
parallel capacitor. Note that I reused the small S-shaped
50-Ω microstrip PCB that was built for my February 2009
article, “Microstrip Techniques ”(Circuit Cellar 223). I
soldered a 22-pF 0805 SMT capacitor in the middle of the microstrip
line,with its other end grounded (see Photo 7). I connected the
microstrip board at the end of the SMA cable used in Photo 4,
connected another 1.5-m cable at the other end of the microstrip
test board, and finally used a 50-Ω SMA load to provide
proper matching.So, the test setup is a 3-m, 50-Ω line with a
50-Ω load at its end, but with a parasitic 22-pF parallel capacitor
to ground at the middle. I switched on the oscilloscope and pulse
generator and, voila, I got what you see in Photo 8a. Comparing it
with the theoretical shape for parallel capacitors, Photo 6 shows
that the overall shape is similar, with a first negative pulse,
then a smaller positive one. There are other small pops probably
due to other impedance mismatches (i.e., far from perfect ground
connection of the capacitor, nonideal capacitor, and nonideal
connectors, and more). But once again, the overall shape is
similar.
Experimental TDR waveforms with
(a) a 22-pF parallel capacitor or
(b) a 22-pF series capacitor in the middle on a microstrip
transmission line. Just compare these shapes with the corresponding
theoretical shapes provided in Figure 3.
Do you want another test? This time, I hooked the same capacitor in
series with the line, just by cutting 1 mm or so out of the
microstrip and soldering the 22-pF capacitor across the gap. The
result is Photo 8b. Once again, it is similar to the theoretical
shape for a series capacitor, but with additional bumps in
particular at the beginning of the pulse.
Another interesting use of TDR techniques is the evaluation of the
performances of connectors, in particular at high frequencies. TDR
will easily show you defective or any less-than-ideal connectors.
Photo 9—The vertical scale is increased to show the difference between the
parasitic reflections with an SMA 50-Ω load (top) and with the same
load connected through two SMA/BNC adapters (bottom). Conclusion: I
don’t like BNC.
I performed a simple test by hooking a good 50-Ω load at the end of
a test 50-Ω cable. Theoretically, a 50-Ω load shouldn’t reflect
anything. But because the load and the SMA connectors were not 100%
perfect, there was a small reflected pulse. I increased the
vertical sensitivity of the oscilloscope and was easily able to see
it. Refer to the top curve in Photo 9. Next, I inserted an SMA to
BNC and BNC to SMA adapters pair between the SMA cable and the same
SMA load. The result is the bottom curve in Photo 9, with the same
vertical settings. Do you see a difference? I conclude that you
shouldn’t use BNC connectors for high-frequency designs if you’re
looking for good impedance matching.
WRAPPING UPI covered some of the potential applications for TDR. Even with a
poorman’s pulse generator and a good oscilloscope, you can easily
pinpoint impedance-matching problems on cables and transmission
lines. Moreover, a quick look at the shape of the reflected pulse
will enable you to qualitatively get a good idea of the kind of
defect.
I read that TDR engineers working on the maintenance of submarine
lines can easily guess if a problem is related to water ingress,
corroded contacts, or something similar just by looking at the TDR
shapes. You now know why.
I haven ’t discussed the mathematical aspects of TDR. This may be
the subject of another interesting article,particularly because a
simple fast Fourier transform (FFT) of the TDR signal can bring you
back in the frequency domain. You can then deduce the line ’s
band-pass simply by looking at its TDR shape, at least if there
aren ’t any losses. As a TDR setup works only by looking at
reflections,it may not detect a signal absorbed in a line and not
reflected back.
I hope this journey into TDR has been enjoyable. Don’t hesitate to
test it, play with it, and send me theresults of your experiments.
TDR is no longer on the darker side for you.
Author’s note: Caution! If you build the pulse generator described
in this article, remember that there is a capacitor inside charged
at 300 VDC, even if the output signal is a low-power 50-Ω signal.
The 300 VDC could be significantly harmful, or even lethal, so
please take care.
Robert Lacoste lives near Paris, France. He has 18 years of
experience working on embedded systems, analog designs, and
wireless telecommunications. He has won prizes in more than 15
international design contests. In 2003, Robert started a consulting
company, ALCIOM, to share his passion for innovative mixed-signal
designs. You can reach him at
rlacoste@alciom.com. Don’t forget to write “Darker Side” in the subject line to bypass
his spam filters.
PROJECT FILESTo download code, go to
ftp://ftp.circuitcellar.com/pub/Circuit_Cellar/2009/225.
RESOURCEST. Engdahl, “Time Domain Reflectometer,” 2007,
www.epanorama.net/circuits/tdr.html.
Hewlett-Packard, “Application note 1304-2: Time Domain
Reflectometry Theory,” 1988,
http://materias.fi.uba.ar/6209/download/HP-AN1304.pdf.
F. Sischka, “TDR Measurements and Calibration Techniques,” Agilent
Technologies, 2002,
http://eesof.tm.agilent.com/docs/iccap2002/MDLGBOOK/1MEASUREMENTS/71TDR/1TDRCalibration.pdf.
J. Williams, “Application Note 47: High Speed Amplifier Techniques:
A Designer’s Companion for Wideband Circuitry,” Linear Technology
Corp., 1991,
www.mit.edu/~6.331/an47fa.pdf.
SOURCESWaveRunner 6100 Oscilloscope
Lecroy Corp. |
www.lecroy.com2N2369 Transistor
Multicomp |
www.farnell.com (Distributor)Qucs project
http://qucs.sourceforge.net
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