easy to do transmission line demonstrations of sinusoidal
TRANSCRIPT
AC 2007-246: EASY-TO-DO TRANSMISSION LINE DEMONSTRATIONS OFSINUSOIDAL STANDING WAVES AND TRANSIENT PULSE REFLECTIONS
Andrew Rusek, Oakland UniversityAndrew Rusek is a Professor of Engineering at Oakland University in Rochester, Michigan. Hereceived an M.S. in Electrical Engineering from Warsaw Technical University in 1962, and aPhD. in Electrical Engineering from the same university in 1972. His post-doctoral researchinvolved sampling oscillography, and was completed at Aston University in Birmingham,England, in 1973-74. Dr. Rusek is very actively involved in the automotive industry with researchin communication systems, high frequency electronics, and electromagnetic compatibility. He isthe recipient of the 1995- 96 Oakland University Teaching Excellence Award.
Barbara Oakley, Oakland UniversityBarbara Oakley is an Associate Professor of Engineering at Oakland University in Rochester,Michigan. She received her B.A. in Slavic Languages and Literature, as well as a B.S. inElectrical Engineering, from the University of Washington in Seattle. Her Ph.D. in SystemsEngineering from Oakland University was received in 1998. Her technical research involvesbiomedical applications and electromagnetic compatibility. She is a recipient of the NSF FIENew Faculty Fellow Award, was designated an NSF New Century Scholar, and has received theJohn D. and Dortha J. Withrow Teaching Award and the Naim and Ferial Kheir Teaching Award.
© American Society for Engineering Education, 2007
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Easy-to-Do Transmission Line Demonstrations of Sinusoidal Standing
Waves and Transient Pulse Reflections
Abstract
Junior, senior, and graduate level courses in electromagnetics often cover issues related to
sinusoidal standing waves and transient pulses on transmission lines. This information is
important for students because a theoretical understanding of such phenomena provides a
concrete foundation for later study involving the general propagation of electromagnetic
fields, and because transmission lines are critical in many different engineering
applications. Unfortunately, however, the somewhat tedious mathematics underlying
transmission line theory can cause students to snooze through lectures. This paper
describes a simple set of classroom demonstrations that can enliven student interest in
this important area. The phenomena demonstrated include:
• Time domain separation of input and output for the forward versus the return
conductor.
• The lossless or almost lossless character of the signal transfer through the
transmission line.
• Signal reflections and transmission line matching.
• Time domain reflectometry applications, including characteristic impedance tests,
terminating impedance tests, and losses.
The demonstrations discussed in this paper, which can be done using either two 2-
channel or one 4-channel oscilloscope, are based on both sinusoidal and pulse excitations.
Our experience has been that students become very enthusiastic as they clearly see the
various types of standing wave patterns that are actively associated with different load
and source impedances, and the various phenomena associated with transient pulse
reflections.
Introduction
Transmission lines first gained use in the mid-1800s to transfer Morse code over long
distances. By the early 1900s, transmission lines had become an important means of
transferring energy. Most recently, transmission lines have become inseparable
components of high-speed electronic circuits and systems. Nowadays, typical
applications of the transmission lines include:
• High voltage transmission lines
• Telephone lines
• Audio and TV cables, TV antenna cables
• Computer network lines
• Printed Circuit Board (PCB) connecting paths and interconnecting cables
• Automotive control system interconnecting cables
• Microwave communication systems, radars, etc.
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• High-speed analog and digital Integration Circuits (IC)
• High-speed measurement systems.
Junior, senior, and graduate level courses in electromagnetics often cover issues related to
sinusoidal standing waves and transient processes in transmission lines.[1, 2] Such
training is valuable not only because of the importance of the transmission lines in many
engineering applications, but also because a theoretical understanding of such phenomena
provides a concrete foundation for further studies of concepts related to the general
propagation of electromagnetic fields and antennas.[3]
Keeping Sight of the Real Phenomena in the Theoretical Analysis
When sinusoidal signals are considered, transmission lines can be analyzed in several
different ways. For lossless transmission lines, TEM wave equations are solved and
basic transmission line parameters, such as delay and characteristic impedance, can be
determined. This is supported by solutions to the differential equations for an infinitely
large number of RLC lumped cells representing a transmission line. On the other hand,
when transient processes in transmission lines are analyzed, graphical methods such as
bouncing wave method or Bergeron diagrams are applied. The characteristic impedance
of the line, as well as line delays, are involved.[4, 5]
Unfortunately, students can lose sight of the existence and function of the return
conductor as a result of formal simplifications during the derivations.[6] The formal
analysis, for example, suggests that then the return conductor constitutes an equipotential
ground, while in reality, the so-called ground or return conductor carries return current
and should be treated in the same way as the forward conductor. In addition, students do
not see or understand the effect of the characteristic impedance, which participates in
transient voltage division and acts as a “lossless” resistor. The goal of the practical
demonstrations discussed in this paper, then, is to show the existence of standing wave
patterns, time domain separation of input and output waves, and existence of the voltage
across the “equipotential” return conductor.
As importantly, the demonstrations discussed in this paper provide for an inexpensive
method to allow students to see concrete effects of theoretical derivations. (See [7, 8] for
alternative cost-effective approaches to this problem.) The more commonly used—and
expensive—demonstrations of sinuoisodal measurements of transmission lines involving
standing wave pattern and power transfer are usually performed at very high frequencies
with the help of expensive instrumentation such as slotted lines, VSWR meters calibrated
to include nonlinearities of the microwave detectors, distributed loads, variable length
short circuit stubs, directional couplers, microwave generators and power meters. The
method suggested here is far simpler and less expensive, and is described in detail below.
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Demonstration Setup
Transmission lines can be assembled in straightforward fashion by using several sections
of coaxial cable with T-connectors, with the cable terminated using a few discrete
components such as resistors, capacitors and coils (Fig. 1). A function generator or
nanosecond pulse generator can be used to provide a signal source. The desired
frequencies of sinusoidal signals are below 20 MHz. The rise time of the function
generator pulses should be less than 20ns. It is advantageous to use a pulse generator
with variable rise time, as presented in this paper, but most of the signals discussed here
could be presented even if this type of the pulse generator in not available. The
demonstration is monitored using a 4-channel or two 2-channel oscilloscopes.
Fig. 1: PSpice model of the experimental setup showing the three 4-meter long
sections (for a total of 12 meters) of the transmission line, the placement of the
probes from the oscilloscope, the source, and the load.
Figures 2-6 below show various aspects of the actual experimental setup
organized for the demonstration of pulsed signals.
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Fig. 2: The equipment necessary for the demonstration, including the transmission line, a
pulse generator, and a four-channel oscilloscope. The image on the scope shows various
points along the line, and clearly reveals the pulse delay due to the length of the line.
Fig. 3: Although the cable
is coiled to minimize space,
the four connection points
for the oscilloscope
problems can be seen. The
‘scope probes are
connected at the beginning,
end, and at two
intermediate points on the
transmission line.
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Fig. 6: The ‘scope
probes are connected
at the beginning,
end, and at two
intermediate points
in the transmission
line, (as shown in
Fig 3 above).
Students can clearly
see how the signal
propagates along the
line.
Table 1 below lists some of the possible pulsed input and reflected signals that instructors
can demonstrate to students, while Figs. 7-14 show some of these signals as they actually
appear on an oscilloscope or on oscilloscope printouts. Figs. 15a and 15b give a sense of
how “real life” transmission line phenomena can be nicely modeled using PSpice.
Fig. 4: A close-up of one of the T-
connectors used to connect the cable
to the oscilloscope.
Fig. 5: Another T-connector—this one
connects the pulse generator to the
oscilloscope.
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Table 1: Pulsed signal input
Load Pulse type Comments Output Probe
Connection
1. matched matched trin = trgen = 120 ns output = delayed input shield grounded
2. “ ” open trgen = 120 ns,
long pulse
trin = 240 ns trout = 120 ns “ ”
3. “ ” “ ” trin = 10 ns,
long pulse
two step input, doubled output “ ”
4. “ ” “ ” trin = 10 ns,
pulse width = 40 ns
two input pulses, doubled
output
“ ”
5. “ ” short trin = 10 ns,
pulse width = 40 ns
two input pulses, second
inverted
“ ”
6. “ ” inductor trin = 10 ns,
long pulse
input with a decaying step (to
zero)
“ ”
7. “ ” “ ” “ ” input with a decaying step (to
zero), different time scale
“ ”
8. “ ” “ ” “ ” input with a delayed decaying
step (to zero), time scale
adjusted to find L
“ ”
9. “ ” capacitor “ ” input with a delayed rising
step to a doubled level
“ ”
10. “ ” matched trin = 10 ns,
short pulse
second input pulse inverted center conductor
grounded
11. “ ” 27-Ω trin = 10 ns,
long pulse
single, small, negative
reflection—input
shield grounded
12. “ ” 100-Ω “ ” single, small, positive
reflection—input
“ ”
13. 25-Ω open “ ” multiple source and load
reflections, first reflection
observed from the output is
positive
“ ”
14. 100-Ω “ ” “ ” positive steps “ ”
15. matched short “ ” single pulse duration 2×Tdelay,
“short” load spike
“ ”
16. “ ” “ ” “ ” single pulse duration 2×Tdelay,
“short” load spike
losses observed
“ ”
17. “ ” “ ” “ ” single pulse duration 2×Tdelay,
“short” load spike
load spike
“ ”
18. 100-Ω “ ” “ ” multiple source and load
reflections, first reflection
observed from the output is
negative, with gradual decay
“ ”
19. 100-Ω “ ” “ ” multiple source and load
reflections, under and
overshoots
“ ”
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Fig. 8: Narrow pulses at the input,
and reflected from an open-ended
transmission line—a radar-like effect.
An echo of doubled amplitude is
observed at the output “double-sized”
nature of the reflected signal.
Students can also observe the effects
of the losses of transmission line—
the echo shows the effects of both
dispersion and attenuation.
Fig. 7: This oscilloscope displays a
narrow pulse at the input, and
reflected from the shorted end of a
transmission line. The inverted return
voltage pulse can be clearly seen.
Fig. 9: The pulse formed by reflection
from a shorted transmission line. The
pulse length is defined by the doubled
delay of the transmission line.
Fig. 10: Center conductor grounded,
line output matched, output pulse
inverted in phase. This shows that the
outer conductor of the transmission line
also participates in the signal delay.
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Fig. 11: The waveforms here are due to a
reflection from an open-ended
transmission line. The input is matched,
and the pulse rise time is much less than
the transmission line delay. The pulse
has been adjusted to distinguish the
reflected wave from the incident wave—
the reflected part is delayed so that
students can see a “second” step.
Fig. 12: This figure shows the same incident and
reflected waves as Fig. 11. It is just that in this
instance, the rise time of the input pulse has been
adjusted to make the reflected wave “extend” the
front edge of the incident wave. The purpose of
this part of the demonstration is to question
students about this unusual phenomenon and make
them aware that the line, as a linear component,
cannot “accelerate” the wave front. Instead, the
incident and reflected waves add to create the more
sharply rising signal seen at the output.
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Fig. 13: Transmission line response to a long source pulse with an inductive
load; the source resistance is matched (50-Ω).
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Fig. 14: Transmission line with a matched (50-Ω) source resistance and a
capacitive load (C = 10nF). .
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Figs. 15a (above) and 15b (below): PSpice configuration used to simulate the
waveforms seen in Figure 12.
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Table 2 below lists some of the possible sinusoidal inputs, outputs, and resulting
waveforms that can be demonstrated with the transmission line set up as shown in Fig. 1.
Several waveform printouts are shown in Figs. 16-19 to provide a feel for the type of
oscilloscope signals that student see on transmission lines with sinusoidal signals.
Table 2: Sinusoidal signal input Note: All sources are matched.
Load Frequency
(MHz)
Comments Output Probe
Connection
1. matched 1 the same amplitudes shield grounded
2. “ ” “ ” CH4-inverted phase, decaying amplitudes center conductor
grounded
3. “ ” 17 almost identical amplitudes shield grounded
4. “ ” “ ” CH4-inverted phase, almost identical
amplitudes
center conductor
grounded
5. open 1 Doubled amplitude shield grounded
6. “ ” 3.5 λ/4 pattern, “short” at the transmission line
input
“ ”
7. “ ” 5.5 “short” moved closer to the end of the
transmission line
“ ”
8. “ ” 11 λ/4 or two minima observed “ ”
9. short 1 maximum voltage at the transmission line
input, zero at the end
“ ”
10. “ ” 5 “ ” “ ”
11. “ ” 7 half wave displayed “ ”
12. “ ” “ ” as above, stray L effect “ ”
13. “ ” 11 “shorter” half wave “ ”
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Fig. 16: Low frequency sine-wave (1MHz), with a matched 50-Ω transmission line.
Observe the small delay between waveforms and the virtually identical amplitudes of the
signal at various points in the line.
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Fig. 17: Low frequency sine-wave (1MHz), with a matched (50-Ω)
transmission line. Channel 4 (output) shows the voltage for grounded
center conductor and a probe input connected to the outer conductor
(shield), observe the phase inversion of the last wave (180 degrees)
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Fig. 18: Sine-wave input of 17 MHz into a matched load. The waves
have the same amplitudes, but the phases are different.
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Conclusions
This paper has demonstrated the ease with which many different transmission line
phenomena can be demonstrated using a generator and an oscilloscope—including phase
shifting, attenuation, matching, reflection, and the effects of capacitive and inductive
loads. These phenomena can also be modeled in PSpice. Two tables provide a summary
of the types of sinusoidal and pulsed phenomena that can be demonstrated, and a number
of different oscilloscope output signals related to the various phenomena have been
shown.
References
[1] M. N. O. Sadiku and L. C. Agba, "A simple introduction to the transmission-line modeling," IEEE
Transactions on Circuits and Systems, vol. 37, pp. 991-999, 1990.
[2] C. W. Trueman, "Teaching transmission line transients using computer animation," IEEE
Frontiers in Education Conference (San Juan, Puerto Rico, 10–13 Nov.), pp. 9-11, 1999.
Fig. 19: Open ended transmission line with sinusoidal input at 11
MHz. Observe the two minima as the signal moves from one end of
the line to the other.
Page 12.567.17
[3] S. H. Mousavinezhad, "Electric & magnetic fields, transmission lines first?," 2006 ASEE Annual
Conference & Exposition: Excellence in Education, 2006.
http://www.asee.org/acPapers/code/getPaper.cfm?paperID=11331
[4] P. C. Magnusson, Transmission lines and wave propagation: CRC Press, 2001.
[5] "The Bergeron method: A graphic method for determining line reflections in transient
phenomena," Texas Instruments, http://focus.ti.com/lit/an/sdya014/sdya014.pdf
[6] L. D. Feisel and A. J. Rosa, "The Role of the Laboratory in Undergraduate Engineering
Education," Journal of Engineering Education, vol. 94, pp. 121-130, 2005.
[7] F. Jalali, "Transmission Line Experiments At Low Cost," 1998 ASEE Annual Conference &
Exposition: Engineering Education Contributing to U. S. Competitiveness, 1998.
http://www.asee.org/acPapers/00580.pdf
[8] D. M. Hata, "A low-cost approach to teaching transmission line fundamentals and impedance
matching," 2004 ASEE Annual Conference & Exposition: Engineering Education Reaches New
Heights, 2004. http://www.asee.org/acPapers/2004-204_Final.pdf
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