Andrew Rusek, Oakland University
Andrew Rusek is a Professor of Engineering at Oakland University in Rochester, Michigan. He received an M.S. in Electrical Engineering from Warsaw Technical University in 1962, and a
PhD. in Electrical Engineering from the same university in 1972. His post-doctoral research involved 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 research in communication systems, high frequency electronics, and electromagnetic compatibility. He is the recipient of the 1995- 96 Oakland University Teaching Excellence Award.
Barbara Oakley, Oakland University
Barbara 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. in
Electrical Engineering, from the University of Washington in Seattle. Her Ph.D. in Systems
Engineering from Oakland University was received in 1998. Her technical research involves biomedical applications and electromagnetic compatibility. She is a recipient of the NSF FIE
New Faculty Fellow Award, was designated an NSF New Century Scholar, and has received the
John D. and Dortha J. Withrow Teaching Award and the Naim and Ferial Kheir Teaching Award.
© American Society for Engineering Education, 2007

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 2channel 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.

• 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.

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.

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.

Fig. 4: A close-up of one of the Tconnectors used to connect the cable to the oscilloscope.
Fig. 5: Another T-connector—this one connects the pulse generator to the oscilloscope.
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.

Load
Table 1: Pulsed signal input
Pulse type Comments
1. matched matched tr in
= tr gen
= 120 ns
2. “ ” open tr gen
= 120 ns, long pulse
3. “ ” “ ” tr in
= 10 ns, long pulse
4. “ ” “ ” tr in
= 10 ns, pulse width = 40 ns
5. “ ” short tr in
= 10 ns, pulse width = 40 ns
6. “ ” inductor tr in
= 10 ns, long pulse
7. “ ” “ ” “ ”
8.
9.
10.
“ ”
“ ”
“ ”
“ ” capacitor matched
“ ”
“ ” output = delayed input tr in
= 240 ns tr out
= 120 ns two step input, doubled output two input pulses, doubled output two input pulses, second inverted input with a decaying step (to zero) input with a decaying step (to zero), different time scale input with a delayed decaying step (to zero), time scale adjusted to find L input with a delayed rising step to a doubled level second input pulse inverted
11.
12.
“ ”
“ ”
27Ω
100Ω tr in
= 10 ns, short pulse tr in
= 10 ns, long pulse
“ ”
13. 25Ω
14. 100Ω
15. matched
16. “ ”
17. “ ”
18. 100Ω
19. 100Ω open
“ ” short
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ” single, small, negative reflection—input single, small, positive reflection—input multiple source and load reflections, first reflection observed from the output is positive positive steps single pulse duration 2 × T delay
,
“short” load spike single pulse duration 2 × T delay
,
“short” load spike losses observed single pulse duration 2 × T delay
,
“short” load spike load spike multiple source and load reflections, first reflection observed from the output is negative, with gradual decay multiple source and load reflections, under and overshoots
Output Probe
Connection shield grounded
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ” center conductor grounded shield grounded
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”

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. 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. 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.

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.

Fig. 13: Transmission line response to a long source pulse with an inductive load; the source resistance is matched (50Ω ).

Fig. 14: Transmission line with a matched (50Ω ) source resistance and a capacitive load (C = 10nF). .

Figs. 15a (above) and 15b (below): PSpice configuration used to simulate the waveforms seen in Figure 12.

10.
11.
12.
13.
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.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Load
Table 2: Sinusoidal signal input Note: All sources are matched.
Frequency Comments
(MHz) matched 1
“ ” “ ” the same amplitudes
CH4-inverted phase, decaying amplitudes
“ ”
“ ” open
“ ”
“ ”
“ ” short
“ ”
“ ”
“ ”
“ ”
17
“ ”
1
3.5
5.5
11
1
5
7
“ ”
11
λ almost identical amplitudes
CH4-inverted phase, almost identical amplitudes
Doubled amplitude
/4 pattern, “short” at the transmission line input
“short” moved closer to the end of the transmission line
λ /4 or two minima observed maximum voltage at the transmission line input, zero at the end
“ ” half wave displayed as above, stray L effect
“shorter” half wave
Output Probe
Connection shield grounded center conductor grounded shield grounded center conductor grounded shield grounded
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”
“ ”

Fig. 16: Low frequency sine-wave (1MHz), with a matched 50Ω transmission line.
Observe the small delay between waveforms and the virtually identical amplitudes of the signal at various points in the line.

Fig. 17: Low frequency sine-wave (1MHz), with a matched (50Ω ) 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)

Fig. 18: Sine-wave input of 17 MHz into a matched load. The waves have the same amplitudes, but the phases are different.

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.
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.
[1]
[2]
References
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[4]
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[8]
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