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.

Page 12.567.3

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.

Page 12.567.8

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.

Page 12.567.9

Fig. 13: Transmission line response to a long source pulse with an inductive

load; the source resistance is matched (50-Ω).

Page 12.567.10

Fig. 14: Transmission line with a matched (50-Ω) source resistance and a

capacitive load (C = 10nF). .

Page 12.567.11

Figs. 15a (above) and 15b (below): PSpice configuration used to simulate the

waveforms seen in Figure 12.

Page 12.567.12

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.

Page 12.567.14

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)

Page 12.567.15

Fig. 18: Sine-wave input of 17 MHz into a matched load. The waves

have the same amplitudes, but the phases are different.

Page 12.567.16

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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