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Standing And Traveling Waves On Transmission Lines:Getting It Right

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2010 Annual Conference & Exposition


Louisville, Kentucky

Publication Date

June 20, 2010

Start Date

June 20, 2010

End Date

June 23, 2010



Conference Session

Innovations in ECE Education II

Tagged Division

Electrical and Computer

Page Count


Page Numbers

15.1089.1 - 15.1089.7



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Paper Authors


Raymond Jacquot University of Wyoming

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Ray Jacquot received his BSME and MSME degrees at the University of Wyoming in 1960 and 1962 respectively. He was an NSF Science Faculty Fellow at Purdue University where he received the Ph.D. in 1969. He joined the Electrical Engineering faculty of the University of Wyoming in 1969. He is a Fellow of ASEE, a Life Senior Member of IEEE and Life Member of ASME. He has been active in ASEE for over four decades serving as Rocky Mountain Section Chair and PIC IV Chair. His professional interests are in modeling, control and simulation of dynamic systems. He is currently Professor Emeritus of Electrical and Computer Engineering. E-mail:

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David Voltmer Rose-Hulman Institute

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David R. Voltmer received degrees from Iowa State University (BSEE), University of Southern California (MSEE), and The Ohio State University (PhD EE). During nearly four decades of teaching, Dr. Voltmer has maintained a technical focus in electromagnetics, microwaves, and antennas. His more recent efforts are directed toward the design process and project courses. He has served in many offices of the ERM division of ASEE and in FIE. Dr. Voltmer is an ASEE Fellow and a Life Senior member of IEEE. E-mail:

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John Steadman University of South Alabama

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John Steadman received degrees from the University of Wyoming (BSEE and MSEE) in 1964 and 1966 respectively. After graduation he was employed by General Dynamics. He received the PhD EE from Colorado State University in 1971 prior to joining the faculty of Electrical Engineering at the University of Wyoming in 1971 where he held all ranks and served as Department Head and Associate Dean. Dr. Steadman served the profession as President of the National Council of Examiners for Engineers and Surveyors and as President of IEEE-USA. He has been active in ASEE for over 3 decades serving as Section Chair and Division Treasurer and is an ASEE Fellow. His professional interests are in bioengineering, digital systems and real-time signal processing. Dr Steadman is currently Dean of Engineering at the University of South Alabama. E-mail:

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Standing and Traveling Waves on Transmission Lines: Getting it Right Introduction

In the recent engineering education literature there have been numerous papers dealing with strategies for teaching electrical transmission lines. These papers approach the assistance in teaching from two points of view. The first is the use of simple low-cost experiments to demonstrate the concepts 1-3 and the second approach employs computer animation 4, 5. Another recent paper discusses the concept of teaching transmission lines early in the electromagnetics sequence 6.

Seeking clarification to the problem of sinusoidally driven, arbitrarily terminated, lossless transmission lines one of the authors asked the question, “How does the voltage on the line behave?” In order to answer this question some MATLABTM scripts were written to animate the voltage on the line. In examining these animations more questions arose about the concept of standing waves. In the examination of the animations the authors were confounded because for arbitrary termination impedance the resulting waveform did not “stand” as is the case for the commonly discussed short-circuit and open-circuit terminations. Consultation of a number of electromagnetics textbooks found that the term “standing wave” is often used to describe the interference pattern created by a combination of forward and backward traveling waves of the same wavelength (or frequency). As we shall show this definition is incomplete and leads to a semantic error in a number of contemporary textbooks.

Standing or Stationary Waves

After the search of electromagnetics textbooks it was decided to look on the web for information which is contained on physics websites. Standing waves are created by the addition of two oppositely traveling waves of equal wavelength and amplitude. There seems to be an agreement that the terms standing waves and stationary waves are synonymous and that such waves are characterized by nodes (points of zero response) and antinodes (points of maximum response) and that there is no energy transport in the direction of propagation 7.

A final resolution to the definition problem came with a search of Lord Rayleigh’s 1891 edition of The Theory of Sound 8 wherein the above stated definition was confirmed. The Rayleigh definition essentially states that sinusoidal waves are stationary (standing) if they are of the form w( z ,t ) = P cos( ωt - ε ) cos( βz - α ) (1) or after employing the appropriate trigonometric identity P w( z , t ) = [cos( ωt + βz - ε - α ) + cos( ωt - βz - ε + α )] (2) 2 We see that expression (2) is the sum of forward and backward traveling waves each of amplitude P/2. A similar result may be found in the handbook of Korn and Korn 9.

Jacquot, R., & Voltmer, D., & Steadman, J. (2010, June), Standing And Traveling Waves On Transmission Lines:Getting It Right Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--15792

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