1. Fields and Waves I Lecture 4 K. A. Connor Pulses on Transmission Lines
Electrical, Computer, and Systems Engineering Department
Rensselaer Polytechnic Institute, Troy, NY
Welcome to Fields and Waves I
Before I start, can those of you with pagers and cell phones please turn them off? Thanks.

2. J. Darryl Michael – GE Global Research Center, Niskayuna, NY
These Slides Were Prepared by Prof. Kenneth A. Connor Using Original Materials Written Mostly by the Following:
Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY
J. Darryl Michael – GE Global Research Center, Niskayuna, NY
Thomas P. Crowley – National Institute of Standards and Technology, Boulder, CO
Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY
Lale Ergene – ITU Informatics Institute, Istanbul, Turkey
Jeffrey Braunstein – Chung-Ang University, Seoul, Korea
Materials from other sources are referenced where they are used. Those listed as Ulaby are figures from Ulaby’s textbook.
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3.
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4. Review So Far & Example Handout – Page 1 Example
Fill out all information
Method of Solution
Example
Find Parameters
Follow Method of Solution
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5. http://www. telegraph-history. org/transcontinental-telegraph/index
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6. Example – Telegraph Line
Parameters (Some are realistic and some are not)
Inductance per meter 1.6x10-6
Capacitance per meter 6.8x10-12
Characteristic Impedance about 500 Ohms
Velocity ?
Assume lossless (bad assumption)
Source 60V (small internal impedance)
Frequency 1000Hz
Large load impedance
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7. Example
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8. Pulses on Transmission Lines
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9. Experiment from the first class
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10. Pulses Measured with the Reels of RG58/U Cable
50 Ohm source
50 Ohm line long reel of cable terminated in 50 Ohms
Look at details of individual pulses
Improperly terminated cable connecting input to scope
Properly terminated cable connecting input to scope
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11. Overview Review the derivation of the wave equation PSpice simulation
General form of voltages and currents
Initial conditions
Reflection at the load and the source
Bounce diagrams
Henry Farny Song of the Talking Wire Taft Museum of Art
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12. Transmission Line RepresentationAs
limit
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13. These are functions that move with velocity u
Transmission Line Representation
Similarly,
Obtain the following PDE:
These are functions that move with velocity u
Solutions are:
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14. Wave Equation Solutions Can Have Any Shape
Pulses will look the same at the input and output except for a delay
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15. Pulse Input and Output Voltages
Source
Load
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16. General Form of Voltage and Current on the Line
The representation is very general or
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17. The Shape of the Pulse Does Not Matter For Lossless Lines
Input
Output
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18. General Form of Solution
In general, both positive and negative traveling pulses will exist on a line.
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19. Workspace 9 April 2019 Fields and Waves I
Show the form of the solution
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20. Simplifying the Solution
As with the time harmonic case, we can use the voltage solution to obtain the current solution. Applying
We have
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21. General Solution Again
Using the voltage information
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22. Compare with Steady State
So far, the solution looks like the solution for steady state.
Pos traveling current looks like pos traveling voltage divided by the characteristic impedance
Neg traveling current looks like neg traveling voltage divided by minus the characteristic impedance
Why should this be the case?
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23. Steady State & Transients
Time varying signals can be broken down into individual frequencies (principle behind Fourier and Laplace analysis).
We can analyze a pulse by first finding these frequencies, analyzing what happens to each one and then combining the results.
A simple example would be a signal with two frequencies, one of which is filtered out by some circuit, with the result that only one frequency will remain.
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24. Spectrum Examples from EE 352 Univ of Saskatchewan
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25. Spectrum Examples
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26. Steady State & Transients
We can just use what we learned for steady state or develop transient analysis independently.
It is best to do this independently so that you can be further convinced that our transmission line solutions make sense.
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27. Reflection Coefficient at the Load
When the incident pulse reaches the load, it will reflect if the load is not matched to the line
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28. Workspace
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29. Reflection Coefficient at the Load
The impedance at the load should equal the ratio of the voltage to the current at the end of the line
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30. Launching the Pulse
At the source end the line is driven by something like a function generator
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31. Launching the Pulse
One very large difference between the transient case and steady state is that, when the pulse is first launched on the line, there can be no negative traveling pulse since the line is assumed to have no voltages before the first pulse is launched.
In steady state, positive and negative waves always exist simulataneously
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32. Launching the Pulse
Like steady state, it is necessary to determine the input impedance of the line to see how a source interacts with it.
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33. Finding Zin
The input impedance will be the ratio of the voltage to the current at the input end for only the positive traveling signal
Why?
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34. Input Voltage to the Line
The input voltage to the line is, thus, determined from the voltage divider relation
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35. Pulse Analysis
Use the voltage divider relationship to find the initial voltage on the line. The pulse is launched and propagates to the load.
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36. Pulse Analysis
The pulse then is either totally absorbed by the load or is partially reflected. If the latter, it then propagates back toward the source.
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37. Pulse Analysis
The pulse then is either totally absorbed by the source impedance or partially reflected and propagates back to the load.
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38. Reflection Coefficient at the Source
The pulse sees the source impedance as the same as the load impedance. Thus,
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39. Each step of the process is included
Bounce Diagram
There is a systematic method for applying this information using what is called a bounce diagram or lattice diagram
Each step of the process is included
Space and time information are included
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40. Bounce Diagram Scope connected to line output
Scope connected to line input
T=d/u is the time to transit from one end of the line to the other
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41. Bounce Diagram See Unit XII for examples 9 April 2019
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42. Bounce Diagram – what happens when everything is matched?
Scribble all over this slide.
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43. Several Kinds of Transients
Short Pulses (like in HW2)
Switching on DC sources (example to follow)
Long Pulses whose duration exceeds the line transit time (basically a combination of the other two)
Combinations of all types of pulses
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44. Example 1 Switching on a 10 Volt DC source
Question: What voltage will eventually appear across the output? That is, what will the voltage become for large time? Hint: How would you have answered this question before taking Fields & Waves I?
Extra switches to maintain ground for PSpice
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45. Voltage divider gives 8.333 V launched on line
Example 1
Voltage divider gives V launched on line
Reflection coefficient at the load is 1
Reflection coefficient at the source is -2/3
Transit time is 800ns (arbitrary for this example, but for completeness, assume a velocity of 2x108 m/s)
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46. Example 1 T 2T 3T t
z=0
z=d
-5.555V
5.56V
-5.555V
11.11V
8.333V
16.67V
8.333V
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47. Example 1
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48. Example 1 Longer time scale (up to 0.1 sec) 9 April 2019
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49. This is much simpler to consider and is the case for HW 2.
Example 2
If the pulse width is much less than the transit time T, then only a single incident and reflected pulse will occur at the load or source end while reflection occurs.
This is much simpler to consider and is the case for HW 2.
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50. Example 2 Let us first begin with the PSpice analysis
Use precisely the same line, load, etc. except for the source, which is now a 50ns pulse. A time delay has been added to match the turn-on time of the switch.
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51. Example 2
Comparison of two cases
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52. Example 2
Expanding the pulse width to 100ns show how reflection occurs. A small Matlab program was written to show the pulses.
Incident
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53. Example 2 Both Incident and Reflected Pulses Must Exist Simultaneously
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54. Example 2
Reflected
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55. Example 2 Both Incident and Reflected Pulses Must Exist Simultaneously
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56. Example 2
Incident
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57. Again, expanding the pulse for clarity, we see that incident and reflected pulses exist simultaneously
Example 2 T 2T 3T t
z=0
z=d
Leading Edge
Trailing Edge
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58. This analysis can be done analytically, but we will only use PSpice
Example 3
Non-Resistive Load
If the load includes either a capacitor or inductor of significant size, one observes the charging and discharging time of these elements.
This analysis can be done analytically, but we will only use PSpice
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59. Example 3
Source and Line Matched (Rs=Zo=), Capacitive Load (C=0.1 microfarad). Length = 2564meters and velocity = 2.564x108 meters per second
Source
Load
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60. Waves and Bounce Diagram
Java Applet
From Georgia Tech
Waves and Bounce Diagram
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