Quickline: A Transmission Line Simulation Package by W. P. Harokopous and P. B. Katehi Technical Report 403182-2 - L-2-;' Center for Research on Learning and Teaching The University of Michigan Ann Arbor, Ml 48109 Abstract: "Quickline" is a simulation package which evaluates the voltage on an ideal transmission line terminated at various loads. The considered terminations are series and parallel combinations of resistors, inductors, and capacitors. The code is written in BASIC with a graphics capability suitable for the IBM PC/XT/AT.

QUICKLINE - A TRANSMISSION LINE SIMULATION PACKAGE by W.P. Harokopus & P.B. Katehi

TABLE OF CONTENTS 1. Introduction II. Running The Program 1. Overview 2. User's Guide 3. Example Output Displays III. Appendix A - Theory IV. Appendix B - Choosing Program Parameters and Troubleshooting 2

I. INTRODUCTION "Quickline" is a simulation package which evaluates the voltage on an ideal transmission line terminated with various loads. The excitation of the transmission line is provided by a DC voltage generator. This software has been developed to aid undergraduate students in understanding transient effects on ideal transmission lines (T.L.) and has been written for IBM/PC/XT/AT personal computers. The program evaluates and displays the voltage responce of any loaded ideal T.L. for a given excitation as a function of time and distance. The terminations treated in this package are series and parallel combinations of resistors, inductors and capacitors. There is a choice of two different excitations (p=pulse, s=step) and six loads. The structure of the programing is such that more terminations or other excitations may be added as needed. This package will become the basis of a number of homeworks where the students will have to run many elaborate and meaningful examples in order to understand the effect of various circuits element on the behavior of ideal transmission lines. The interactive nature of the program will allow the advanced student to experiment with problems he/she may find interesting. 3

II. RUNNING THE PROGRAM A. Overview While preparing this package two principles were kept in mind. 1. To make the program as versatile as possible. 2. To make it as simple to use as possible. The versatility of the program lies in its organization. As shown in the flow chart, the program will follow the same path with the specific relationships governing each type of load in a subroutine. Therefore, if a new type of loading is desired to be considered, it can be added easily. The equations for new terminations can be included in the subroutine with very few other additions to the program. The package is written in such a way that anyone familiar with transmission line theory can run it without the use of this literature. The program displays comments and calculations on the screen to help the user choose parameters and make decisions. Errors on input data will not cause the program to fail, but will result in a prompt and message to the user. Circuit diagrams and labeling make the graphs and plots self explanatory. 4

LDO= LD = 1 L = L+l I ength T= T'+ I T=T+ 1 QEND) rl

B. User's Guide The following sections explain important aspects of running the program. For questions on the theory behind it refer to appendix A. Appendix B contains guidelines for choosing program parameters and help in troubleshooting. The Main Menu Upon entering the program the user sees the following screen. MENU Choose the line loading 1) Resistive Load 2) Capacitive Load 3) Inducative Load 4) Parallel LC Load 5) Parallel RLC Load 6) Series RLC Load 9) Exit Quickline Enter Choice The user may enter the desired load. Nine exits the program. Next, the program displays a picture of the chosen configuration and asks for confirmation. Also the program gives a choice of pulse (P) or step(s) excitation and the user has to respond accordingly. 6

RS Vi n c Is This The desired configuration(Y/N)? Do yoLt want to excite the line with a ptlse(p), or a step(s)? At this point the program automatically decides what parameters are needed for the specified load and asks for them. (See appendix B-choosing Program parameters). Exit from the program is possible at any time. Resistive Load Simulation* The resistive load simulation differs from all others. It displays moving steps (pulses) and follows these steps (pulses) until steady state. As seen in the flow chart the voltages are calculated until the reflected step (pulse) decays to zero. Then the load voltage is displayed as a function of time. This is the only simulation which allows an unmatched source resistance; all other assume that the source resistance matches the characteristic impedance of the line. Other Simulations (C,L,LC,RLC) For the more complex simulations the program calculates the time a step or pulse transits the line in and displays it. It then asks for the time at which the user wishes to see the line voltage. This time can take any value from 0 to twice the transit time as shown below. *Note - All simulations are lossless 7

The pulse can travel from end to end of the line in T1= 3.333333 ns At what t ie in nanoseconds do yoLu want to see the line vol tae(ENTER 0 -2XT1)? Upon entering the time, the line voltage is displayed. By entering a prompt the user can see the load voltage. In all simulations, the program automatically adjusts the voltage scales by the given input voltage. Printing Messages are often displayed on the screen for copying to a printer. These can be treated as reminders. Actually, the user can print the screen at any time by punching shift-Prtsc. The program waits until printing is complete. 8

Example Output Displays 9

Closed TransMission Line T>0 RS | ---VW2~1 ---- -----------— ~ Uin ' RL 20 Press key to continue U UF 10l......... UINC 08 -- ---------------------— ~....n~ I- V N -10 Uin= 10 Zo= 100 ohms Rs= 25 ohms RL= 200 ohPRESS SHIFT-PRTSC TO GET COPY Load Uoltage Response T= 3. 333333 ns Uolta e F-. L.-r -a T 3T 5T 7T Voltage Step Applied on a Transmission Line Terminated on a Resistive Load 10

Closed TransMission Line T>0 RS Vin ) - RL 200 Prtsc to print < space> to continue 100 -100 Uin= 100 Zo= 100 ohMs Rs= 50 ohMs RL= 1E+907 ohqms Closed TransMission Line T>) RS Ui n.) >RL 200 U 180 0............................ -100 Uin=_e 10 Zo= 100 ohns Rs= 50 ohMs RL= Pulse Reflecting of Load 11

Closed TransMission Line T>0 RS i. Uin > > RL r _I u 100 0 -100 Uin= 100 Zo= 100 ohms Rs= 50 ohms RL= 1E+07 ohms Load Voltage Response T= 3.333333 ns Uol tage i i II - I I Is T 5T 7T TiMe Pulse Reflecting at Generator 12

CLOSED LINE T= 600 ns Rs -Vin '" Uin () 1r L 100 U 50 Press key to continue - ii:i --- io."~ 0 Vin= 50 Zo= 100 ohms L=.01 wh PRESS SHIFT-PRTSC TO GET COPY Load Uoltage Response T= 333.3333 ns Press <space> to continue Uol tasre U.N I I i 4.... l II I.. T....- 3 — I.1 -v ti 4 5T Time Voltage Pulse Applied to Inductively Loaded Line 13

CLOSED LINE T= 1688 ns Rs Vin 25 V 12 -13 L Press key to continue....? I, V I N 580 Zo = 1880 Ohms C= I n f L=.881 mh PRES S S HI FT -PRT SC TO0 GET COPY~ Load VolItage Response T= 999. 9999 ns Vol tare Q 4 4 i, 4 1., i i I i I i II 4 li, i 3 I.1 i 4 1 d i I, I. Ji,,,i. i!, I i.I; I. i I 1 ", I.1.1.i 71 i j I I I 'l I i I! I I.1 I I i A i i i i i 4 - 0.. I t i i j., 1 1 I il!,!, I 1. I ! 1. 4 1! I q I 1 1i., i I j i i I, Ii It.; I I I I ii I il i,, v I. A t I I 11 i. 3T I I" 4 4 11 j, I 5T Time Voltage Pulse Applied to LC Loaded Line 14

Closed Line T= 6 ns Rs Uin 50 L Press key to continue II I~ U 25 -25 Uin= 100 RL=. 001 PRESS 1000 ohms CL=. 01 nf L= SHIFT-PRTSC TO GET COPY Load Uoltage Response T= 3.333333 ns Uol tare -~ -- -- -'~ 'L~U"~~UO _ - 3T Tine Voltage Step Applied to a RLC Parallel Loaded Transmission Line 15

CLOSED LINE T= 1600 ns RS Vin (I I T I 20 10 0 -10 Press key to continue ____ -—. Vin= 10 Zo= 100 ohMs Rs= 100 ohms CL= 0 nf PRESS SHIFT-PRTSC TO GET COPY Load Uoltage Response T= 999.9999 ns Press <space> to continue Uo Itage.1 I 11.k I N II.ll-ll% T 3T 5T TiMe Voltage Pulse Applied to a Capacitely Loaded Line 16

CLOSED LINE T= 1860 ns Rs ___ V-V RL Vin C L t T 10 u 5 J i q t I 1 - -5 Uin= 20 RL= 10 ohms CL=.1 nf L=.005 Mh Load Voltage Response T= 999.9999 ns Uol tare.. —,I 1 k, n T 3T 5T Tine RLC Series Configuration with Applied Voltage Step 17

APPENDIX A-THEORY In developing this program all Transmission lines are considered lossless, and the velocity of propagation is equal to the speed of light. For the resistive load case the source resistance can be chosen different from the characteristic impedance of the line; for all other cases, the source resistance is assumed to match the line. 1) Incident Voltage When a step or pulse is transmitted on a transmission line the incident voltage is given by the voltage divider between the source resistance and the characteristic impedance of the line. = V~ (z0R) v =v (. 1 nc i n (0 + RO 2) Resistive Load When the incident pulse reaches the load a portion is reflected back towards the generator given by the equation. zL - z VR = Vnc wherec =L 0 inc L 0 The resistively loaded case may have an unmatched source resistance. Then, the reflected voltage from the source will be. R - z V = where -g = ____ 18

3) Capacitive Load The reflected voltage from a capacitive load is. V = V.n R inc (1 - 2 exp(-t/CZ0)) and the load voltage is: VL Vi nc + R Vnc( 1 - exp(-t/CZo)) 4) Inductive Load The reflected voltage is: VR Vinc (-1 + 2 exp(-tZo/L)) and the load voltage is V V. +V L inc R = 2 exp(-tZo/L) 5) LC Parallel Load VR =Vnc 1 exp(-t/2Z C) 4ZL 0Zo -1 L 2 ci 4Z - L 19

if 2Z 0 -VC7L > 1 or 1 VR =i Vn c sinh4Z 2C 2Z 0C) } L 2Z 0 "GIC/L < 1 RLC La VR(t) = V.n 0u(t) 1 (~R) s in 2C (zo:R 4CR2 (~ 2R I if 2RZ 0 z0+ RC/ or VR(t) = Vi no u(t) {1 - exp( 1 Z0+ R 2CR z (R 0 R r r /X 1 - 4CR (0ZR 2 sinh C I 4CR 2 L Izo \Z0+ R) 2) 2RZQ Z0 + R 20

Series RLC VR(t) = u(t)Vinc { 1 (+ o R ) -Z0 + R ) exp ( ZL t) -.... sin 4L 1 C(Z + R) C(Z + R)2 ZL+ R (\ZL 4L 2 C(Zo + R)2 if 2 ZO + R or VR(t) = u(t)Vinc -Z + R t) 1 ( Z exp 2L R (-Zo-+ R 1 + 0 sinh 0 t_ - 4L o + R Il 4L C(Z + ) C(Zg + R)2 Zif Z0 + R /FC < 1 Responses to pulses assume u(t)V(t) is any of the responses to a step above. The response to a pulse is: VR(t) = u(t)V(t) - u(t-T)V(t-T) where t is the pulse width of the incident pulse. 21

CLOSED LINE T= 12088 ns Rs Uin 25 L Press key to continue A.; u 12 i h". -13 U IN= 5 0 Zo- 1I 0 OhMs C= 1 n f L=. 661 Mh PRESS SH I FT-PRTSC TO GET COPY CLOSED LINE T= 120 ns Rs Uin L 5 2 A.Z u -3 UIN= 10 Zo= 100 OhMs C= 1 nf L=-.001 Mh 22

APPENDIX B - CHOOSING PROGRAM PARAMETERS AND TROUBLESHOOTING. A degree of care must be taken in the choice of program parameters to give meaningful results. Due to the limits of the program's graphics, the student is advised to do some preparation. Reasonable guidlines are given below. This section will conclude with some suggestions on troubleshooting confusing results. 1) Resistive Load The simple resistive load can be simulated with no preparation. Some easily remembered guidlines are: a) Never use a pulse longer than the time it takes to traverse the line. PW < Length/3 x 108 b) For larger incident voltages make ZO > RS. 2) Capacitive Load Make the time constant 1/ZOC comparable to the time a pulse traverses the line in Z C - L/3 x 108 m/s. 0 For example with ZO 100 A, C L(meters) /3 x 1010 23

3) Inductive Load As above, make the time constant ZO/L comparable to the transit time. L(INC)/Z L(m)/3 x 108m/s Again with ZO = 100. L(INC) - L(meter)/3 x 106 4) LC Load The quantatity 2ZOC should be comparable to the time it takes to reverse the line. And: 4Z2C. 1 < 10 L With Z = 100 C - L(m)/6 x 1010 and L - C * 4 x 104 5) Parallel RLC In this case, the line. z0 2CRL x -+ R L + RL should be comparable to the transit time of 24

and: 4CR2 L Zo.1< L Z +R 0 L if Z = R 00 0 = RL 100 Then C - L(meters) 3 x 1010 L C x 1 x 104 Series RLC 2 < 10 For this load, and: 2L/(Zo+RL) should be chosen comparable to the transit time of the line, 1 < < 10 C(Z0 + RL) If ZO = RL ~ 100 L(INC) = L(meters) 3 x 10 C L x 0-4 C - L x l0 25

CLOSED LINE T= 1200 ns Rs Uin 25 L U 12 -13 UIN= 50 Zo= 100 Ohms C= 1 nf L=. 001 lh CLOSED LINE T= 600 ns Rs Uin L 5 2 U -.A -3 26

TROUBLESHOOTING 1) If a very large source resistance is used with a open or shorted load, the simulation may run for a very long time. If this occurs you can CTRL-Break and then rerun the program. 2) If in a simulation (L,C,LC,RLC) too long a line is used for the other parameters diagram A.1 may result. To correct simply rerun again with a shorter line and do not change other parameters as shown in B.1. 3) If too short a line is used A.2 may result. Rerun again with a longer line and do. not change other parameters (B.2). 27