EE361 Lab3 Assignment

7/28/2019 EE361 Lab3 Assignment

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EE361

Lab 3: Transients on Transmission Lines

1. IntroductionWe have thus far focused on techniques for understanding transmission lines under

sinusoidal excitation. Powerful analytic insight is available here, permitting

straightforward design of interesting circuits.

In contrast, the analysis of transients is generally more difficult and less amenable to

simple closed-form analysis, especially when loads are reactive. This laboratory will

explore the propagation of transients on transmission lines with the aid of numericalexperiments in SPICE.

2. Purely Resistive Termination

First, let's use SPICE to investigate the propagation of pulses on a transmission lineterminated by purely resistive loads.

2.1 A step function, matched load

First, create a 50 transmission line with total length (time delay) of 25 ns, and excite it

with a Thevenin source 10u(t), with a source resistance Rg = 50 . With the loadresistanceRL = 50 , run the simulation.

To create the voltage source, use the VPWL source. Using VPWL allows various times

and the voltages at those times to be specified using the T1, T2, T3, ... and V1, V2, V3, ...parameters. The voltage source will be piece-wise linear, connecting each specified point.

Using VPULSE allows specification of the initial voltage, V1, the voltage of the pulse,

V2, the delay time, TD, the rise time, TR, the fall time, TF, the pulse width, PW, and the

period, PER.

The VPWL source is piece-wise linear and allows the user to specify voltages at specific

times using T1, T2, T3 and the corresponding V1, V2, V3 parameters. Please note thatthe source will connect each specified point in the most direct way. Additionally, two

voltages cannot be specified for the same time, so that instantaneous changes must be

approximated.


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For Example: to specify a VPWL source that produces a 10 V square pulse starting at t=0

and lasting for 10 ns, would have the following specified parameters: T1=0, V1=0,

T2=0.001n, V2=10, T3=10n, V3=10, T4=10.001n, V4=0. (Making V3=0 would form asawtooth wave because of the reasons stated above.)

Using VPULSE allows specification of an initial voltage, V1, the voltage of the pulse, V2,the delay time, TD, the rise time, TR, the fall time, TF, the pulse width, PW, and theperiod, PER. Single pulses can be formed with this source. More complex signals can be

formed by combining multiple sources.

Problem 1 Plot the voltage at the source and load ends of the transmission line for t =

050 ns. Using your understanding of bounce diagrams, explain whether this plot

makes sense and shows what you would expect to see in the exact answer. Do the two

agree? If not, why not? A full credit answer will describe the bounce diagram until areasonable (whatever you consider reasonable) number of bounces, which can explain

what exactly is happening in this situation. Please do the same in any other bounce

diagram questions that may follow.

2.2 A step function, mismatched load

Now, change the load impedance in the previous case to 20 .


0100 ns. Using your understanding of bounce diagrams, compare this with what you

would expect to see in the exact answer. Do the two agree? If not, why not? How longdoes it take the answer to settle to the final answer?

2.3 A step function, mismatched load and source

Now, change the load impedance in the previous case to RL=20 , and change the sourceimpedance toRg=200 .


0300 ns. Using your understanding of bounce diagrams, compare this to the exactanswer. Do the two agree? If not, why not? How long does it take the answer to settle

down to the final answer?

2.4 A short pulse

Now break the transmission line into two equal pieces, with total length 25 ns (youshould now have two different transmission lines, both with the same 50 characteristic

impedance, but each with a time delay of only 12.5 ns). This permits us to sample


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inside the transmission line. With the same transmission line, and Rg=200 and

RL=20 apply a pulse of duration 10 ns to the transmission line, namely vg(t) = 10(u(t)-

u(t-10ns)).

Problem 4 Plot the voltage at the source, middle, and load ends of the transmission

lines for t = 0100 ns. Sketch the bounce diagram; do you understand the voltage plots?How long before the ghost pulse (the pulse you are seeing at the middle of thetransmission line) arrives at the load end? How large is the ghost pulse?

2.5 A longer pulse

In the previous problem, the pulse was brief (10 ns) compared to the length of thetransmission line (25 ns). Now investigate a more complicated system.

Problem 5 Using the same transmission line and source impedance, define a new

source for which vg= +10 V for t = 0 20 ns, and gv V for t = 20 40ns. Plotthe voltage at the source, center, and load end of the transmission line for t = 0100 ns.Is the transition from high to low perfectly clear at the load end?

2.6 An Impedance Bump

Transmission lines must be protected against damage, or their impedance propertiescould be compromised. In this section well damage the transmission line by putting a

weak load in the middle. In particular, at the center of the transmission line, add a shunt

resistance of 50

(a shunt resistance connects the node at the middle to ground).

Problem 6 With the shunt resistance in place, repeat the previous problem. How did

the presence of the bump (break in the transition line) affect the voltage plots? Did any

new ghosts show up? Looking only at the source and end voltages, could youdetermine where the bump is? Can you explain what you see in terms of a bounce

diagram?

3. Reactive Termination

As mentioned in class, it is frequently the case that the loads at the end of a data bus arereactive (and often capacitive).

3.1 A step into a capacitive load

For this exercise, again form a circuit with a source vg(t) = 10u(t), a source impedance

Rg=25 , and a transmission line with characteristic impedance 50 and length 25ns.


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Problem 7 Terminate the transmission line with a 1 nF capacitor. Plot the voltage at

the source and load ends of the transmission line for t = 0400ns. If you see any

exponential charging or discharging, estimate the time constant, and solve for the R.

You may use the following formulas.

Problem 8 Repeat the previous problem, but with a load capacitance of 100 pF.

Problem 9 Repeat the previous problem, but with a load capacitance of 10 nF.

Problem 10 Repeat the previous problem, but with a load inductance of 2.5 H.

Problem 11 Repeat the previous problem, but with a load inductance of 0.25 H.

Problem 12 Repeat the previous problem, but with a load composed of a parallel

combination ofRL=1000 ,L= 1 H and C= 100 pF.

Problem 13 How important is the value ofRgin these exercises?

4. Coupling

Many data buses are in parallel, in close proximity, such as the 32 bit and 64 bit buses

found in computers. These transmission lines will have mutual impedance which

causes signals on one transmission line to show up on another one.

In EE571 students analyze this coupling in great detail, but we can simulate a simplified

model of a two-wire data bus using SPICE1:

1 Note that your SPICE library contains a model for coupled lines; you could use this, but it does the

modeling with an explicit form of the Telegraphers Equation, and is painfully slow. I tried to use it, but

realized that it would take about one day to run every simulation!


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Here T1 and T4 represent the actual transmission lines, while T2 and T3 represent thecross coupling. The coupling is slightly faster (95 ns instead of 100 ns) and has a higher

characteristic impedance.

Connect a thevenin signal pulse (10 V, 50 ) to A and 50 loads to B, C and D2.

4.1 A simple pulse

Inject a 10ns pulse with the thevenin source at A. Use a rise and fall time of 1ns.

Problem 14 Simulate the problem for 250 ns, and plot the voltage at A, B, C, and D.

Describe what you observe. How big is the VC compared to VD when the pulse arrives?

Which arrives first?

Problem 15 When does a signal arrive at B? If you change the values of the load

resistances at C and D, can you eliminate the reflection? If so what value should the load

have?

5. Impedance Matching

5.1. Pre-lab Assignment

5.1. A. Design a quarter-wave transformer to match a 150 load to a source resistance

of 75 . State the length of your transmission line(s) in terms of the wavelength.

5.1. B. Using the Smith Chart, if the characteristic impedance is given as 75 , design a

stub-matching network to match a 150 load to a 75 source. Do this for both a shorted

2 To make this model even closer to the real thing, the signal injected into T2 should have opposite sign of

that injected into T1. However, this lab will not require this.


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EE361 Lab3 Assignment

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