EELE 461/561 – Digital System Design
Homework #3
Name:
________________
Grade (EELE461): ________ / 10
Grade (EELE561): ________ / 15
NOTE: Print this sheet and use as a cover for your homework set.
EELE 461 & EELE 561
A) Verifying the Sum-of-Squares System Risetime Rule-of-Thumb
(2 POINTS)
You have an RC circuit (R=50ohms, C=2pF) that is being driven with a source risetime of 100ps. Calculate the
system risetime by hand. Then use DxDesigner to prove the accuracy of your hand calculation. Use the v_exp
source in the SpicePrimative library in DxDesigner to drive your RC circuit. This component allows you to
enter a time constant for the step voltage. Print out your simulation waveforms showing the input exponential
source risetime (100ps) and the system output risetime on the same plot. Put risetime measurements on both the
input and output waveforms. Clearly mark what the system risetime is. Remember when you print the
waveform you can turn the background to "white" to make the plot more readable. Enter both results below.
Hand Calculation for tsys = _______________
Simulation Result for tsys = _______________
B) FFT of a Square Wave
(2 POINTS)
Use DxDesigner to perform an FFT of a 3.125 GHz square wave driving an RC circuit (R=50ohms, C=1pF).
The procedure for performing an FFT is outlined in the SPICE tutorial on the course website. Produce a plot
with the magnitude of the FFT of the input square wave (ideal edges), and the magnitude of the FFT of the
output square wave. You can select magnitude under the "advanced" options in the FFT window. Plot the
FFTs out to 40GHz. Change the background to white. You should see the input square wave FFT harmonics
having a magnitude following 2/(n·π) while the output FFT harmonics will be attenuated by the RC circuit.
Place markers on each harmonic so that the magnitudes of each are clearly visible. Increase the line width of
the waveforms to 3 to make them easier to see. Your FFT results should look like the plot below. Print out
your schematic, transient waveforms showing 10 periods of the square wave, and your FFT results.
C) Reflections on a Transmission Line (RS < Z0, RL=∞)
(3 POINTS)
You are going to analyze the following distributed system where RS =25 & Z0=50. You will need to simulate
the following configuration in DxDesigner. Run the transient simulation for 10ns plotting Va and Vb on the
same plot. There is an ideal T-line model in DxDesigner called "t" that you will use where you can specify
TD=1ns and Z0=50. Use an ideal voltage step (v_pulse). To model an open circuit at the end of the
transmission line, use a 1Meg resistor.
For this circuit, provide the analytical solution for the voltages (i.e., by hand) for the first three major events in
transient response. Clearly mark these three events on the simulation plot showing the resultant voltages using
cursors.
Event #1: The initial voltage observed on Va at t=0ns.
Event #2: The voltage observed at Vb at t=1ns.
Event #3: The voltage observed at Va at t=2ns.
D) Reflections on a Transmission Line (RS > Z0, RL=∞)
(3 POINTS)
Repeat the analysis from part C on the following circuit where RS =100 & Z0=50. Again, provide the analytical
solution for the voltages (i.e., by hand) for the first three major events in transient response. Clearly mark these
three events on the simulation plot showing the resultant voltages using cursors.
Event #1: The initial voltage observed on Va at t=0ns.
Event #2: The voltage observed at Vb at t=1ns.
Event #3: The voltage observed at Va at t=2ns.
EELE 561 Only
E) Dispersion refers to when different frequencies travel through a medium at different velocities. This can be
detrimental to digital signals because harmonics of a square wave will be out of phase and lead to a distorted
signal at the receiver. Create a simulation of the effect of dispersion in DxDesigner by building a 1 GHz square
wave using sinusoidal sources in series. Provide frequencies up to the 11th harmonic. For each successive
harmonic, increase the delay by 100ps (i.e., t_delay(f0)=0ps, t_delay(f3)=100ps, t_delay(f3)=200ps, etc...
Provide a print out of your schematic, the original square wave (i.e., no dispersion) and the final square wave.
Your schematics and results should look similar to this:
(5 POINTS)