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ECE 391: Transmission Lines
Winter Term 2024
Homework Assignment #1
due Friday, Jan. 19, 3pm
1. A SiGe digital chip has a rise and fall time of about 40ps. On a PCB with a Teflon
dielectric (ϵr = 2.33), up to what lengths (in mm) can transmission line effects be ignored?
(Assume an effective dielectric constant equal to the dielectric constant.) How does your
result change if you use an FR4 PCB with ϵr = 4.5?
2. Consider the following two resistor components:
(i) 1/4W axial leaded resistor (length = 6.5 mm, diameter = 2.5 mm)
(ii) 0402 SMD resistor
Assume that these elements will be used in an RF circuit with sinusoidal excitation.
Further, assume the velocity of propagation across the elements is equal to 0.66c, where
c = 3e8 m/s. For each component, compute the upper frequency below which it can
safely be considered to be a lumped element. Use the component body size versus lambda
criterion (d/λ < 0.01).
3. You want to connect a pulse generator (5V, 1ns rise and fall times, 10 ns pulse width,
200 ns period, 50Ω source resistance) to the input of an amplifier (Rin = 1 MΩ) via a 3
meter long coaxial cable. Instead of a 50Ω coaxial cable, you only have a 75Ω coaxial cable
available from your cable TV setup. Using computer simulation, determine and plot the
voltage response across the load resistor for 0 ≤ t ≤ 200 ns. Assume the wave velocity on
the coaxial line as vp = 15cm/ns. Show the circuit diagram implemented in the simulator
and the plot of the voltage waveform at the input of the amplifier. Also simulate the
voltage response across the load resistor R if you have available a 50Ω coaxial cable (same
wave velocity) and compare with the results obtained for the 75Ω coaxial cable. Discuss
your observations.
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