# EE43005300 Microwave and RF circuits by sofiaie

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```									EE4300/5300 Microwave and RF circuits

Homework #3 Due Wednesday March 1st

1. a) Find the high frequency model of a 500  resistor with 2.5 cm copper wire connections (radius =
.2032 mm) and a stray capacitance Ca of 5 pF. Give an expression for the equivalent impedance.
b) Plot using Mathcad (EE5300) or sketch (EE4300) the impedance magnitude as a function of
frequency (use a frequency range of 106 – 1011 Hz and a log-log plot).

2. a) Find the high-frequency model of a 100 pF capacitor whose dielectric medium consists of an
aluminum oxide with a loss tangent of 10-4 (assumed to be frequency independent) and whose leads are
0.5 cm long copper wires with radius of 0.0508 mm. Give an expression for the equivalent impedance.
b) Plot using Mathcad (EE5300) or sketch (EE4300) the impedance magnitude as a function of
frequency (use a frequency range of 106 – 1011 Hz). In your plot also include the ideal behavior of the
capacitor.
c) (EE5300 only) Derive an expression for the self-resonant frequency (SRF) of the capacitor in terms
of the elements in the model. Find the SRF of this capacitor.
d) Derive an approximate expression for the self-resonant frequency (SRF) by assuming the losses in
the dielectric are negligible. Find the SRF using this expression.

3. Calculate the effective dielectric constant for a parallel plate transmission line filled partially with a
dielectric medium as shown below.


r                 d
r           xd

4. A copper microstrip line is to be designed for a characteristic impedance of 50 . The substrate
thickness is 0.16 cm, r = 2.2 and the frequency of operation is 5 GHz. Do NOT use Ansoft Designer to
solve this problem.
a) Find the width of the microstrip line (W)
b) Find the wavelength on this transmission line.
c) If the microstrip line is 16 long with tan  = 0.001, find the signal attenuation in dB.

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