ECE 2100
Spring 2010
Homework assignment 6
Due May 8, 2010
Covered: Chapters 1113:
Laplace transforms, impulse functions, partial fractions,
transfer functions, initial, final value theorems, poles/zeros, passive filters, active filters,
Bode plots.
1. Prelab
: Considering the following RLC filter circuit.
a) Derive a voltage transfer function
H(s)=Vout/Vin
for the circuit.
Where are it’s poles
and zeros?
b) Add a series resistance for the inductor of 2.3
Ω
and derive the voltage transfer
function
H(s)
including the effects of the inductor series resistance.
Where are the poles
and zeros now?
c) Now, in the frequency domain (s = j
ω
), plot on an expanded linear frequency scale
(about resonance) the magnitude of the voltage transfer function [
H(j
ω
)
] in decibels with
and without the inductor series resistance. What is its effect here? On these plots illustrate
the circuit's bandwidth and resonant frequency.
d) Plot with a normal Bode magnitude presentation the voltage transfer function
magnitude of the circuit!
The frequency range should be from
100
to
10
5
Hz.
2. Prelab
: consider the active RC filter shown.
a) Derive the transfer function H(s).=Vout/Vin
b) What are the locations of the poles and zeros of this circuit?
c) Plot the Bode plot of H(j
ω
) for the frequency range
100
to
10
5
Hz.
Show both
magnitude and phase.
Name this circuit.
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3. Prelab
: Equalizer design:
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 Spring '05
 KELLEY/SEYLER
 Signal Processing

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