ECE 2100 Homework 4
Due April 1, 2010
Professor Alyosha Molnar
Subjects: Sinusoidal steadystate analysis, phasors, complex impedance, complex circuit
analysis, AC power transfer, transformers, mutual inductance.
1)
Prelab: Looking at the overlaid input/output sinewaves below, extract:
2.5
2
1.5
1
0.5
0
0.5
1
1.5
2
2.5
0
0.2
0.4
0.6
0.8
1
1.2
time, microseconds
Voltage
Input
Output
a.
The frequency in Hz.
b.
The frequency in radians per second.
c.
The change in amplitude between input and output (that is the ratio of
output to input amplitudes)
d.
The change in phase between input and output (Remember that time delay
corresponds to negative phase)
e.
Write the transformation from input to output as a phasor, and as a
complex number.
That is, Vout = (A+jB)Vin.
What are A and B?
2)
Prelab: You will be analyzing the impedance and voltagedivision characteristics
of a several “black box” circuits in lab.
Several example circuits are given below.
In each case analyze the impedance across each pair of terminals (a complex
number, as a function of
ω
), and in particular analyze Z for f=0Hz.
Also use
voltage divider analysis to find the phase and amplitude of V
2
for
V
1
=1V·cos(2
π
ft), as a function of f, and find it explicitly for f=1kHz and 100kHz.
Also, find the frequency (in the range from 1kHz to 100kHz) at which the
amplitude of V
2
is maximized.
Perform the same analyses for V
1
when
V
2
=1V·cos(2
π
ft).
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Pure resistors: analyze the circuit in Fig. 2a
i.
What are Zac, Zbc and Zab?
What are they at f=0Hz?
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 Fall '05
 KELLEY/SEYLER
 Impedance, Resistor, Electrical impedance, ZBC, Book problem, voltage divider results

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