Download EX: a) Draw a frequency-domain circuit model for the above circuit. b

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Transcript
QUIZ 4 PROBLEM 2 SOLUTION
1250
F 14
EX:
a)
Draw a frequency-domain circuit model for the above circuit.
b)
Find the Thevenin equivalent of the above circuit in the frequency domain.
That is, find the phasor value, VTh, and the impedance, zTh.
SOL'N: a) We use a phasor for the current source, and convert the other components
to impedance values.
b) To find zTh, we can turn off the independent source and look in from the a
and b terminals.
The L and C are in series with each other, and that impedance is in parallel
with R.
zTh = ( j2k − j1k) ||1k Ω = j1k ||1k Ω
or
zTh = 1kΩ ⋅ j ||1= 1kΩ ⋅
j(1)
j
= 1kΩ ⋅
j +1
1+ j
or
zTh = 1kΩ ⋅
j 1− j
1+ j
⋅
= 1kΩ ⋅
= 500Ω + j500Ω
1+ j 1− j
2
To find VTh, we find the voltage across the a, b terminals. Our circuit is a
current divider, with currents I1 and I 2.
The branch with current I 1 has impedance R + jωL, and the other branch
has impedance –j/ωC.
I1 = I s
− j1kΩ
−j
−j
= Is
= Is
1kΩ + j2kΩ − j1k Ω
1 + j2 − j
1+ j
or
I1 = 10e
j0° e
− j90°
2e
j 45°
mA = 5 2e− j135° mA
Using Ohm's law, we find the voltage from a to b from the current.
VTh = I1R = 5 2e− j135° mA ⋅1kΩ = 5 2e− j135° V