vị(t)u(t) + R L eeeee C + vo(t) See the dynamic RLC circuit shown above. It has a time dependent input of vi(t)u(t). A. Redraw the CCT in the s-domain labeling polarities, current directions, and circuit variables. Assume zero initial conditions and label nodes if node voltage analysis is used. B. Derive the transfer function, T(s), from Vi(s) to Vo(s) by combining and reducing the rightmost parallel inductor and capacitor branches into an equivalent impedance. (Hint: create series circuit and use voltage division) Help on part C: C. At the output interface, derive the Thévenin equivalent voltage, VT (s) using the transfer function. Then use the lookback method to derive the Thévenin equivalent impedance, ZT (s), at the output.

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v¡(t)u(t)
R
L
00000
ellee
L
R
C
vo(t)
See the dynamic RLC circuit shown above. It has a time dependent input of vi(t)u(t).
A. Redraw the CCT in the s-domain labeling polarities, current directions, and circuit variables.
Assume zero initial conditions and label nodes if node voltage analysis is used.
B. Derive the transfer function, T(s), from Vi(s) to Vo(s) by combining and reducing the rightmost
parallel inductor and capacitor branches into an equivalent impedance. (Hint: create series circuit
and use voltage division)
Help on part C:
C. At the output interface, derive the Thévenin equivalent voltage, VT (s) using the transfer function.
Then use the lookback method to derive the Thévenin equivalent impedance, ZT (s), at the output.
Transcribed Image Text:v¡(t)u(t) R L 00000 ellee L R C vo(t) See the dynamic RLC circuit shown above. It has a time dependent input of vi(t)u(t). A. Redraw the CCT in the s-domain labeling polarities, current directions, and circuit variables. Assume zero initial conditions and label nodes if node voltage analysis is used. B. Derive the transfer function, T(s), from Vi(s) to Vo(s) by combining and reducing the rightmost parallel inductor and capacitor branches into an equivalent impedance. (Hint: create series circuit and use voltage division) Help on part C: C. At the output interface, derive the Thévenin equivalent voltage, VT (s) using the transfer function. Then use the lookback method to derive the Thévenin equivalent impedance, ZT (s), at the output.
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