This module describes how to find the Thevenin and Norton
equivalent circuits of an RLC circuit and sources.
When we have circuits with capacitors and/or inductors as wellas resistors and sources, Thévenin and Mayer-Norton
equivalent circuits can still be defined by using impedances andcomplex amplitudes for voltage and currents. For any circuit
containing sources, resistors, capacitors, and inductors, theinput-output relation for the
complex amplitudes of
the terminal voltage and current is
with
.
Thus, we have Thévenin and Mayer-Norton equivalentcircuits as shown in
[link] .
Let's find the Thévenin and Mayer-Norton equivalent circuitsfor
[link] . The open-circuit voltage and
short-circuit current techniques still work, except we useimpedances and complex amplitudes. The open-circuit voltage
corresponds to the transfer function we have alreadyfound. When we short the terminals, the capacitor no longer
has any effect on the circuit, and the short-circuit current
equals
.
The equivalent impedance can be found by setting the source tozero, and finding the impedance using series and parallel
combination rules. In our case, the resistor and capacitor arein parallel once the voltage source is removed (setting it to
zero amounts to replacing it with a short-circuit). Thus,
.
Consequently, we have
Again, we should check the units of our answer. Note in
particular that
must be dimensionless. Is it?
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