Passive circuit elements:
Resistor: V = IR; Capacitor: V = Q/C; Inductor: V = LdI/dt.
Assume V(t), I(t), ε(t) are all proportional to exp(iωt).
Assume idealized circuit elements. Define the impedance Z = V/I. Then
Kirchhoff’s rulesfor filamentary circuits:
For each loop for each node
Any two-terminal network of passive elements is equivalent to an effective impedance Zeff.
Thévenin equivalent circuits: Any two terminal network can be replaced by a generator εeff in series with an impedance Zeff.
Norton equivalent circuits: Any two terminal network can be replaced by a current source Ieff in parallel with an impedance Zeff.
Pavg = (1/2)Re(VI*) = I2rmsR. The maximum power is delivered to a load when Zload = Zeff*.
Consider an infinite ladder network of elements, for example the network shown below.
The network is equivalent to a network terminated by Z0, if
If Z0 is real the circuit absorbs energy, if Z0 is imaginary, it does not absorb energy. If Z0 is real signals can pass to the load, if Z0 is imaginary, signals cannot pass to the load, we have a filter.