AC circuits

Assume V(t),  I(t), e(t) are all proportional to .

Assume idealized circuit elements.  Define the impedance Z as  . Then

Kirchhoff’s rules for filamentary circuits:

For each loop   for each node   

Thévenin equivalent circuits: Any two terminal network can be replaced by a generator e_eff in series with an impedance Z_eff.

Norton equivalent circuits: Any two terminal network can be replaced by a current source I_eff in parallel with an impedance Z_eff.

The maximum power is delivered to a load when Z_load=Z_eff*.

Ladder networks:

Consider an infinite ladder network of elements as shown.

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.