This circuit contains coupled coils. These coils are represented by three parameters: the primary inductance L1, the secondary inductance L2 and the mutual inductance M. (The primary coil is the coil on the left. The secondary coil is on the right.) The coupling coefficient, k, of coupled coils is defined as
The coupling coefficient must satisfy .
The input to this circuit is the voltage
provided by the voltage source. The response, or output, of the circuit is the voltage vo(t).
To analyze this circuit, first model it in the frequency domain using phasors and impedances:
Next, write mesh equations:
Eliminating I1(), and doing some algebra provides the network function
describes the relationship between the phasors corresponding to the input, vs(t), and the output, vo(t).
The steady state response of this circuit is given by
In this case , A=5, R1=8, and R2=12 this simplifies to