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Impedance Parameter Model

From equation (71) it is easy to find the impedance parameters for the transformer in the s-domain. We assume zero initial conditions. Then we have

$$\begin{array}{rl} V_1(s) & = sL_1 I_1(s) + sM I_2(s) \\ \\ V_2(s) & = sM I_1(s) + sL_2 I_2(s) . \end{array}$$ (72)

In an AC circuit calculation, we use the phasor version:

$$\begin{array}{rl} {\mathbf V_1} & = j\omega L_1 {\mathbf I_1 ... ...omega M {\mathbf I_1} + j \omega L_2 {\mathbf I_2}. \end{array}$$ (73)