Question 17.7: Find the t-parameters of the two-port network in Figure 17–1......

With the output open (-I_{2} = 0), we use KVL to write V_{1} = V_{2} and V_{2} = Z_{1}I_{1}. Hence

A = \frac{V_{1}}{V_{2}}|_{-I_{2}=0}= 1       and       C = \frac{I_{1}}{V_{2}}|_{-I_{2}=0}= \frac{1}{Z_{1}}

With the output shorted (V_{2} = 0), we use current division and KVL to write

-I_{2} = \frac{Z_{1}}{Z_{1}  +  Z_{2}}I_{1}      and      V_{1} = Z_{2}(-I_{2})

hence

D = \frac{I_{1}}{-I_{2}}|_{V_{2}=0}= \frac{Z_{1}  +  Z_{2}}{Z_{1}}      and       B = \frac{V_{1}}{-I_{2}}|_{V_{2}=0}= Z_{2}

Note that this two-port network is reciprocal since

AD  –  BC = \frac{Z_{1}  +  Z_{2}}{Z_{1}}  –   \frac{Z_{2}}{Z_{1}}= 1