Question 19.5: Find the hybrid parameters for the two-port network of Fig. ......

To find h_{11}   and  h_{21}   , we short-circuit the output port and connect a current source I_{1}   to the input port as shown in Fig. 19.23(a). From Fig. 19.23(a),

V_{1}  =  I_{1} (2  +  3 \parallel  6) =  4I_{1}

Hence,

h_{11}  =  \frac{V_{1}}{I_{1}} =  4  Ω

Also, from Fig. 19.23(a) we obtain, by current division,

– I_{2} =  \frac{6}{6  +  3} I_{1}  = \frac{2}{3} I_{1}

Hence,

h_{21}  =  \frac{I_{2}}{I_{1}} = – \frac{2}{3}

To obtain h_{12}   and  h_{22}   , we open-circuit the input port and connect a voltage source  V_{2} to the output port as in Fig. 19.23(b). By voltage division,

V_{1}  =  \frac{6}{6  +   3} V_{2}  =  \frac{2}{3} V_{2}

Hence,

h_{12}  = \frac{V_{1}}{V_{2}} =  \frac{2}{3}

Also,

V_{2}  =  (3  +  6)I_{2}  =  9I_{2}

Thus,

h_{22}  =  \frac{I_{2}}{V_{2}} =  \frac{1}{9} S