Question 19.15: Find the h parameters of the network in Fig. 19.49.
Find the h parameters of the network in Fig. 19.49.
From Eq. (19.16),
(19.16): \pmb{h} _{11}=\left.\frac{ \pmb{V} _1}{ \pmb{I} _1}\right|_{ \pmb{V}_2=0}, \quad \pmb{h} _{12}=\left.\frac{ \pmb{V} _1}{ \pmb{V} _2}\right|_{ \pmb{I} _1=0} \\ \pmb{h} _{21}=\left.\frac{ \pmb{I} _2}{ \pmb{I} _1}\right|_{ \pmb{V} _2=0}, \quad \pmb{h} _{22}=\left.\frac{ \pmb{I} _2}{ \pmb{V} _2}\right|_{ \pmb{I} _1=0}
\pmb{h} _{11}=\left.\frac{ \pmb{V} _1}{ \pmb{I} _1}\right|_{ \pmb{V}_2=0}, \quad \pmb{h} _{21}=\left.\frac{ \pmb{I} _2}{ \pmb{I} _1}\right|_{ \pmb{V} _2=0}
showing that \pmb{h}_{11} \text{ and } \pmb{h}_{21} can be found by setting \pmb{V_2} = 0. Also by setting \pmb{I}_1 = 1 A, \pmb{h}_{11} \text{ becomes } \pmb{V_1}/1 \text{ while } \pmb{h}_{21} \text{ becomes } \pmb{I}_2/1. With this in mind, we draw the schematic in Fig. 19.50(a). We insert a 1-A dc current source IDC to take care of \pmb{I}_1 = 1 A, the pseudocomponent VIEWPOINT to display \pmb{V_1} and pseudocomponent IPROBE to display \pmb{I_2} . After saving the schematic, we run PSpice by selecting Analysis/Simulate and note the values displayed on the pseudocomponents. We obtain
\pmb{h} _{11}=\frac{ \pmb{V} _1}{1}=10 \Omega, \quad \pmb{h} _{21}=\frac{ \pmb{I} _2}{1}=-0.5
Similarly, from Eq. (19.16),
\pmb{h} _{12}=\left.\frac{ \pmb{V} _1}{ \pmb{V} _2}\right|_{ \pmb{I}_1=0}, \quad \pmb{h} _{22}=\left.\frac{ \pmb{I} _2}{ \pmb{V} _2}\right|_{ \pmb{I} _1=0}
indicating that we obtain \pmb{h}_{12} \text{ and } \pmb{h}_{22} by open-circuiting the input port (\pmb{I}_1 = 0). By making \pmb{V_2} = 1 V, \pmb{h}_{12}\text{ becomes }\pmb{V_1}/1 \text{ while } \pmb{h}_{22} \text{ becomes } \pmb{I}_2/1.
Thus, we use the schematic in Fig. 19.50(b) with a 1-V dc voltage source VDC inserted at the output terminal to take care of \pmb{V_2} = 1 V. The pseudocomponents VIEWPOINT and IPR OBE are inserted to display the values of \pmb{V_1} \text{ and } \pmb{I_2}, respectively. (Notice that in Fig. 19.50(b), the 5-Ω resistor is ignored because the input port is open-circuited and PSpice will not allow such. We may include the 5-Ω resistor if we replace the open circuit with a very large resistor, say, 10 MΩ.) After simulating the schematic, we obtain the values displayed on the pseudocomponents as shown in Fig. 19.50(b). Thus,
\pmb{h} _{12}=\frac{ \pmb{V} _1}{1}=0.8333, \quad \pmb{h} _{22}=\frac{ \pmb{I} _2}{1}=0.1833 S
