Two Port Networks – GATE ECE Network Theory Practice Questions & PYQs – Page 2 | BattleExam | BattleExam

A two-port network shown below is excited by external dc sources. The voltages and the currents are measured with voltmeters $V_1, V_2$ and ammeter $A_1, A_2$ (all assumed to be ideal), as indicated. Under following switch conditions, the readings obtained are: (i) $S_1$ -Open, $S_2$ -Closed $A_1$ =0A, $V_1$ =4.5V, $V_2$ =1.5V, $A_2$ =1A (ii) $S_1$ -Closed, $S_2$ -Open $A_1$ =4A, $V_1$ =6V, $V_2$ =6V, $A_2$ =0A The h-parameter matrix for this network is

🚀 Solve in Practice Mode

📖 Explanation

\begin{aligned} V_{1} &=h_{11} I_{1}+h_{12} V_{2} \\ I_{2} &=h_{21} I_{1}+h_{22} V_{2} \\ h_{12} &=\left.\frac{V_{1}}{V_{2}}\right|_{I_{1}=0}=\frac{4.5}{1.5}=3 \\ h_{22} &=\left.\frac{I_{2}}{V_{2}}\right|_{I_{1}=0}=\frac{1}{1.5}=0.67 \\ h_{11}&=\left.\frac{V_{1}}{I_{1}}\right|_{V_{2}=0} \\ \text{When} \quad V_{2}&=0, Z_{21} I_{1}+Z_{22} I_{2}=0 \\ I_{2}&=-\frac{Z_{21} I_{1}}{Z_{22}}\\ \Rightarrow \quad V_{1}&=Z_{11} I_{1}+Z_{12}\left(-\frac{Z_{21} I_{1}}{Z_{22}}\right) \\ \Rightarrow \quad \frac{V_{1}}{I_{1}}&=\left(Z_{11}-\frac{Z_{12} Z_{21}}{Z_{22}}\right)=h_{11} \\ \Rightarrow \quad h_{11}&=1.5-\frac{4.5 \times 1.5}{1.5}=-3 \\ \Rightarrow \quad h_{21}&=\left.\frac{I_{2}}{I_{1}}\right|_{V_{2}=0}=\frac{-Z_{21}}{Z_{22}} \\ &=\frac{-1.5}{1.5}=-1 \\ \end{aligned}

So, h-parameter matrix is

\left[\begin{array}{cc}-3 & 3 \\ -1 & 0.67\end{array}\right]