Figure: Obtain $h$-parameter of inter connected network.

Solution:

Given circuit consist of 2 tur port networks connected in SIPO mode considering neatwork-1.

KVL to loop (1)

$\begin{aligned} \\ &V_1(s)-10 I_1(s)-4\left(I_1(s)+I_2(s)\right)-3 V_x(s)=0 \\\\ &V_1(s)-14 I_1(s)-4 I_2(s)-3\left(10 I_1(s)\right)=0 \\\\ &V_1(s)=44 I_1(s)+4 I_2(s)...(1) \\\\ &K V L \text { to } 100 \\\\ &V_2(s)-8 I_2(s)-4\left[I_2(s)+I_1(s)-3 \cdot V_x(s)=0\right. \\\\ &V_2(s)-4 I_1(s)-12 I_2(s)-3\left(10 I_1(s)\right)=0 \\\\ &V_2(s)=+34 I_1(s)+12 I_2(s)...(2) \\ \end{aligned} \\ $

$\begin{aligned} \\ &\text { Reammanging eq-n. (2) }\\\\ &12 I_2(S)=-34 I_1(S)+V_2(S)\\\\ &I_2(s)-\frac{-17}{6} I_1(s)+\frac{1}{12} V_2(s)....(3)\\\\ &\text { put } e q q^{-n} \text { (3) in (1) }\\\\ &V_1(s)=44 I_1(s)+\frac{-34}{3} I_1(s)+\frac{1}{3} V_2(s)\\\\ &V_1(s)=\frac{9.8}{3} I_1(S)+\frac{1}{3}-V_2(S).....(4)\\\\ &\text { from } \mathrm{eq}^{-} \text {(3) and (4) }\\\\ &\left[\begin{array}{cc} h_{11}^{\prime} & h_{12}^{\prime} \\\\ h_{21}^{\prime} & h_{22}^{\prime} \\ \end{array}\right]=\left[\begin{array}{cc} \frac{98}{3} & \frac{1}{3} \\\\ \frac{-17}{6} & \frac{1}{12} \\ \end{array}\right]....(5)\\ \end{aligned}\\ $

$\text { Now considering circuit }-2 \\ $

$K V L$ to loop (1)

$\begin{aligned} \\ &V_1(s)-2 I_1(s)-\frac{6}{5}\left(I_1(s)+I_2(s)\right)=0 \\\\ &V_1(s)-\frac{16}{5} I_1(s)-\frac{6}{5} I_2(s)=0 \\ \end{aligned} \\ $

$\begin{aligned} \\ &V_1(9)=\frac{16}{5} I_1(9)+\frac{6}{5} I_2(5)....(6)\\\\ &K V L \text { to loop. (2) }\\\\ &V_2(S)-3 I_2(S)-\frac{6}{5}\left(I_2(S)+I_1(S)\right)=0\\\\ &V_2(S)-\frac{6}{5} I_1(S)-\frac{21}{5} I_2(S)=0\\\\ &V_2(s)=\frac{6}{5} I_1(S)+\frac{21}{5} I_2(s)...(7)\\\\ &\text { Rearranging eq-n (7) }\\\\ &\frac{21}{5} I_2(S)=\frac{-6}{5} I_1(S)+V_2(S)\\\\ &I_2(S)=-\frac{2}{7} I_1(S)+\frac{5}{21} V_2(s) ...(8)\\ \end{aligned} \\ $

put eq-n (8) in 6)

$V_1(s)=\frac{16}{5} I_1(s)+\frac{6}{5}\left(\frac{-2}{7} I_1(s)+\frac{5}{21} V_2(s)\right) \\ $

$V_1(s)=\frac{20}{7} I_1(s)+\frac{2}{7} V_2(s) ...(9)\\ $

from eq-n (8) \& (9)

$\left[\begin{array}{ll}h_{11}^{\prime \prime} & h_{12}^{\prime \prime} \\ h_{21}^{\prime \prime} & h_{22}^{\prime \prime}\end{array}\right]=\left[\begin{array}{cc}\frac{20}{7} & \frac{2}{7} \\ -\frac{2}{7} & \frac{5}{21}\end{array}\right]...(10) \\ $

We know, for SIPO confection H - parameters are additive.

$\left[\begin{array}{ll}h_{11} & h_{12} \\ h_{21} & h_{22}\end{array}\right]=\left[\begin{array}{ll}h_{11}^{\prime} & h_{12}^{\prime} \\ h_{21}^{\prime} & h_{22}^{\prime}\end{array}\right]\left[\begin{array}{ll}h_{11}^{\prime \prime} & h_{12}^{\prime \prime} \\ h_{21}^{\prime \prime} & h_{22}^{\prime \prime}\end{array}\right] \\ $

$\left[\begin{array}{ll}h_{11} & h_{12} \\ h_{21} & h_{22}\end{array}\right]=\left[\begin{array}{cc}-\frac{98}{3}+\frac{20}{7} & \frac{1}{3}+\frac{2}{7} \\ -\frac{17}{6}-\frac{2}{7} & \frac{1}{12}+\frac{5}{21}\end{array}\right]\\ $

$\left[\begin{array}{ll}h_{11} & h_{12} \\ h_{21} & h_{22}\end{array}\right]=\left[\begin{array}{cc}\frac{746}{21} & \frac{13}{21} \\ -\frac{131}{42} & \frac{9}{28}\end{array}\right] \\ $