Two Port Networks · Electric Circuits · GATE EE
Marks 1
Marks 2
Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is $Z_P = \begin{bmatrix} 40 \Omega & 60 \Omega \\ 80 \Omega & 100 \Omega \end{bmatrix}$. The admittance matrix of network Q is $Y_Q = \begin{bmatrix} 5 \, \text{S} & -2.5 \, \text{S} \\ -2.5 \, \text{S} & 1 \, \text{S} \end{bmatrix}$. Let the ABCD matrix of the two-port network R in the figure be $\begin{bmatrix} \alpha & \beta \\ \gamma & \delta \end{bmatrix}$. The value of $\beta$ in $\Omega$ is ______________ (rounded off to 2 decimal places).
The admittance parameters of the passive resistive two-port network shown in the figure are
$${y_{11}} = 5\,S,{y_{22}} = 1\,S,{y_{12}} = {y_{21}} = - 2.5\,S$$
The power delivered to the load resistor $$R_L$$ in Watt is __________ (Round off to 2 decimal places).
$$\begin{array}{l}Given:\\V_1=A_1V_2+B_1I_2\\I_1=C_1V_2+D_1I_2\\V_2=A_2V_3+B_2I_3\\I_2=C_2V_3+D_2I_3\end{array}$$
$$A_1,\;B_1,\;C_1,\;D_1,\;A_2,\;B_2,\;C_2,\;and\;D_2$$ are the generalized circuit constants. If the Thevenin equivalent circuit at port 3 consists of a voltage source VT and impedance ZT connected in series, then
(i) 1 Ω connected at port B draws a current of 3 A
(ii) 2.5 Ω connected at port B draws a current of 2 A
For the same network, with 6 V dc connected at port A, 1 Ω connected at port B draws 7/3 A.
If 8 V dc is connected to port A, the open circuit voltage at port B is(i) 1 Ω connected at port B draws a current of 3 A
(ii) 2.5 Ω connected at port B draws a current of 2 A
W ith 10 V dc connected at port A, the current drawn by 7 Ω connected at port B is
$${R_i} = 1\,\,M\,\Omega ,\,\,{R_0} = 10\,\Omega ,\,\,A = {10^6}\,\,V/V.$$ If $${V_i} = 1\,\,\mu V,\,\,$$ the output voltage, input impedance and output impedance respectively are
$$\left[ {\matrix{ {{E_1}} \cr {{{\rm I}_2}} \cr } } \right] = \left[ {\matrix{ {{h_{11}}} & {{h_{12}}} \cr {{h_{21}}} & {{h_{22}}} \cr } } \right]\left[ {\matrix{ {{{\rm I}_1}} \cr {{E_2}} \cr } } \right].$$
For the two $$-$$ port network shown in Fig. the value of $${h_{12}}$$ is given by
$$\eqalign{ & {{\rm I}_1} = {Y_{11}}\,\,{E_1} + {Y_{12}}\,\,{E_2} \cr & {{\rm I}_2} = {Y_{21}}\,\,{E_1} + {Y_{22}}\,\,{E_2} \cr} $$
The admittance parameters, $${Y_{11}},\,\,{Y_{12}},\,\,{Y_{21}}$$ and $${Y_{22}}$$ for the network shown are
$${i_1} = 2{v_1} + {v_2}$$ and $${i_2} = {v_1} + {v_2}$$
Its impedance parameters $$\left( {{z_{11}},\,\,{z_{12}},\,\,{z_{21}},\,\,{z_{22}}} \right)$$ are given by
