The admittance parameters of a 2-port network shown in Fig. are given by $${Y_{11}} = \,2\,\,mho$$, $${Y_{12}}$$ = - 0.5 mho, $${Y_{21}}$$ = 4.8 mho, $${Y_{22}}$$ = 1 mho. The output port is terminated with a load admittance $${Y_L}$$ = 0.2 mho. Find $${E_2}$$ for each of the following conditions:

(a) $${E_1} = \,10\,\angle \,{0^{ \circ \,}}\,V$$
(b) $${I_1} = \,10\,\angle \,{0^{ \circ \,}}\,A$$
(c) A source $$10\,\angle \,{0^{ \circ \,}}\,V$$ in series with a 0.25 $$\Omega $$ resistor is connected to the input port.

Find the input resistance $${R_{in}}$$ of the infinite section resistive network shown in Fig.

The open circuit impedance matrix $${Z_{OC}}$$ of a three-terminal two-port network with A as the input terminal, B as the output terminal, and C as the common terminal, is given as $$$\left[ {{Z_{OC}}} \right] = \left[ {\matrix{ 2 & 5 \cr 3 & 7 \cr } } \right]$$$

Write down the short circuit admittance matrix $${{Y_{SC}}}$$ of the network viewed as a two-port network, but now taking B as the input terminal, C as the output terminal and A as the common terminal.

Show that the system shown in Fig. is a double integator. In other words, prove that the transfer gain is given by
$${{{V_0}\,(s)} \over {{V_s}\,(s)}} = - {1 \over {{{(CR\,s)}^2}}}$$, assume ideal OP-Amp