The two-port network P shown in the figure has ports 1 and 2, denoted by terminals (a, b) and (c, d), respectively. It has an impedance matrix Z with parameters denoted by z_ij. A 1 Ω resistor is connected in series with the network at port 1 as shown in the figure. The impedance matrix of the modified two-port network (shown as a dashed box) is

The parameters of the circuit shown in the figure are
$${R_i} = 1\,\,M\,\Omega ,\,\,{R_0} = 10\,\Omega ,\,\,A = {10^6}\,\,V/V.$$ If $${V_i} = 1\,\,\mu V,\,\,$$ the output voltage, input impedance and output impedance respectively are

Two networks are connected in cascade as shown in the Fig. With the usual notations the equivalent $$A,B,C$$ and $$D$$ constants are obtained. Given that, $$C$$ $$ = 0.025\angle {45^ \circ },$$ the value of $${Z_2}$$ is

The $$Z$$ matrix of a $$2$$ $$-$$ port network is given by $$\left[ {\matrix{ {0.9} & {0.2} \cr {0.2} & {0.6} \cr } } \right].$$ The element $${Y_{22}}$$ vof the corresponding $$Y$$ matrix of the same network is given by