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

Find the current-transfer-ratio, $${{I_2}}$$/$${{I_1}}$$, for the network shown below (Fig). Also, mark all branch currents.

Assuming that the amplifier shown in the Fig., below, is a voltage-controlled voltage source, show that the voltage transfer function of the network is given by
$$T(s) = {{{V_2}\,(s)} \over {{V_1}\,(s)}} = \,{K \over {{s^2} + \,(3 - K)\,s + 1}}$$