For the two-port network shown in the figure, the transmission parameter C is:

Concept:

Transmission or ABCD parameters

General two-port network and Transmission parameters two-port network is shown below.

Transmission 2 port network

The direction of I2 is opposite to the standard form so it is taken as negative.

Transmission parameters are defined as:

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} A&B\\ C&D \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_2}}\\ { - {I_2}} \end{array}} \right]\)

V1 and I1 are dependent and V2 and I2 are independent.

Calculation:

From the ABCD parameters matrix, we get the following equations.

V1 = A V2 – B I2   ---(1)

I1 = C V2 - D I2   ---(2)

To calculate C, we open circuit the output terminal as shown:

Using Equation (1), we get:

I1 = C V2 

\(C=\frac{I_1}{V_2}\)

Since I₂ = 0, the current across Z_b will be I₁, i.e.

V₂ = I₁ × Z_b

\(\frac{I_1}{V_2}=C=\frac{1}{Z_b}\)