For a two-port network, V₁ and V₂ are given by

V₁ = 60I₁ + 20I₂

V₂ = 20I₁ + 40I₂

The Y-parameters of the network are

Y (Admittance) Parameters:

They are also called the short circuit parameters, as they are calculated under short circuit conditions, i.e. at V1 = 0 and V2 = 0.

Expressed in Matrix Form as:

\(\left[ {\begin{array}{*{20}{c}} {{I_1}}\\ {{I_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{Y_{11}}}&{{Y_{12}}}\\ {{Y_{21}}}&{{Y_{22}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{V_2}} \end{array}} \right]\)

I1 = Y11V1 + Y12V2

I2 = Y21V1 + Y22V2

With the output short-circuited, i.e. V2 = 0, the two parameters obtained are:

\({Y_{11}} = {\left. {\frac{{{I_1}}}{{{V_1}}}} \right|_{{V_2} = 0}}\)

\({Y_{21}} = {\left. {\frac{{{I_2}}}{{{V_1}}}} \right|_{{V_2} = 0}}\)

With the input short-circuited, i.e. V1 = 0, the two parameters obtained are:

\({Y_{12}} = {\left. {\frac{{{I_1}}}{{{V_2}}}} \right|_{{V_1} = 0}}\)

\({Y_{22}} = {\left. {\frac{{{I_2}}}{{{V_2}}}} \right|_{{V_1} = 0}}\)

Analysis:

V1 = 60I1 + 20I2

V2 = 20I1 + 40I2

This is in the form of Z - parameters i.e. 

Z₁₁ = 60, Z₁₂ = 20, Z₂₁ = 20, Z₂₂ = 40

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{V_2}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} Z_{11}&Z_{12}\\ Z_{21}&Z_{22} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{I_1}}\\ { {I_2}} \end{array}} \right]\)

\(Y= \left [{\begin{array}{*{20}{c}} Z_{11}&Z_{12}\\ Z_{21}&Z_{22} \end{array}}\right]^{-1}\)

\(Y = \frac{1}{Z_{11} Z_{22} - Z_{12} Z_{21}} \left[ {\begin{array}{*{20}{c}} {{Z_{22}}}&{{-Z_{12}}}\\ {{-Z_{21}}}&{{Z_{11}}} \end{array}} \right]\)

\(\)\(Y = \frac{1}{60 × 40 - 20 × 20} \left[ {\begin{array}{*{20}{c}} {40}&{{-20}}\\ {{-20}}&{60} \end{array}} \right]\)

Y₁₁ = 20 × 10^-3

Y₁₂ = -10 × 10^-3

Y₂₁ = -10 × 10^-3

Y₂₂ = 30 × 10^-3