For the two-port network shown, the parameter Y₁₂ is equal to

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:

We can see that, 

Y₁₁ = YA + YC

Y₁₂ = Y₂₁ = -Y_C

Y₂₂ = Y_B + Y_C