In the two port network shown below, if V₁ & V₂ are expressed in terms of I₁ & I₂ using the expression V₁ = Z₁₁I₁ + Z₁₂I₂ & V₂ = Z₂₁I₁ + Z₂₂I₂ then Z₁₁ and Z₂₂ are called

Z-parameters:

Z-parameters are also known as the Open-Circuit impedance parameters as they are calculated under open-circuit conditions, i.e. at I1 = 0 and I2 = 0, In the matrix form, they are expressed as:

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

V1 = z11I1 + z12I2

V2 = z21I1 + z22I2

With the input open-circuited, i.e. I1 = 0, the two parameters obtained are:

\({z_{12}} = {\left. {\frac{{{V_1}}}{{{I_2}}}} \right|_{{I_1} = 0}}\)

\({z_{22}} = {\left. {\frac{{{V_2}}}{{{I_2}}}} \right|_{{I_1} = 0}}\)

With the output open-circuited, i.e. I2 = 0, the two parameters we obtain are:

\({z_{11}} = {\left. {\frac{{{V_1}}}{{{I_1}}}} \right|_{{I_2} = 0}}\)

\({z_{21}} = {\left. {\frac{{{V_2}}}{{{I_1}}}} \right|_{{I_2} = 0}}\)