In ABCD parameters, A and C are called

SOLUTION

ABCD Parameters:

ABCD parameters relate the variables at the input port to those at the output port.

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

V1 = AV2 - BI2

I1 = CV2 - DI2

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

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

A = Reverse voltage ratio, as it is the ratio of output voltage and the input voltage

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

C = Transfer admittance, as it is the ratio of current to the voltage

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

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

\({\left. {D = \frac{{{I_1}}}{{{I_2}}}} \right|_{{V_i} = 0}}\)

Z-parameter 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:

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

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

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:

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

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

Hybrid parameters:

They represent the relationship between the voltage and the current in a two-port network and are expressed in the matrix form as:

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

V1 = h11I1 + h12V2

I2 = h21I1 + h22V2

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

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

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