In hybrid parameters, h 11 and h 21 are called as
![In hybrid parameters, h 11 and h 21 are called as](http://storage.googleapis.com/tb-img/production/19/08/26%20June_1.png)
A. input impedance and forward current gain
B. reverse voltage gain and output admittance
C. input impedance and reverse voltage gain
D. output impedance and forward current gain
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Hybrid parameters represent the relationship between the voltage and current in a two-port network and is 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 shorted, i.e. V2 = 0, the two parameters we obtain are:
\({h_{11}} = {\left. {\frac{{{V_1}}}{{{I_1}}}} \right|_{{V_2} = 0}}\).
The above is the expression for the input impedance
\({h_{21}} = {\left. {\frac{{{I_2}}}{{{I_1}}}} \right|_{{V_2} = 0}}\).
The above is the expression for a current gain.
With the input open-circuited, i.e. I1 = 0, the two parameters we obtain are:
\({h_{12}} = {\left. {\frac{{{V_1}}}{{{V_2}}}} \right|_{{I_1} = 0}}\).
The above is the expression for the inverse voltage gain.
\({h_{22}} = {\left. {\frac{{{I_2}}}{{{V_2}}}} \right|_{{I_1} = 0}}\).
The above is the expression for the output admittance.
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:
\({z_{11}} = {\left. {\frac{{{V_1}}}{{{I_1}}}} \right|_{{I_2} = 0}}\)
\({z_{21}} = {\left. {\frac{{{V_2}}}{{{I_1}}}} \right|_{{I_2} = 0}}\)
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:
\({Y_{12}} = {\left. {\frac{{{I_1}}}{{{V_2}}}} \right|_{{V_1} = 0}}\)
\({Y_{22}} = {\left. {\frac{{{I_2}}}{{{V_2}}}} \right|_{{V_1} = 0}}\)
Transmission Parameters: It relates 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:
\(A = {\left. {\frac{{{V_1}}}{{{V_2}}}} \right|_{{I_2} = 0}}\)
\({\left. {C = \frac{{{I_1}}}{{{V_2}}}} \right|_{{I_2} = 0}}\)
With the input short-circuited, i.e. V1 = 0, the two parameters we get are:
\({\left. {B = - \frac{{{V_1}}}{{{I_2}}}} \right|_{{V_2} = 0}}\)
\({\left. {D = \frac{{{I_1}}}{{{I_2}}}} \right|_{{V_i} = 0}}\)