Z parameters of the network shown below are:
Z parameters of the network shown below are:
A. Z<sub>11</sub> = 2R, Z<sub>22</sub> = 2R, Z<sub>12</sub> = R, Z<sub>21</sub> = R
B. Z<sub>11</sub> = R, Z<sub>22</sub> = R, Z<sub>12</sub> = 2R, Z<sub>21</sub> = 2R
C. Z<sub>11</sub> = 2R, Z<sub>22</sub> = 2R, Z<sub>12 </sub>= 2R, Z<sub>21</sub> = 2R
D. Z<sub>11</sub> = R, Z<sub>22</sub> = R, Z<sub>12</sub> = R, Z<sub>21</sub> = R
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
Concept:
Z Parameters:
V1 = Z11 I1 + Z12 I2
V2 = Z21 I1 + Z22 I2
\(Z = \left[ {\begin{array}{*{20}{c}} {{Z_{11}}}&{{Z_{12}}}\\ {{Z_{21}}}&{{Z_{22}}} \end{array}} \right]\)
\({Z_{11}} = {\left. {\frac{{{V_1}}}{{{I_1}}}} \right|_{{I_2} = 0}}\) is the input driving point impedance or open circuit input impedance
\({Z_{12}} = {\left. {\frac{{{V_1}}}{{{I_2}}}} \right|_{{I_1} = 0}}\) is the open circuit transfer impedance from port 1 to port 2
\({Z_{21}} = {\left. {\frac{{{V_2}}}{{{I_1}}}} \right|_{{I_2} = 0}}\)is the open circuit transfer impedance from port 2 to port 1
\({Z_{22}} = {\left. {\frac{{{V_2}}}{{{I_2}}}} \right|_{{I_1} = 0}}\) is the output driving point impedance or open circuit output impedance
Application:
By writing the KVL equations on both input and output loops,
V1 = (I1 + I2) R = I1 R + I2 R
V2 = (I1 + I2) R = I1 R + I2 R
By comparing with the Z parameter equations,
Z11 = R, Z22 = R, Z12 = R, Z21 = R