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I am reading about two port network and I come to about Z-parametrs

$$\begin{bmatrix} \mathbf{V_1} \\ \mathbf{V_2} \end{bmatrix}=\begin{bmatrix} \mathbf{Z_{11}} & \mathbf{Z_{12}} \\ \mathbf{Z_{21}} & \mathbf{Z_{22}} \end{bmatrix} .\begin{bmatrix} \mathbf{I_1} \\ \mathbf{I_2} \end{bmatrix} $$

but then it introduces the concept of input and output impedance which is $$Z_{in} = Z_{11}-\frac{Z_{12}Z_{21}}{Z_{22}+Z_L}$$and also $$Z_{out} = Z_{22}-\frac{Z_{12}Z_{21}}{Z_{11}+Z_S}$$ Where \$Z_L\$ is load impedance and \$Z_S\$ is source impedance. I don't know how writer concluded these impedance. Please provide me the explanation.

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  • \$\begingroup\$ Well, ZL is the load impedance, isn't it? I would say, the one connected to port 2, okay? For me, the second equation has something strange... maybe you meant Zsource instead of ZL? I will assume that when you compute Zout, ZL will be connected to port 1 :) \$\endgroup\$ – NotANumber Feb 18 '17 at 10:13
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    \$\begingroup\$ For the input impedance, expand the matrix equation and then use the output condition: \$Z_L=-\frac{V_2}{I_2}\$. Similar approach for the output impedance. \$\endgroup\$ – Chu Feb 18 '17 at 10:15
  • \$\begingroup\$ @Chu you might want to make that comment an answer, I'd vote it up. \$\endgroup\$ – Neil_UK Feb 18 '17 at 10:24
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For the input impedance, expand the matrix equation and then use the output condition: \$Z_L=-\large \frac{V_2}{I_2}\$

Similar approach for the output impedance.

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  • \$\begingroup\$ Can someone show/explain me the expansion please? Thanks a lot! \$\endgroup\$ – RisingSun Sep 12 '17 at 8:31

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