# Input and Output Impedance parameters of two port network

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.

• 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 :) – NotANumber Feb 18 '17 at 10:13
• 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. – Chu Feb 18 '17 at 10:15
• @Chu you might want to make that comment an answer, I'd vote it up. – Neil_UK Feb 18 '17 at 10:24

For the input impedance, expand the matrix equation and then use the output condition: $Z_L=-\large \frac{V_2}{I_2}$