# Finding Z-parameters from a two-port network and using them to find S-parameters

So I have the two-port network

and I want to find out the Z-parameters of it (and later, use that to find the S-parameters). For the assignment, $$\R_x=8Ω\$$.

From what I understood, I should null the ports in turn to have no current on left-hand side and no current on right-hand side respectively and calculate the current equations when ignoring the sides on each scenario ($$\2Ω\$$ and $$\10Ω\$$), but I'm not exactly sure what I should get from that or how I should proceed on with that.

calculate the current equations when ignoring the sides on each scenario (2Ω and 10Ω),

I'm not sure what you mean about ignoring "the sides". You shouldn't ignore any component in your analysis. Of course, if you find there is no current flowing through a resistor, then the voltage across it will be zero.

but I'm not exactly sure what I should get from that or how I should proceed on with that.

The Z parameters allow you to calculate

$$\begin{bmatrix}v_1\\v_2\end{bmatrix}=\begin{bmatrix}Z_{11} & Z_{12} \\ Z_{21} & Z_{22}\end{bmatrix}\begin{bmatrix}i_1\\i_2\end{bmatrix}$$

meaning if you know the two port currents, you can calculate the port voltages.

So to work out the Z matrix from circuit analysis, you apply a fixed current at each port (one at a time), and see what voltages result.

If you apply 1 A at port 1, and measure a certain voltage $$\v_2\$$ at port 2, then that immediately gives you the value of $$\Z_{21}\$$, for example.

• Should it look something like: $Z11 = 2+(5*(6+8))/((5)+(6+8)) = 108/19 = 5.68421… (Ohm)$, $Z12 = (8*(6+5))/((8+(6+5)) = 88/19 = 4.63157… (Ohm)$, $Z21 = (5*(6+8))/((5+(6+8)) = 70/19 = 3.68421… (Ohm)$, $Z22 = 10+(8*(6+5))/((8+(6+5)) = 278/19 = 14.631579 (Ohm)$ ? – Grak Jan 30 at 9:23