I am failing z-parameters, but I don't know why

I need your help to see where am going wrong.

A two port network driven at both ports such that the port voltages and currents have the following values:

• $Z_0$ = 50 ohm
• $V_1$ = 10 < 90 - degrees
• $I_1$ = 0.2 < 90
• $V_2$ = 8 < 0
• $I_2$ = 0.15 < -90

Determine input impedance seen at each port, and find the incident and reflected voltages at each port.

I got:

$$Z_{12} = \frac{-V_1}{I_1} = \frac{-10 < 90}{0.16 < -90} = 62.5$$

and

$$Z_{21} = \frac{-V_2}{I_1} = \frac{-8}{0.2 < 90} = 40 <- 90$$

But they say $Z_{12}$ and $Z_{21}$ should be equal. What am I doing wrong?

(Original image for question here.)

• Is there any particular reason your whole question is a picture, which means the text can't be searched? – David Feb 23 '14 at 23:13
• the reason is that I had a picture to post, so I figured I should just put everything on one internet page, so that I could access it whenever or email it to my friends – user124627 Feb 24 '14 at 1:59
• I reworked the question so that it is more readable and not contained strictly within the image. Let me know if I introduced any technical errors. You're welcome. – JYelton Feb 24 '14 at 8:31

The Z parameters are the open circuit parameters. So, for example,

$$Z_{21} = \frac{V_2}{I_1}, \, I_2=0$$

But, for the voltages and currents given, $I_2$ isn't zero. In fact, it says this in the problem statement:

A two-port network is driven at both ports...

The voltages and currents given can't be used to directly compute the Z parameters as you are attempting to do.

However, recall that, in general:

$$V_1 = Z_{11}I_1 + Z_{12}I_2$$

$$V_2 = Z_{21}I_1 + Z_{22}I_2$$

• am pretty much still stuck. I know that in the equations you gave me, I could swap Z12 with Z21. But now, I will still be left with 3 variables in 2 equations. simultaneously, that's not possible. – user124627 Feb 24 '14 at 0:49