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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.

Two-Port Network Image

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.)

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    \$\begingroup\$ Is there any particular reason your whole question is a picture, which means the text can't be searched? \$\endgroup\$ – David Feb 23 '14 at 23:13
  • \$\begingroup\$ 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 \$\endgroup\$ – user124627 Feb 24 '14 at 1:59
  • \$\begingroup\$ 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. \$\endgroup\$ – JYelton Feb 24 '14 at 8:31
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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:

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

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

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  • \$\begingroup\$ 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. \$\endgroup\$ – user124627 Feb 24 '14 at 0:49

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