# Calculating Z21 of a two port network

Discussion in 'Homework Help' started by anhnha, Jan 8, 2014.

1. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
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49
I need help to find Z21 of the circuit below.

$Z_{21} = \frac{ V_{2} }{ I_{in} } \mid I_{out} = 0$

$V_{2} = - ( g_{m}* V_{gs} + I_{2} )* r_{o} + I_{in}*s* L_{s}$

But how can I calculate V2/Iin in this case?

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2. ### The Electrician AAC Fanatic!

Oct 9, 2007
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Can you write the two loop equations for the circuit?

Edit: I notice that you have posted this same circuit on another forum and there you said that it isn't homework. If it isn't homework, why did you post it in the homework help forum here? It it homework or not?

Last edited: Jan 9, 2014
3. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
783
49
Yes, but the problem is that I can't express I1 and I2 in terms of Iin. In this case I1 and I2 are constant. It seems that there is no way to get V2/Iin, an expression that doesn't depend on V1, V2 and Iin.

Yes, it isn't homework. I posted here because it is similar to homework and usually I will be more likely to receive the answer here than other forums.

BTW, did you mean the forum: http://www.physicsforums.com/showthread.php?t=731877

They are not the same both in topologies and results. One is Z21 and the other is Z11.

Last edited: Jan 9, 2014
4. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,393
355
This circuit looks like a model for an amplifier of AC signals. If so, then constant sources like I1 and I2 have no bearing on the small signal (AC) behavior. You can't express I1 and I2 in terms of Iin because they don't depend on Iin.

The circuit you have posted here is obviously the full version. The circuit over there is just the first half, or am I mistaken?

If you eliminate I1 and I2, you can easily write the two KVL equations for the circuit by inspection. Putting them in matrix form gives the Z matrix directly:

Now you have Z11, Z12, Z21 and Z22, all at once.

• ###### Z21.png
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5. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
783
49
I1 and I2 are noise sources in cascode LNA. I was mistaken to include it in Z parameters.
Without I1, I2 I can calculate all Z parameters easily.
Yes, but what I wanted to say is that they are not exact the same.

6. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,393
355
Yes, but it's obvious that the first half of the circuit posted here is exactly the same as the circuit posted over there.

But I think you miss the point of why I even mentioned the similarity. I mentioned it because you said over there that it was not homework, yet here you posted in the homework help section. I wondered how it could be that the first half of the circuit was not homework, but the full circuit was?

The help I would give you here depended on your answer. That was the only reason I mentioned the similarity. I wasn't ascribing a nefarious purpose to your posting of the "same" circuit on two different forums. Your repeated assertion that the circuits aren't "exactly" the same makes it seem as if you're defending yourself against a suspicion of some malfeasance. Rest assured, I don't think you've done anything wrong.

7. ### anhnha Thread Starter Well-Known Member

Apr 19, 2012
783
49
I usually post this kind of questions in homework help section while they are not homework at all.
Long time ago, I posted a similar questions in General Electronics Chat but I got no answer. So I prefer to post it here.

I thought that you meant I posted two identical circuits with the same questions in two different forums.
I hope so.