# Two port network

Discussion in 'Homework Help' started by xxxyyyba, Jul 29, 2013.

1. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
Hi!
My task is to calculate z parameters of network below:
Code ( (Unknown Language)):
1. http://i42.tinypic.com/211m7hg.jpg
It consist of two networks connected in series:
Code ( (Unknown Language)):
1. http://i44.tinypic.com/10nyo45.jpg
and
Code ( (Unknown Language)):
1. http://i41.tinypic.com/dputyx.jpg
I calculated z parameters of both networks:
z'=[3 1;1 3] - first network
z''=[(j*w-j/w) (j*w);(j*w) (j*w-j/w)] - second network

z=z'+z''=[(3+j*w-j/w) (1+j*w);(1+j*w) (3+j*w-j/w)]

Is it correct?

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Firstly it's difficult to view the circuit image(s) since you've embedded the links as code snippets. Try using the web link option - the world globe with the chain link icon on the second line about midway.

How can we know if you are correct if you post a rather cryptic collection of equations? Try to post a more complete analysis - even a paper photocopy of your working would be OK

3. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
Probably not. In several places you have things like 3 + j*w - j/w. Now, it could just a result of being so sloppy with your units, but this expression is adding something that is dimensionless to something that has units of radian/second to something that has units of seconds/radian.

If you track your units, then you have a built in set of checks, both at the end and along the way, and if the units stop working out, you KNOW you have made a mistake.

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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Attaching a copy of schematic

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5. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
That's a confusing way of drawing the schematic. How about just doing this:

File size:
68.2 KB
Views:
89
6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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I simply copied what the OP had linked in their first post. I wasn't giving any assistance for the time being.

7. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
Oh, I very much assumed that it was a direct posting of his first schematic.

I can't do much to assist until he, or someone, posts the others showing the breakout of the network. I don't go to tinypics anymore because I spend too much time telling it not to load up my machine with all their advertisers' cookies.

8. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790

I'm on an android tablet for the moment as I'm away from the usual desktop.

Pity some posters still use tinypics. The options we have within the AAC system are quite adequate for posting images.

Looks like a tricky little problem to solve anyway.

9. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
Sorry for images, I will use web link option in future. I will upload complete solution.

Aug 7, 2012
289
7
11. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
Is there any way we can talk you into uploading your images to the AAC server? That we they are part of the forum database and someone five or ten years from now searching the archives doesn't have to rely on some external third-party server still being in existence at the same URL and still having you files stored and accessible there.

12. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
I used web link option as t_n_k suggested to me.

Is it ok now?

Last edited: Jul 30, 2013
13. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
They will work -- thanks. I have to leave now and don't know if I can get back to them today, but others might.

The only thing I would say about these images is that (at least in my browser) they display way to large. You might use an image editor (even Paint) and rescale the images to about 40% of their present size in both directions. Then edit your post and delete the ones that are there and replace them with your scaled down images.

But, as I said, these will work.

14. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,720
496
The method of solution you have chosen will not work. You have a couple of two-ports, and you derive the z parameters of the individual two-ports. You then make the series-series connection of those two-ports and assume that the z parameters of the series-series connection are the sum of the z parameters of the individual two-ports.

This method is subject to some restrictions. See:

http://en.wikipedia.org/wiki/Two-port_network

A little over halfway down the page under the heading "Combinations of two-port networks" is a discussion of the necessity of not violating the "port condition". Since your two-port consisting of resistors only is a lattice network, the port condition is violated, and the method you chose to solve the problem is invalid.

I think it would be easier to analyze the full circuit as a stand-alone entity, although I suppose you could use the trick shown in Figure 12 of the Wikipedia page.

Last edited: Jul 30, 2013
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15. ### t_n_k AAC Fanatic!

Mar 6, 2009
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It's not a trivial problem. The Z12 & Z21 parameters in particular require some careful algebraic manipulation.

I made use of delta-wye transformation for Z11 & Z22 analysis.

Good luck.

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16. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
@The Electrician,
I tried already analysis of full circuit but I gave up since it was too complicated so I tried to find better solution.
I read that ideal transformer will ensure that "port condition" wouldn't be violated so I should place transformers on output (like in Fig. 12, wiki) and my calculations will be ok? Or I should start with calculations from beginning? I'm a little bit confused

17. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,720
496
I've been basing my analysis on the redrawn schematic provided by WBahn in post #5.

What methods of circuit analysis have you learned? You could use delta-wye transformations to simplify the circuit, or you could just solve the whole thing with node or loop analysis.

Keep in mind that z11 is just the impedance seen at node 1, and z22 is the impedance seen at node 2. Do you know how to calculate the impedance seen at node 1, for example?

18. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
Here is my attempt to find z11 and z21 using node analysis:

I should solve that system and find z11 and z21. To find another two parameters I will get another system to solve... You will agree that it's complicated. I will try delta-wye tranform.

Last edited: Aug 1, 2013
19. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,720
496

Now you must solve the system as you have it labeled, which will give you V(B), V(C) and V(D). Then to get z11 you must calculate V1/I1.

But I think you have made some choices which make more work for yourself. Look at the circuit in post #1, which WBahn redrew in post #5--why didn't you use node 6 as your reference node? It is the obvious choice--it's already the "ground" terminal of the overall two-port.

Furthermore, you will need the voltage at node 2 for some of your calculations, so you shouldn't leave that node unlabeled. You will need it to calculate the rest of the z parameters.

Instead of giving the nodes letters of the alphabet as designators, I would label them V1, V2, V3, V4 and V5.

I think if you do these things you will make it easier on yourself (and those of us offering to help you).

20. ### xxxyyyba Thread Starter Active Member

Aug 7, 2012
289
7
Thanks a lot for all suggestions! I will try to finish it and I will upload photos (rescaled ).