# Two port network answer for clarification only

Discussion in 'Homework Help' started by ham3388, Jul 4, 2012.

1. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
Hi every body

I am appearing for exam, I got two questions here

I have answered them both, I just wanted to know weather the answers are correct.

Please guide me if you find an error in the solutions.

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2. ### WBahn Moderator

Mar 31, 2012
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Regarding Q-1:

You always want to do sanity checks as you work a problem - these basically amount to finding simple questions that you can quickly answer that ask "does this make sense?" as many different ways that you can. The two most critical points are when you set the problem up and when you get to your solution.

So, look at your setup and ask yourself, in terms of the z parameters, what does the impedance of one port look like if the other port is open circuited (i.e., if the current in the other port is forced to be zero)? Then ask whether your choices for Z_A, Z_B, and Z_C are consistent with that?

3. ### WBahn Moderator

Mar 31, 2012
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Regarding Q-2:

You need to refresh my memory (it has been over a quarter-century since I've worked these kind of problems). What is the definition of Z_o as is being used here?

4. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3

As a student these kind of problems for me are not so simple.

About the Q-1 your comment is not clear for me,I mean I dont know where I did the mistake.

But about Q-2 , Zo is called CHARASTRISTEC IMPEDANSE

http://imageshack.us/photo/my-images/254/84636962.jpg/

5. ### WBahn Moderator

Mar 31, 2012
18,088
4,917
If they were simple, you wouldn't learn nearly as much. You want to have to fight with them, and you do NOT want someone to give you too much of a direct hand, because you learn most effectively by fighting with them. So I want to guide your fight and nothing more.

So, using ONLY the TPN in Q-1 (forget about the external resistors for the time being).

Q1) What are the two equations that relate the port voltages to the port currents using the z-parameters?

Q2) If Port 2 is left unconnected, what is the impedance looking into Port 1? Remember that impedance is defined by V_1/I_1.

Q3) Now, looking at the TPN as you have it on the top of your page 2, what will the impedance looking into Port 1 (the left hand port) be if Port 2 is left unconnected?

Q4) What do you know about what the relationship between the answers to Q2 and Q3 should be? Do they satisfy that requirement?

Q5) In terms of Z_A, Z_B, Z_C (i.e., don't use specific values, leave them as variables) what are the two equations that relate the port voltages to the port currents for your TPN?

Q6) What do you know about the relationships between the equations from Q1 and the equations from Q5?

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6. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
FYI, ham3388, you've essentially got the answer to your Q-2 correct but you didn't carry enough digits in your arithmetic. You should do the arithmetic with a calculator that can do complex arithmetic. If you don't have such a calculator you can probably find an online calculator that can do it. I think that even Excel can do this.

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7. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
Hi Wbahn...

The attached is an example exactly similar to the Q-1. I have used that

method for solving Q-1.( Ignore the section iv and v )

Just have a look on that and let me know your openion.

Bye the way I thank you and the Electricain for your help.

Please give me some more guidence if Im mistaken somewhere.

My regards

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8. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,301
339
I can't read this .pdf file; Adobe reader says that it's damaged or not in .pdf format.

You might repost a file you have verified is ok.

9. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
its opening here...

But I will send it again

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10. ### WBahn Moderator

Mar 31, 2012
18,088
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But your solution doesn't track with theirs. Look at what they have done in section (i) very carefully and match that up, step by step, with yours. Notice that if R=2Ω, then their inner TPN network is the same as the one in the problem you are working.

I'm a bit concerned that you aren't willing and/or able to approach the problem by answering my questions step by step. This has me wondering whether you are being taught a "cookbook" approach that has you applying a sequence of steps based on essentially identical problems without understanding exactly where those steps came from and why they work so that you can solve problems that aren't anything like anything you've seen before. If that's the case, then that is not a good way to learn this material and will not serve you well as an engineer.

So I really do suggest you struggle through answering the questions I've posed one-by-one. Get as far as you can and we'll help you get back on track and move a bit forward in each iteration.

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11. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
OK Wbahn....

I will redo the Q-1 based on your openion ,,,,then I will come back to you

12. ### WBahn Moderator

Mar 31, 2012
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If

$
Z_o\;=\;\sqrt{Z_{oc}Z_{sc}}
$

Then I'm assuming that the open circuit impedance means the impedance seen looking into Port 1 with Port 2 open and that the short circuit impedance means the impedance seen looking into Port 1 with Port 2 shorted. Correct?

If so, then it would seem that

$
Z_{oc}\;=\;Z_{AC}||\left( Z_{AB}\;+\;Z_{BC}\right)
\;
Z_{sc}\;=\;Z_{AC}||Z_{AB}
$

13. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
This if you want to use the second formula which contains Zsc and Zoc but for me I have used the first formula since the circuit is symetrical, so what do you think ,Have I used a right method?

14. ### WBahn Moderator

Mar 31, 2012
18,088
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Unfortunately, I have NO idea what Z1 and Z2 are in that formula, and I don't just throw formulas at problems hoping something sticks.

If you can explain that, clearly, then I can check your work.

I'm going to assume that, in this context, "characteristic impedance" means basically the same thing that it does in the case of transmission lines. One way of stating it there is that the characteristic impedance of a line is the impedance seen looking into the line when the line, itself, is terminated in the characteristic impedance.

I'm pretty sure this is correct because, using that definition, I get the same answer as sqrt(Z_oc*Z_ss).

When I plug in the numbers, I get the same answer as your final answer, so it would appear you got it to stick.

Now, I notice that you follow the common practice of throwing units away as if they don't matter. I highly recommend you get over that. Most of the mistakes you will make (and we all make them all the time) will mess up the units. If you are tracking your units, then you can catch these mistakes as they happen or shortly thereafter. But if you aren't tracking your units, mistakes go uncaught. In school, it means you don't get as good of grades as you could have. In the real world, it could mean you let a mistake go that gets a whole bunch of people killed and have to convince a judge and jury that it wasn't criminal negligence (and, in my opinion, it would be).

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15. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
Thanks alot Wbahn...
My regards

Jul 3, 2012
97
3
Hi Wbahn...

my regards

Jul 3, 2012
97
3
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18. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
Wbahn...where are you?

19. ### WBahn Moderator

Mar 31, 2012
18,088
4,917
Sorry, I wasn't able to open your external post and then didn't come back to download the pdf file.

Most of your work is just fine. A few points (if I were the grader):

On the first page you just give Z_12 as R (no subscript).

You don't indicate what the port voltages and currents are. Don't make the grader guess - they can choose to deliberately interpret them in a strange way and mark your stuff wrong and when you complain they just smile and say, "The way I interpreted your work was completely consistent with the information you provided. If you wanted it interpreted in a specific way, you should have been specific. Learn and do better next time."

You disregard units pretty much everywhere. Your instructor and grader may tolerate that. I won't. As others have discovered, I will harp on units for a while, but then I will simply not provide assistance until the work is redone and presented with units properly tracked.

It has been so long since I have done anything with two-port networks, that I don't see the method you used on the second page as being obviously correct. To be more specific, I don't recall the conditions that have to be met that will allow you to just add the matrices for two TPN's in order to get the matrix for a third made up of the first two. So while it looks like you got the correct answer, I can't say for certain that the method used is, in general, correct. It probably is, I just don't recall.

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20. ### ham3388 Thread Starter Member

Jul 3, 2012
97
3
Thank you Wbahn
Since people like you are there to help us, we always get encouraged to learn more and more.
This is my begenning ,we shall continue the journey together with the other members further and enjoy the study.
My regards