Two-port network hybrid parameters problem

WBahn

Joined Mar 31, 2012
26,141
So... what's the question that you are asking?

We don't just solve homework problems for you.

Show YOUR best attempt to solve YOUR homework. Then we can look that work over and try to help you see what you are doing wrong or how to get back on a valid path.

A good place to start would be with the definitions of the hybrid parameters you are trying to find.
 

Thread Starter

Pedro Turati

Joined Nov 20, 2017
6
I asked the question because i already tried a solution, but the book doesn't have an answer for that problem.
I got two different answers (for the first parameter h11), for two different methods: -4, and 4/19: i didn't continued due to this difference.
 

WBahn

Joined Mar 31, 2012
26,141
My crystal ball is in the shop, so there is no way I can possibly tell you what you did wrong unless you show us what you did.

Again, start with the definition of the parameters you seek. This not only allows us to confirm that you are starting from a valid place, but also let's us ensure that we are on the same page in case your text happens to use a different nomenclature than we are used to -- that happens quite a bit, particularly with non-English texts, but those things happen even in same-language, same-country texts because engineering terminology is not static and universally agreed upon.
 

Thread Starter

Pedro Turati

Joined Nov 20, 2017
6
I got -4 by:

The hybrid parameters of a circuit are given by:
V1 = h11 * i1 + h12 * V2
i2 = h21 * i1 + h22 * V2

Where:
- h11, h12, h21 and h22 are the hybrid parameters;
- V1, V2, i1 and i2 can be found in the image;

Using the definition of the hybrid parameters, i can use h11 = V1/i1 for V2 = 0.
In this situation ( for V2 = 0) we have a short circuit in the right side of the original circuit. Therefore, we can "ignore" the dependent current sources, so we just use the dependent voltage source to get the answer.

Any problems in this solution?
 

WBahn

Joined Mar 31, 2012
26,141
I got -4 by:

The hybrid parameters of a circuit are given by:
V1 = h11 * i1 + h12 * V2
i2 = h21 * i1 + h22 * V2

Where:
- h11, h12, h21 and h22 are the hybrid parameters;
- V1, V2, i1 and i2 can be found in the image;

Using the definition of the hybrid parameters, i can use h11 = V1/i1 for V2 = 0.
In this situation ( for V2 = 0) we have a short circuit in the right side of the original circuit. Therefore, we can "ignore" the dependent current sources, so we just use the dependent voltage source to get the answer.

Any problems in this solution?
Why can you ignore the dependent current sources?

You can ignore the right hand one because it's control signal is forced to zero.

But while the voltage across the left-hand dependent current source is zero, it's control signal is not and therefore it can have a non-zero current flowing in it.

Keep in mind also that, while V2 is forced to zero, there is nothing that says that I2 is also zero.

With all of that in mind, see what you get. In particular, see what assumptions you are making about the circuit with V2 = 0 that are not valid based on the above information.
 

Thread Starter

Pedro Turati

Joined Nov 20, 2017
6
Thats the question: can i ignore the "5*V1" current source?
My professor told me that the current generated by that source would "stay in a loop", so it can be ignored. The following sketch illustrates the idea:

Question.png

In this situation, I3 (current generated by the source) would be "traped" due to the present short circuit, so i2 would "pass through" it, resulting in a circuit with the dependent voltage source only, represented by the equations:
V1 = -4*i2
i1 = -i2

Resulting in: V1/i1 = -4

I also do not thought that the current source could be ignored.
So that's exactly my doubt, should I consider the effects of the current source?
 

WBahn

Joined Mar 31, 2012
26,141
NOW you are showing enough work for us to get at your misconceptions! Thanks!

You replaced the right-hand dependent current source with a short circuit. Why?

If the controlling voltage, V2, is identically zero, then the current in that source will be identically zero, meaning that NO current can flow throw that path. But by replacing it with a short circuit, you have made it so that ANY current can flow through that path. What do you need to replace it with to ensure that NO current flows through that path.
 

Thread Starter

Pedro Turati

Joined Nov 20, 2017
6
You mean something like that?
Question.png

If yes, one more question:
Can i assume that i3 = i2?
Because i2 is a current originally "entering" the network: after I put the short circuit,can i2 be considered as part of the new circuit, or as an "entering" current? I mean, will i2 be part of the mesh created with the insertion of the short circuit?
 
Last edited:

WBahn

Joined Mar 31, 2012
26,141
I think the answers to all of your questions are Yes.

I2 is defined as the current going from right to left in the wire that has the upper terminal of the right hand port. Imagine putting a current meter in that wire. The current meter doesn't care how or why the current flowing through it is created, it merely knows that a current is flowing through it and that current is, by definition, I2.

So, because no current will flow in the right hand dependent current source, the current I3 is the same as the current I2.
 

MrAl

Joined Jun 17, 2014
7,799
Hello there,

If there is any question as to whether or not your answers are correct or not, you can test them in the equations for the 'h' params.

To check by calculation, you can generate two specific non zero cases (because there was a question about zeroing some variable here and its effect on the rest of the circuit) and then set up four equations in the four unknowns h11 through h22.

For example, V1=1, V2=2, then the two currents are easy to calculate, and that gives you two of the required equations. Then V1=1 and V2=4 for example, and that gives you the other two equations. Solve those four for the four unknown 'h' params and that gives you all four. Check them in the original two equations to make sure they are all right by doing a few different cases. In this way you do not have to zero any sources.

I can verify that h11 is 4/19, and that there are two positive and two negative in the group of four params.
 

MrAl

Joined Jun 17, 2014
7,799
Hi,

Since the time is up for this question here are a couple other ideas.

First, the network equations are easy to write so the solutions for the variation of parameters V1 and V2 come out to:
4*V1=19*h11*V1+4*h12*V2a+3*h11*V2a
V1-V2a=19*h21*V1+4*h22*V2a+3*h21*V2a
4*V1=19*h11*V1+4*h12*V2b+3*h11*V2b
V1-V2b=19*h21*V1+4*h22*V2b+3*h21*V2b

and here only V2 is varied into two different voltages V2a and V2b.

Since these are linear equations and the only requirement for the different varied parameters is that they be different, we can make first:
V2b=V2a+1

and we can make:
V2a=V1+1

and finally we can make:
V1=1

and then we end up with:
4=8*h12+25*h11
-1=8*h22+25*h21
4=12*h12+28*h11
-2=12*h22+28*h21

and these are four equations in four unknowns and can be solved for the four parameters. In fact, these are really two sets of two equations in two unknowns each, so it's even simpler (take equations 1 and 3 for example and solve for h11 and h21, then equations 2 and 4).

I think this is a good fall back method when a question comes up as to whether or not we can zero a certain source or sources in a given circuit where it looks like it could be tricky.
 
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