Is my transfer function correct?

Click For Summary

Discussion Overview

The discussion revolves around the correctness of a transfer function related to a circuit analysis problem. Participants explore the structure of loops and paths in the circuit, addressing potential errors and clarifying concepts related to feedback loops and summing junctions. The scope includes technical explanations and mathematical reasoning.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants suggest that there are missing loops in the transfer function representation.
  • One participant argues that a specific loop is not a proper loop due to the direction of arrows.
  • There is a discussion about the correct expression for the transfer function, with some participants proposing different methods for calculating it.
  • Participants debate the significance of certain loops and paths, with one claiming that a loop does not change anything in the circuit.
  • There is confusion regarding the terminology used for circuit components, with terms like "reductors" and "summing junctions" being discussed.
  • One participant mentions that their result differs from another's due to the presence of additional factors in the equations.
  • Several participants express uncertainty about the application of their methods and the validity of the proposed formulas.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the transfer function or the significance of certain loops. Multiple competing views remain regarding the proper approach to circuit analysis and the terminology used.

Contextual Notes

Limitations include unresolved mathematical steps and differing interpretations of circuit components. The discussion reflects varying levels of understanding and familiarity with circuit analysis techniques.

Who May Find This Useful

This discussion may be useful for students and practitioners in electrical engineering or circuit analysis, particularly those grappling with transfer functions and feedback systems.

Physics news on Phys.org
There seem to be a couple of loops missing.
 
Hi ILS! Hmm you're right.

I need to add to the R line the following:

+G2H1 +G2H1
 
Yes, but that's not all (and you should only add it once and not twice ;).
 
The bottom one is not a proper loop, since one of the arrows is in the wrong direction.

Actually, you have mentioned each of the loops at least once, but I haven't seen the proper expression for it yet.

There is also something missing from the C line.
 
Before I give you the proper expression (with the missing C line stuff) I'm trying to understand why the bottom one isn't a proper loop. I start from R, but I can't go through minuses?
 
You can and should go through the minuses, but you should not go against the arrows.
 
I like Serena said:
You can and should go through the minuses, but you should not go against the arrows.

LOL - good point.

But what's the point of this loop being there? It doesn't change anything.
 
  • #10
Which loop?
 
  • #11
The bottom one, the one you told me to discount.
 
  • #12
So why is the loop there?
Did someone tell you it should be there?
 
  • #13
I like Serena said:
So why is the loop there?
Did someone tell you it should be there?

Well, nobody's told me YOU going to be there! :wink: Sorry, I had to :smile: :biggrin:

Anyway, that loop doesn't contain anything and just goes back to R, so I say it's pointless.

As for the function:

http://img819.imageshack.us/img819/7867/gggzo.jpg

I just hope all the signs are right, too..
 
Last edited by a moderator:
  • #14
:)

Looks like you have your paths and loops almost straight now.
Where does the ##-G_1## come from in the denominator?Btw, last time you said you were taught:
C/R = Sum of all the paths / 1- sum of all the loops

This was for your basic exercise at that time.
However, I found it's not so simple for this circuit.
I tried to apply it. The result comes close, but is not quite what it should be.

I think you should build up your equations inside out, similar to the process of replacing resistors in series by one resistor, and replacing parallel resistors by one resistor.
 
  • #15
Where does the −G1 come from in the denominator?

http://img841.imageshack.us/img841/567/thisloop.jpg

Here.

This was for your basic exercise at that time.
However, I found it's not so simple for this circuit.
I tried to apply it. The result comes close, but is not quite what it should be.

I think you should build up your equations inside out, similar to the process of replacing resistors in series by one resistor, and replacing parallel resistors by one resistor.

We weren't really taught how to do that, we were just told to use the fast path.
 
Last edited by a moderator:
  • #16
Femme_physics said:
http://img841.imageshack.us/img841/567/thisloop.jpg

Here.

That one accounts for the ##+G_1## in the denominator, but not for the ##-G_1##.
We weren't really taught how to do that, we were just told to use the fast path.

Well, I'll give you a hint of what I mean.
In your circuit you could replace the loop you just marked, by a block with ##G_1 \over 1 + G_1## in it, which is the response function of just that path/loop with the G1 block in it.
This simplifies the circuit.
 
Last edited by a moderator:
  • #17
That one accounts for the +G1 in the denominator, but not for the −G1.

You're right...

So,http://img39.imageshack.us/img39/8605/g0g0.jpg
Well, I'll give you a hint of what I mean.
In your circuit you could replace the loop you just marked, by a block with G11+G1 in it, which is the response function of just that loop with the G1 block in it.
This simplifies the circuit.

I really respect your methods and don't mind trying them but I have so much to study and relatively short period of time. Should I really try to understand this? I know it may not "sound" difficult but over the internet...u know how things can be.
 
Last edited by a moderator:
  • #18
Femme_physics said:
You're right...

Yep.
That is the proper result of the application of your path/loop formula. :)
I really respect your methods and don't mind trying them but I have so much to study and relatively short period of time. Should I really try to understand this? I know it may not "sound" difficult but over the internet...u know how things can be.

No, I did not expect you would want to learn this now.
I only wanted to give you a hint that there is more to it.
Especially since your result is not quite right now.

I'll just give you the result I get:
$${C(s) \over R(s)} = {2G_1G_2 + G_2 \over 1 + G_1 + 2G_1G_2H_1 + G_2H_1}$$

As you can see it is close to what you got, except for two factors of 2 in it.
I leave it up to you what you want to do with it.
 
Last edited:
  • #19
I think I understand. There are two "reductors" (which I believe is the same as voltage sources) therefor your result makes sense. Thanks :smile:

Edit: That "IS" why you added that factor, yes?
 
  • #20
Femme_physics said:
I think I understand. There are two "reductors" (which I believe is the same as voltage sources) therefor your result makes sense. Thanks :smile:

Edit: That "IS" why you added that factor, yes?

Sorry, but I do not know what you mean by "reductor".

I calculated the result of the circuit with 2 sure-fire methods that are different from yours, which appears to be a rule of thumb.
Both came up with the extra factors 2.
 
  • #21
By "reductors" I mean the circly-thingies with the plus and minus signs, like the one that appears right after "R". If they are not reductors, what are they?
 
  • #22
Femme_physics said:
By "reductors" I mean the circly-thingies with the plus and minus signs, like the one that appears right after "R".

Ah okay, I looked them up before and came up with "summing junctions".
Are they also called reductors?

Either way, apparently it depends on how the reductors are placed whether they introduce a factor 2 or not.
Normally they wouldn't, but in this particular circuit they do.
 
  • #23
I'll go with "summing junctions", then! Whatever you say. I just thought they were said to be reductors from some reason, but summing junctions sounds more right.

Normally they wouldn't, but in this particular circuit they do.

Hmm...and how do you know when they do, and when they do not?

EDIT: Off to bed..will check again tomorrow :)
 
  • #24
Femme_physics said:
Hmm...and how do you know when they do, and when they do not?

When my 2 sure-fire methods say they do or do not. ;)

Your formula of paths/loops was new to me and it is pretty slick.
However, I was not ready to rely on it, so I checked...
 
Last edited:
  • #25
Last edited by a moderator:
  • #26
My methods are:
  • the replace-subcircuit-by-block-and-repeat method,
  • the trace-signal-with-formula-and-solve method.

The first is similar to finding an equivalent impedance for an electrical circuit.
The second is similar to analyzing a circuit with KVL/KCL.

I'll get back to you about your new circuit later.
 
  • #27
Femme_physics said:
Also,...

In this case

http://img20.imageshack.us/img20/3033/clarify.jpg
(used a pencil to clarify text)
Should I use a factor of 3 on the routes because I have 3 summing junctions at the beginning?

No, you do not get a factor of 3.
Your rule C/R=(sum paths)/(1 - sum loops) works for this circuit.

In your original circuit, the factor of 2 seems to be caused by the extra forward path that bypasses a loop.
 
Last edited by a moderator:
  • #28
I finally got it, and resolved that exercise and others and got the right result. So just wanted to say a belated thanks! Test is this tuesday :)
 
  • #29
Femme_physics said:
I finally got it, and resolved that exercise and others and got the right result. So just wanted to say a belated thanks! Test is this tuesday :)

You're welcome!

Will you let me know what the result of the test was?
 
Last edited:
  • #30
Of course :)

My hydraulics test wasn't so good, but we had a terrible teacher. I had no resolved all the question from the test successfully and will go for second term this friday.

The engineering test is this tuesday. I still have a question about Mason's Gain formula!

In this case - did I get it right?

http://img163.imageshack.us/img163/9947/tfun.jpg
 
Last edited by a moderator:

Similar threads

Why Does Current Flow in a Capacitor if the Plates Aren't Connected?
  • · Replies 12 ·
Replies
12
Views
3K
Engineering What is wrong in this 2nd order transfer function?
  • · Replies 2 ·
Replies
2
Views
2K
Process Control (transfer function) problem
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Is it possible for a low pass filter to have such a transfer function?
  • · Replies 16 ·
Replies
16
Views
2K
Engineering 2 j-terms in a transfer function?
  • · Replies 14 ·
Replies
14
Views
2K
From differential equations to transfer functions
  • · Replies 5 ·
Replies
5
Views
3K
Steps from state space to transfer function
  • · Replies 3 ·
Replies
3
Views
3K
Engineering RLC circuit -- Phasor Transfer Function calculation
  • · Replies 9 ·
Replies
9
Views
3K
Engineering How do I draw the Bode diagram of this transfer function?
  • · Replies 3 ·
Replies
3
Views
3K
Finding R and C values for an active second-order bandpass filter
  • · Replies 16 ·
Replies
16
Views
4K