Understanding Transfer Functions: Am I On the Right Track?

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Discussion Overview

The discussion revolves around understanding transfer functions in the context of signal processing and control systems. Participants are attempting to clarify their understanding of how to derive transfer functions, analyze signal pathways, and identify loops in a given system diagram.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant shares a diagram and asks if their understanding of transfer functions is correct.
  • Another participant suggests that the original poster needs to provide formulas for each point between blocks to derive the correct transfer function.
  • There is a discussion about the proper method for calculating transfer functions, with references to summing paths and loops.
  • Participants express confusion about the derivation process and seek clarification on specific steps in the calculation.
  • One participant mentions a formula for transfer functions: C/R = Sum of all the paths / 1 - sum of all the loops.
  • There are multiple references to the need to rectify diagrams and identify loops correctly, with some participants suggesting different interpretations of the loops present in the system.
  • Participants discuss the implications of summing junctions on the loops and how they affect the calculations.
  • There are playful exchanges among participants, indicating a collaborative and friendly atmosphere despite the technical challenges.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to deriving the transfer function or identifying the loops. There are competing views on how to interpret the diagrams and the calculations involved.

Contextual Notes

Participants express uncertainty about specific steps in their calculations and the definitions of terms like "rectify." There are unresolved questions regarding the correct identification of loops and pathways in the system.

Who May Find This Useful

This discussion may be useful for students and practitioners in electrical engineering, control systems, or signal processing who are learning about transfer functions and their applications.

Femme_physics
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I don't think so...
Do you have some work to go with that?
 
What do you mean some work to go with that?
 
Well, at each point between the blocks you should have a formula representing the signal there.
Solving the entire formula should give you C/R.
 
Well, at each point between the blocks you should have a formula representing the signal there.
Solving the entire formula should give you C/R.

Hmm..I still don't get where exactly my mistake is in the C/R I created?

If you can help me see that, please... :)
 
Femme_physics said:
Hmm..I still don't get where exactly my mistake is in the C/R I created?

If you can help me see that, please... :)

I don't know how you derived it.
If you could say how you got it...?Let's start on the left, where you have the input signal R, which is combined with the output signal C.
The circle signifies how they are combined, which will result in (+R-C) between the circle and block G1.

Next step is between blocks G1 and G2.
A block multiplies the signal, meaning the resulting signal is G1(+R-C).

Can you say what the next step is?
And the resulting signal?
 
I don't know how you derived it.
If you could say how you got it...?

OK. The formula says

C/R = Sum of all the paths / 1- sum of all the loops


This is actually my NEW attempt. Pathways in black. Loops in orange.

http://img545.imageshack.us/img545/7681/laster.jpg




Let's start on the left, where you have the input signal R, which is combined with the output signal C.
The circle signifies how they are combined, which will result in (+R-C) between the circle and block G1.

Next step is between blocks G1 and G2.
A block multiplies the signal, meaning the resulting signal is G1(+R-C).

Can you say what the next step is?
And the resulting signal?

G1(+R-C)+G2(+R-C)+G3(+R-C)


(IMO that's only 1 pathway, there are 2 pathways since there's a pathway that skips over G1)
 
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Femme_physics said:
OK. The formula says

C/R = Sum of all the paths / 1- sum of all the loops

Okay. That's another way to solve it.
Femme_physics said:
This is actually my NEW attempt. Pathways in black. Loops in orange.

http://img545.imageshack.us/img545/7681/laster.jpg

This is a different diagram than your problem states...

You have the sum of the paths right though.

For the loops you should first rectify you diagram.
After that you should consider that you also have a large loop.

Perhaps you can list the loops that you see with their corresponding formulas?

Femme_physics said:
G1(+R-C)+G2(+R-C)+G3(+R-C)(IMO that's only 1 pathway, there are 2 pathways since there's a pathway that skips over G1)

You're moving to fast with this method.
Let's make a stop immediately to the right of G2.
So left of G2 you have G1(+R-C).
What would you have immediately to the right of G2?
 
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Okay. That's another way to solve it.
That's the method we're being taught :smile:

You have the sum of the paths right though.

For the loops you should first rectify you diagram.
After that you should consider that you also have a large loop.

What do you mean by "rectify"?

I agree, I forgot the large loop.

http://img440.imageshack.us/img440/7948/gotitj.jpg


Perhaps you can list the loops that you see with their corresponding formulas?


of course. It's the lower row in the image I've just made.

You're moving to fast with this method.
Let's make a stop immediately to the right of G2.
So left of G2 you have G1(+R-C).
What would you have immediately to the right of G2?

Oh, sorry :smile: That would be G3(+R-C)
 
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  • #10
Femme_physics said:
That's the method we're being taught :smile:

Okay, so that's what we'll do. ;)

If you'd like we can also do it my way, if only as a verification.


Femme_physics said:
What do you mean by "rectify"?

You just did. You have the proper diagram now.


Femme_physics said:
I agree, I forgot the large loop.

http://img440.imageshack.us/img440/7948/gotitj.jpg

of course. It's the lower row in the image I've just made.

You have the right diagram now, but not the right loops.

Let's start with the small loop.
It contains G3 and H, but that does not match either of the loops you got.


Femme_physics said:
Oh, sorry :smile: That would be G3(+R-C)

No, not quite.
We had G1(+R-C) and we apply block G2.
How did you get G3?
And where did G1 go?
 
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  • #11
That's the method we're being taught

Okay, so that's what we'll do. ;)

If you'd like we can also do it my way, if only as a verification.

Oh, I don't mind at all, you always give me new insights. :smile:
You just did. You have the proper diagram now.

'the hell is wrong with my English? :wink:
You have the right diagram now, but not the right loops.

Let's start with the small loop.
It contains G3 and H, but that does not match either of the loops you got.

Oh, I thought loops can only start with the "R". I guess that's not the case. So, here, I coloured all the R (loops) only.Oh and...PIKABOO! :) Just in case u missed my cameo appearances.

http://img163.imageshack.us/img163/1453/pikabo.png
No, not quite.
We had G1(+R-C) and we apply block G2.
How did you get G3?
And where did G1 go?

Well, it didn't go anywhere, but you asked me what's the the right of G2, and G1 is not at the right of G2.

To the right of G2 is what appears to be a voltage source?
 
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  • #12
Femme_physics said:
Oh, I don't mind at all, you always give me new insights. :smile:
Femme_physics said:
'the hell is wrong with my English? :wink:

rec·ti·fy (rkt-f)
tr.v. rec·ti·fied, rec·ti·fy·ing, rec·ti·fies
1. To set right; correct.
2. To correct by calculation or adjustment. See Synonyms at correct.
3. Chemistry To refine or purify, especially by distillation.
4. Electronics To convert (alternating current) into direct current.
5. To adjust (the proof of alcoholic beverages) by adding water or other liquids.It turns out there's even a specific electronics meaning, but that's not the one I intended. ;)
Femme_physics said:
Oh, I thought loops can only start with the "R". I guess that's not the case. So, here, I coloured all the R (loops) only.
Femme_physics said:
Oh and...PIKABOO! :) Just in case u missed my cameo appearances.

http://img163.imageshack.us/img163/1453/pikabo.png

Yes, I did miss your cameo appearances. :redface:
Thanks! :smile:

There!
You have the right loops now:
1. G1G2G3
2. G3
3. G3H

Only one thing... the loops go through summing junctions.
If a loop goes through the minus of a summing junction, it becomes negative...
Femme_physics said:
Well, it didn't go anywhere, but you asked me what's the the right of G2, and G1 is not at the right of G2.

To the right of G2 is what appears to be a voltage source?

No, not a voltage, but a summing junction.
It sums the signals that come in (or subtracts them if there is a minus).

I asked what the signal would be to the right of G2.
To the left of G2 the signal is G1(+R-C).
(Note the + and - signs that have resulted from the summing junction.)
Since a block multiplies the signal, the resulting signal is G2G1(+R-C).
 
  • #13
It turns out there's even a specific electronics meaning, but that's not the one I intended. ;)

I know! :smile: You didn't have to go through the full explanation! It's the electronics definition that confused me because I was aware of it. I was worried it has a system engineering definition. Heh. Nevermind.

Yes, I did miss your cameo appearances.
Thanks!

*kissy winky*

Only one thing... the loops go through summing junctions.
If a loop goes through the minus of a summing junction, it becomes negative...

That's exactly what all my loops are minused!

No, not a voltage, but a summing junction.
It sums the signals that come in (or subtracts them if there is a minus).

Gotcha.

I asked what the signal would be to the right of G2.
To the left of G2 the signal is G1(+R-C).
(Note the + and - signs that have resulted from the summing junction.)
Since a block multiplies the signal, the resulting signal is G2G1(+R-C).

Ah, thanks. But I did get the right answer, eh? :wink:
 
  • #14
Femme_physics said:
*kissy winky*

:blushing:


Femme_physics said:
That's exactly what all my loops are minused!

But they aren't!
You said yourself: "C/R = Sum of all the paths / 1- sum of all the loops"
There is already a minus in your formula.
It the loop has a minus too, it becomes a plus!



Femme_physics said:
Ah, thanks. But I did get the right answer, eh? :wink:

Nope.
 
  • #15
But they aren't!
You said yourself: "C/R = Sum of all the paths / 1- sum of all the loops"
There is already a minus in your formula.
It the loop has a minus too, it becomes a plus!

You mean ALL of the minuses at the bottom row should have been written as pluses then?
 
  • #16
Femme_physics said:
You mean ALL of the minuses at the bottom row should have been written as pluses then?

Yep!
 
  • #17
Thanks ILS, we solved it in class and you were of course all right :wink:
 

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