how to determine feedback factor

Actually f in the Gray/Meyer's book is β/α (I've shown this in my post, 13 April).

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I don't agree. Gray/Meyer is not describing a structure where a feedforward factor similar to α place a role. They are actually discussing
structures with α=1. As you surely remember, the question in doubt was, if the authors use something like β/α and call it a feedback
factor. They don't and you shouldn't try to obscure this simple fact.

Hi.

LvW said:

to clarify things and to come to a common understanding, I have one final request to you:
Can you please define the term "feedback factor" for an electronic circuit according to your understanding ? That also means: How can this parameter be measured/calculated/simulated?
Because I am interested in a general definition applicable to the domain you are speaking of, please don't use any circuit example and no block diagram representation.
(Here I repeat the definition I rely upon: The feedback factor is defined as a portion of the output signal of an amplifier which is fed back to the input of this amplifier. For measurement, calculation or simulation of this portion the input signal which is applied in normal operation has to be set to zero).

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Feedback factor (f) is ratio of output signal (Sout) to the feedback signal (Sf), feedback signal is difference between signal at the input of the feedback amplifier (Sin) and signal at the input of the basic amplifier (Se). This feedback signal (Sf) can be represented as superposition of three signals: Sf = f1*Sin + f2*Sout + f3*Se. Feedback factor is characteristic of feedback network and doesn't depend on basic amplifier, so feedback factor will be the same with finite gain of basic amplifier (A) or with infinite gain (A -> inf) . When A -> inf, Se -> 0 and Sout/Sin -> 1/f. Thus Vf = f1*f*Sout + f2*Sout <=> f = Vf/Sout = f1*f + f2 <=> f = f2/(1-f1). The algorithm: set input signal to zero and calculate Sf/Sout (f2), set output signal to zero and calculated Sf/Sin (f1), then determine f using the last equation.

You can see that this feedback factor incorporates both β and α from your model (f2 = β and (1 - f1) = α).

FvM said:

I don't agree. Gray/Meyer is not describing a structure where a feedforward factor similar to α place a role. They are actually discussing
structures with α=1. As you surely remember, the question in doubt was, if the authors use something like β/α and call it a feedback
factor. They don't and you shouldn't try to obscure this simple fact.

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You are considering model from Fig. 8.1 (Gray) as particular case of another model (with feedforward parameter) with α = 1. But this is wrong, as I've shown earlier in this post f incorporates both β and α and equal to β/α.

Please read my post (13th April) and answer these questions:

1) Don't you agree that models in the Fig. 1 and Fig. 2 are equavalent? If you don't agree than why?
2) If you agree, please compare the second figure and Fig. 8.1 from Gray. Don't you agree that these block diagrams are the same if f = β/α and a = α*A? If no, than again, why?

Also in the page #554 (4th ed.) you can read the following:

So/Si = A = a/(1+a*f) (8.5)

Equation 8.5 is the fundamental equation for negative feedback circuts where A is the overal gain with feedback applied.

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Do you think that fundamental equation cannot be applied to all feedback amplifiers? If it cannot, why autors "forgot" to mention this?

I don't hear new aspects addressed in your post. Anything has been said.

dedalus said:

Feedback factor (f) is ratio of output signal (Sout) to the feedback signal (Sf), feedback signal is difference between signal at the input of the feedback amplifier (Sin) and signal at the input of the basic amplifier (Se). This feedback signal (Sf) can be represented as superposition of three signals: Sf = f1*Sin + f2*Sout + f3*Se. Feedback factor is characteristic of feedback network and doesn't depend on basic amplifier, so feedback factor will be the same with finite gain of basic amplifier (A) or with infinite gain (A -> inf) . When A -> inf, Se -> 0 and Sout/Sin -> 1/f. Thus Vf = f1*f*Sout + f2*Sout <=> f = Vf/Sout = f1*f + f2 <=> f = f2/(1-f1). The algorithm: set input signal to zero and calculate Sf/Sout (f2), set output signal to zero and calculated Sf/Sin (f1), then determine f using the last equation.
You can see that this feedback factor incorporates both β and α from your model (f2 = β and (1 - f1) = α).

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DEDALUS, thank you for your (pretty long) explanation/definition of the parameter which you call "feedback factor". As mentioned already in one of my answers in another thread () I do not claim that your calculation is wrong.

However, for heaven's sake, where are the advantages of your complicated approach? It is based on a modification of the classical block diagram for a system with feedback - thereby loosing the direct relation to the circuit you are analyzing.
But why not rely on the simple block diagram structure containing (a) the amplifier and (b) two blocks which simply define the signals (forward and feedback) which are superimposed at the amplifiers input? Read again the first two sentences of your "definition" of f above and ask yourself, whether it sounds simple and logical.

Are you still claiming that this approach to define a feedback factor is "common" in the field of analog IC's? And why? What is the advantage if compared with the approach which I think is the "common" one ?

What are you doing when there is more than only one feedback path? Did you already consider this case?
Regards
LvW

Hi, LvW.

LvW said:

It is based on a modification of the classical block diagram for a system with feedback

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Actually before this discussion I haven't encountered model of the feedback amplifier you are describing. In all books and articles which I've seen feedback network is represented with single block and parameter f (β/α). Thus from my point of view "my" block diagram is classical and "your" is modification.

LvW said:

However, for heaven's sake, where are the advantages of your complicated approach?

....

thereby loosing the direct relation to the circuit you are analyzing.

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But why not rely on the simple block diagram structure containing (a) the amplifier and (b) two blocks which simply define the signals (forward and feedback) which are superimposed at the amplifiers input?

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From your post, 6th April:

LvW said:

Because the quickest and simplest method to calculate transfer functions for inverting structures is to divide the process in three steps:
(a) find α and (b) find β and then (c) find the ratio of both.

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I thinks your approach is simple and have direct relation to the circuit only in the case when effect of loading of the feedback network on the basic amplifier can be neglected. The common approach to include this effect is the two-port analysis: basic amplifier and feedback network are represented with two-port networks (set of parameters depends on type of feedback). The feedback system in this case is described with 8 parameters (with 6 parameters, if bilateral behavior is neglected) and the equations for the closed-loop gain, loop gain and input/output impedances are derived using these parameters.

I suppose in active filters characteristics of amplifiers are quite close to ideal, so effects of loading can be neglected and your approach will give fast and accurate results. But in the field of analog ic design basic amplifiers are not limeted to op amps/OTAs (e.g. common transimpedance amplifier is common-source amplifier with shunt resistor).

If we apply two-port analysis to your model, the feedback amplifier will be represented by 12 (9) parameters instead of 8 (6), thereby loosing it's simplicity. So how this effect can be included in your model? And will it still be simple?

Hello DEDALUS,
I think, it’s best to stop the discussion at this point because we don`t understand each other.
What I do not understand is the following:
*You claim to be in accordance with some book authors (cited by you on April 16th), however, your „personal“ definition of the feedback factor sounds a bit different (superposition of THREE signals – including the input signal!). In contrary, I feel to be in accordance with the cited definitions (see FvM’s contribution regarding alpha).
* You claim that „my definition“ neglects amplifier loading effects due to the feedback network. Of course, that’s not true since each load is and must be considered during calculation/simulation of the forward gain of the main amplifier. You may remember that‘s one of the the main points to be considered for exact loop gain simulation.
*Quote DEDALUS: In all books and articles which I've seen feedback network is represented with single block and parameter f (β/α). Thus from my point of view "my" block diagram is classical and "your" is modification.

This explains the misunderstanding: Of course, the block diagram itself is „the classical one“. But it is important what the contents of each block is. If the input signal arrives directly at the amplifiers input (example: noninverting opamp stage), we are in agreement (no difference in block diagram represenation) .
But in case of an input circuitry which combines the input and the feedback signal – thereby reducing the effective input signal by a factor alpha – I prefer to explicitely show this factor as a separate box, which for my opinion is the most logical way. Contrary to this, you are going to implement this forward factor alpha into the feedback transfer function (is this logical?), and you claim this would lead to the „classical“ feedback topology.

*To make my position clear, please look at the attached pdf document which defines a „general feedback model“.
Regards and good luck with your method.
LvW

MODERATOR ACTION: Attachment is deleted

Hi Dedalus,
I only find that your block diagram and theory to be mainly useful in general "control systems" and not in "Analog IC Design" contrary to your claims.
The general block diagram used to explain the feedback factors easily for analog circuits consists of the basic loop, a gain block prior to the summer and a direct feed-forward term from input to output.

Can you find a block diagram representation that represents the feedback loop in a source follower going by your logic?
Technically you can find two port networks for A and beta, but see what intuitions you can build on that and how difficult it is to build such a model.

I really hope you take a look at the book Feedback amplifiers: Theory and design" https://books.google.com/books?id=X...&resnum=1&ved=0CAYQ6AEwAA#v=onepage&q&f=false

and the following paper by P.J.Hurst that analyse the two approaches to feedback
https://www.google.com/url?sa=t&sou...jLbTU_HH8EaOTpdWg&sig2=p77tR8v3WdUtmylcrFyreQ

Cheers,
Saro

Hi, LvW.

LvW said:

*You claim to be in accordance with some book authors (cited by you on April 16th), however, your „personal“ definition of the feedback factor sounds a bit different (superposition of THREE signals – including the input signal!).

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I haven't seen definition of feedback factor "by words" and this is my "personal" definition based on the expression of feedback factor f = Sf/So. I don't claim that it is absolutely correct. It is possible to present feedback signal as superposition of two signals (instead of three): input and output (Se = So/A), but I find derivation of final expression for feedback factor in this case somewhat tangled.

LvW said:

Contrary to this, you are going to implement this forward factor alpha into the feedback transfer function (is this logical?)

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We add some feedback network to the basic amplifier in order to get feedback amplifier. Part of this network appears between the input of the feedback amplifier the input and the input of the basic amplifier. Both input and output signals propagate through the same feedback network to the input of the basic amplifier, so I think there is logic in combining alpha and beta in one parameter that represents this network.

LvW said:

* You claim that „my definition“ neglects amplifier loading effects due to the feedback network. Of course, that’s not true since each load is and must be considered during calculation/simulation of the forward gain of the main amplifier. You may remember that‘s one of the the main points to be considered for exact loop gain simulation.

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The key question here was how it is possible to calculate forward gain including loading effect. But I admit my statement about two-port method was quite rash. In the inverting case feedback network represents not only "feedback block" but also subtractor at the input and it is not possible to represent feedback network by a single two-port network.

Here is my position (final, I think) on this question:

1) There are many possible definitions of feedback factor. Thus when we are speaking about it, we must explicitly give definition of this parameter to avoid misunderstanding (which took place in this discussion). It's absolutely no matter how we define feedback factor.. The main parameters of feedback system are loop gain and closed-loop gain, which have just one possible definition regardless of the representation of the feedback system (if we neglect bilateral behavior of amplifier and feedback network). To further illustrate my point of view I'm attaching page from Thomas Lee's "The design of CMOS RF integrated circuits".

2) My statement that f = β/α is common "definition" of feedback factor in the field of analog ic design is based on the fact that I've not seen any book that covers analog ic design, where other definition was used. If you know such book, please give me reference to it.

Hi, Saro

I'm familiar with these book and article. I absolutely agree that my block digram is incomplete (it neglects the fact that basic amplifier and feedback network are bilateral in general). But the question was is it common to use feedforward parameter α (which represents transmission from input of the feedback amplifier to the input of the basic amplifier, not direct feedforward parameter, which represents direct transmission from input to output of the feedback amplifier) instead of combining it with feedback factor β in the single parameter f (that is also called feedback factor) in the analog ic design.

Hi DEDALUS !

I was of the opinion that the discussion about feedback factor has finished some days ago.
However, I cannot resist to give you an answer again.

1.) At first two corrections:
(a) Quote: Both input and output signals propagate through the same feedback network to the input of the basic amplifier, so I think there is logic in combining alpha and beta in one parameter that represents this network.

Only in some cases there is a common network for the forward and the feedback signal (see pdf attachement). More than that, you should not suppress that in these cases both signals propagate through this network in different directions!

(b) Quote: There are many possible definitions of feedback factor.

No, I don’t think so. The definition – also in your examples – is always the same. But you (and possibly some authors) apply this definition to a manipulated block diagram which includes not the „basic amplifier“ (in your terms) but another active block having a gain which is reduced by the forward factor „alpha“. Therefore, alpha has to be known in advance! Why then using it twice (!) in your kind of block diagram ?

2.) Question: Your definition leads to a feedback factor – realized by only passive parts – which could be larger than unity ! Do you really consider this as helpful, reasonable and wise?

3.) Quote: To further illustrate my point of view I'm attaching page from Thomas Lee's "The design of CMOS RF integrated circuits".

Even Th. Lee does not support your opinion . He analyzes the inverting opamp under the assumption resp. condition (!):
„If we insist on equating the opamp gain G with the forward gain alpha ... (correction: a, instead of alpha) “
Further, please read the comments below Lee’s Fig. 14-13. For my understanding, he considers this procedure only as one possible alternative (...if we insist..).

4) Quote: My statement that f = β/α is common "definition" of feedback factor in the field of analog ic design is based on the fact that I've not seen any book that covers analog ic design, where other definition was used.

I suppose you misinterprete some authors. In most cases, the „generic“ feedback model (with an input directly at the basic amplifier with alpha=1) is used - and, of course, they consider an additional factor alpha in front of this amplifier by simply multiplying the gain of the generic model with this factor - but without special mention (because it is quite logical). I think, the book from Gray/Mayer (referenced by you) is a good example for this (as mentioned some day ago already by FvM).

5.) Quote: If you know such book, please give me reference to it.

I have not enough time and motivation to respond to this request. However, I already gave you some references on April 6th.

6.) Finally, in the attached pdf-doc I have collected some simple opamp circuits which possibly can convince you that „your method“ for creating a block diagram with the aim to find a loop gain expression is rather involved and not logical, either evident or clear. The situation is even more complicated for transistor stages when finite input impedances and bias networks are to be considered.

Regards to you.
LvW

Hi, LvW.

LvW said:

(b) Quote: There are many possible definitions of feedback factor.

No, I don’t think so.

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I will quote Lee:

Lee said:

It turns out that there is not necessarily one correct model in general: that is, there are potentially many equivalent models. Operationally speaking, it doesn't matter which of these we use since, by definition, equivalent models all yield the same answer. A procedure for generating one such model is as follows:

(1) select f equal to the (magnitude of the) reciprocal of the ideal closed-loop transfer function;

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α/β is ideal closed-loop gain in your model. In the previous page (460) you can see that f is called "feedback factor". Thus using first item from procedure we are obtaining f = abs(β/α). Does this "definition" of feedback factor differ from your (β) or mine (β/α)?

Do you think that feedback factor is fundamental parameter of the feedback system? If yes, what information can you get from feedback factor without other parameters? E.g. loop gain (which I consider as fundamental parameter) gives stability margins, gain desensitivity factor, etc.

LvW said:

Even Th. Lee does not support your opinion. He analyzes the inverting opamp under the assumption resp. condition (!):
„If we insist on equating the opamp gain G with the forward gain alpha ... “
Futher, please read the comments below Lee’s Fig. 14-13. For my understanding, he considers this procedure only as one possible alternative (...if we insist..).

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You have confused "α" (Greek letter) with "a" (Latin letter) which represents gain of the basic amplifier (forward gain, not feedforward gain). Please re-read carefully this example.

LvW said:

Only in some cases there is a common network for the forward and the feedback signal (see pdf attachement). More than that, you should not suppress that in these cases both signals propagate through this network in different directions!

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It doesn't follow from this fact that feedback network cannot be represented with single parameter f (ratio of two transfer functions).

LvW said:

2.) Question: Your definition leads to a feedback factor – realized by only passive parts – which could be larger than unity ! Do you really consider this as helpful, reasonable and wise?

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Feedback factor f can be considered as ratio of two transfer functions (β/α, both β and α are less than unity) of the same network, so I don't see any strangeness in the fact the the result (f) can be either less or greater than unity.

LvW said:

I have not enough time and motivation to respond to this request. However, I already gave you some references on April 6th.

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You are disputing what definition of feedback factor is commonly used in analog ic design field, but none of the books you've referenced in those post cover analog ic design. Also as you suggested I found some books on control theory (A Mathematical Introduction to Control Theory, Engelberg; Modern Control Engineering, Ogata), but the model without feedforward parameter is used there.

LvW said:

I suppose you misinterprete some authors.In most cases, the „generic“ feedback model (with an input directly at the basic amplifier with alpha=1) is used - and, of course, they consider an additional factor alpha in front of this amplifier by simply multiplying the gain of the generic model with this factor - but without special mention (because it is quite logical).
I think, the book from Gray/Mayer (referenced by you) is a good example for this (as mentioned some day ago already by FvM).

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The argument of FvM (17th April) is

FvM said:

But there isn't anything like β/α, neither at this place nor anywhere in chapter 8 Feedback or 9 Frequency Response and Stability of Feedback Amplifiers.

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Why there must be something like β/α if nor β, nor α are used??? Instead of A, β and α other set of parameters is used: A', f. I have shown (and you have agreed) that these two models are equivalent if this parameters are related in the next way: A' = α*A, f = β/α. Indeed, block diagram that corresponds to set (A', f) visually resembles the block diagram that corresponds to (A, α, β) with α = 1. But this is not enough to contend that the model (A', f) can be used only in particular cases when α = 1, because when α != 1 => A' != A and f != β.

Example from Lee (with explicit analysis of inverting amplifier) is a good confirmation of the correcness of my interpretation. If we choose f equal to reciprocal of the ideal closed-loop gain (including sign), we'll get exactly my definition of feedback factor.

Your mainly repeating your mantra:

I have shown ... that these two models are equivalent if..

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I don't like an only "equivalent" model and the "if". I prefer the clearness of "β/α" feedback model with it's related block structure,
that is representing real phsyical entities.

Hi DEDALUS,

Now I am arrived at that point, which FvM has described already some days ago: "Everything has been said". Perhaps a direct personal discussion face to face between us would be the only way to clarify some misunderstandings.

You are disputing what definition of feedback factor is commonly used in analog ic design field, but none of the books you've referenced in those post cover analog ic design. Also as you suggested I found some books on control theory .... but the model without feedforward parameter is used there.

In this context, one simple and final remark:
I think, nearly all books on control theory and analog IC design (!!) define loop gain and feedback factor for a real circuit based on the "generic" feedback model which does not contain any forward factor in front of the summing junction. Why? Because it is quite logical to consider such a factor which is outside the feedback loop - if it exists - simply by multiplication without touching the loop.
Can you give any reasonable reason why to complicate the analysis by manipulating the loop with the aim to include such a factor into the loop - thereby loosing the direct and visual equivalence to the actual circuit?

Oh yes, as cited by you, Thomas Lee has mentioned a (good?) reason:
If we choose f equal to reciprocal of the ideal closed-loop gain (including sign), we'll get exactly my definition of feedback factor.

That's the only justification for doing this:
To get a closed-loop gain which is identical to the reciprocal of "his" (and yours) feedback factor. Do you consider this really as a sufficient justification?
Don't overlook the fact, that Lee has restricted himself on the simple example of the inverting opamp application. More than that, of course, he does not claim that this procedure leads to a general definition in the field of analog IC design (as you do!).
In contrary, he considers this only as a possible alternative (if we insist.....) - and, perhaps, for this simple example one can do it. In particular, if his aim is to show that there are always several alternatives to create a block diagram which reflects the actual circuit properties.
Certainly, you know that there are tables which contain rules for allowed block diagram manipulations - with the aim to find a circuit representation which is (a) easy to analyze and (b) which clearly shows and separates the most important functions in order to find optimum design strategies.
But, what you propose, is just the opposite: To define an important parameter based on an artificial block diagram which is neither transparent nor does it simplify design and analyses of the system.

Final question: Did you try to apply "your" definition on the circuit examples I gave you with my last posting? Did you realize that in some cases there is also a forward factor in front of the non-inverting terminal (which of course is isolated from the feedback network)? Do you intent to "shift" such a factor also into the feedback loop ? I think it would be silly and crazy to do something like this. (Or - as you have indicated - has the field of analog IC design it's own rules?)

Best regards
LvW