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who determines stability? return ratio or loop gain?

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qslazio

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from P.J. Hurst's paper, I kown that they model the different things so they are not the same in the most of the case.
But I want to know, which of these two terms can decide whether or not the circuit is stable?

Anyone has ideas about it?

thanks!
 

Is there anyone having solid understanding of feedback theory who can help me?
 

Hi, qslazio,

The circuit stability depends on its poles locations. To decide whether a pair of uncompensated poles is in the LHP or in RHP of the closed-loop gain s-plane, one can analyze the behavior of either loop gain or return ratio (Nyquist criterion).

There is no principal difference between the loop gain and the return ratio.

Moreover, all this cookbook-type feedback analysis: (1) do this…, (2) do that…, (3) then do something else, is no more than a lack of common sense.

Most practical feedback circuits can exactly be solved ‘in head’ for loop gain, feedback and feedforward transmission, etc., with no help of a cookbook.

Please let me know if you need more details.
 

    qslazio

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hi jasmin_123
thanks for reply.
I agree that loop gain and return ratio should agree on whether or not the circuit is stable.
But in designing the circuit, we have to quantify how much stable or how much unstable. So we have to use phase margin and gain margin. Since in loop gain calculation, it lumps all the feedforward zero into forward dependent source, the loop gain expression will contain zeros (whether LHP or RHP) which are not contain in return ratio expression.
As a consequence, the phase margin get from loop gain and return ratio may differ. So someone may get the wrong intuition that feedforward zero (LHP) may increase phase margin or increase the stability. My question is when we talk about phase margin or gain margin, which of these two terms should I use?

I'm not familiar with nyquist criterion. Is it based on return ratio or loop gain?
thanks again!
 

I am also puzzled with the stability judgement!

return ratio or loop gain? I see some papers say that in some situations they are the same.

so we should do return ratio or loop gain simulation in circuit desinging?

expect someone could explain, thx very much!
 

Hi, qslazio,

Calculate and analyze what you and Hurst call return ratio and forget about what you and Hurst call loop gain. I would also suggest forgetting about all this mess with lumping one transmission into another; simply consider the following equation for closed-loop gain:

AF=G*AOL/(1+AOL*B)+G*BF

where G is the input transmission (Sin/Ss for aol=0), aol is the dependent source value, AOL is the open-loop gain (So/SinM for Sin=0, SinM means that the dependent source must remember the Sin value that it had seen before applying superposition), AOL*B is the loop-gain, or return ratio, whatever you like (Sin/Sinm for Sin=0), B is the feedback transmission of the feedback network (Sin/So for Sin=0), G*BF is the direct signal feedthrough (So/Ss for aol=0), and BF is feedforward transmission of the feedback network (So/Sin for aol=0).

Calculate all the above transmissions by applying superposition with DEPENDENT source, without ANY breaking the feedback. Just like this (attached):
https://users.ece.gatech.edu/~mleach/papers/superpos.pdf

This works very fine for circuits with a single dependent source (most practical cases).

Superposition is especially handy in noise analysis.
It is a fun to do noise analysis just 'in head' by applying superposition to many noise sources. You have to only calculate Gi and Gi*BFi for each noise source and then use one and the same AOL/(1+AOL*B) for all the sources. Try it out!

Do not be too formal! Down with cook books.

PS: Nyquist criterion is one of many stability criterions. It is not usually used to analyze phase or gain margins.
 

This paper describes feedback as SUPERPOSITION.
It took 75 years to understand such a simple thing!
 

Just to illustrate that the difference between the loop gain, a, and the return ratio, rr, is not principal.

For a single-loop circuit, the closed-loop gain is either

Acl=a/(1+a*b)

or

ACL=G*AOL/(1+rr)+G*bfwd=G*[AOL+bfwd*(1+rr)]/(1+rr)=A/[1+A*(rr/A)];

ACL=A/(1+A*B),

where A= G*[AOL+bfwd*(1+rr)], and B=rr/A.

Note, however, that despite the same form of the two above equations for ACL,
A is not equal a, and a*f is not equal A*B.

For example: 10/(1+4)=6/(1+2), but 10 is not equal 6, and 4 is not equal 2.

The only difference between a and A (and between b and B) is
how much gain you lump into them.
 
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