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Design >> Analog Design >> loopgain
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Message started by raja.cedt on Apr 22^nd, 2009, 12:09pm

Title: loopgain
Post by raja.cedt on Apr 22^nd, 2009, 12:09pm

hi,
i had a basic question on the following circuit.
in fig 1 -ve feedback loop gain -gm1*R and overall loop gain is gm1*gm3/(1+gm1*r)*gm2*gm4.So how to find +ve loop gain here? i know that if -ve feedback loop gain is grater than +ve feedback loop gain circuit is stable or +ve feedback loop gain is less than 1.So in this circuit i am getting overall L.G is lees than 1,does it mean overall feedback is +ve but LG is less than 1 and -ve feedback loop gain is less than +ve feedback?

Same thing i did for 2nd circuit and here loop gain is >1,so it wont be stable at required bias,it will be reach either of the rail? can any body explain intuitively why 2nd wont work?
i hope this question will clarify lot of doubts in feedback basics for me ,please let me know any thing wrong in the above explanation?

Thanks,
Rajasekhar.

Title: Re: loopgain
Post by buddypoor on Apr 22^nd, 2009, 2:25pm

Hi raja.sedt !

Up to now I didn´t have time to check your circuit in detail.
However, your collection of questions is rather confusing, because several times you speak about loop gain greater or lower than 1.
Please note, that the loop gain is a FUNCTION and not a specific value !
Thus, it it is not easy to understand your problem.
If you are interested in stability questions you have to consider, of course, also the PHASE of the loop gain function. But I suppose you are aware of that, don´t you ?

Title: Re: loopgain
Post by raja.cedt on Apr 23^rd, 2009, 7:02am

hi buddypoor,
thanks for your question..i am aware of the things what you have told,ok any how i will re frame my question?
In fig 1 i am getting loop gain +ve but L.G less than 1,so it works.Where as fig 2 L.G +ve ,but grater than 1. so it will have multiple operating points and it may reach rail.please tell if any thing wrong in the above.
So can any body please tell me intuitively why fig 2 wont work? i think now question is clear.

thanks,
Rajasekhar.

Title: Re: loopgain
Post by subgold on Apr 23^rd, 2009, 9:47am

i dont understand why fig.2 wont work, as long as the transistors are sized correctly.

Title: Re: loopgain
Post by thechopper on Apr 23^rd, 2009, 7:27pm

Hi Rajasekhar,

I agree with subgold. I guess you are thinking that in figure two, at low frequencies you get gm2*gm4*(1+gm1R)/(gm3*gm1). If you use the proper sizing for each transistor then you can get a +ve loop gain < 1 at low frequencies.

Intitively you can think that in figure 2 M1 gate voltage variation due to a delta i generated at M4 will be larger (due to R at M1 source) than M2 gate voltage variation due to M3 in figure 1. Since the other gains involved in the loop are the same then the loop gain is larger for figure 2 assuming same sizing as in figure 1

Tosei

Title: Re: loopgain
Post by nobody on Apr 24^th, 2009, 12:54am

In the figure2, I have another opinion. I do not think M1 is a source degeneration mosfet. The overall loop gain is different in those figures @ DC.

Title: Re: loopgain
Post by raja.cedt on Apr 24^th, 2009, 9:19am

hi nobody,
its degenerated mosfet only,why you got that doubt.And booth loop gains are different and thats why my opinion is 2nd wont work
hi Tosei,
thanks for your reply,certainly it will if you resize..but whole point in doing in this specific values is to get gm=1/R, so i should n't.Finally i have one question..what is the +ve feedback loop gain.I got overall loop gain and -ve feedback loop gain.So i think if i subtract it may come.So please clarify my doubt.

Thanks,
rajasekhar.

Title: Re: loopgain
Post by nobody on Apr 25^th, 2009, 12:34am

Hi,Rajasekhar

Those ckts look like they have a source degeneration but there is a diode-connection with or without a source degeneration. The second figure does not work definitely. There is problem set 10.12 in "The design of CMOS radio-frequency integrated circuits" by Thomas Lee, which might be helpuf if you got that book or try to find that in http://books.google.com.

Thanks

Title: Re: loopgain
Post by thechopper on Apr 25^th, 2009, 11:46am

Hi Rajasekhar,

The overall loop gain is +ve. The -ve gain is just a local feedback on the degen stage. So when you consider the overall gain gm2*gm4*(1+gmR)/(gm3*gm1) you are already considering the -ve local feedback loop. The net result is the +ve feedback.

Tosei

Title: Re: loopgain
Post by raja.cedt on Apr 25^th, 2009, 12:56pm

hi Tosei ,
thanks for your clarification and now my question is is there any way to find only +ve loop gain.This is just to enhance my feedback knowledge, but i think if we subtract gm*r from the overall loop gain . it will come.but i am not sure.
Thanks,
Rajasekhar.

Title: Re: loopgain
Post by thechopper on Apr 25^th, 2009, 6:23pm

Hi Rajasekhar,

Look at it in this way:
The two circuits are +ve feedback one. By using -ve feedback in the circuit 1 you ensure the +ve feedback is < 1 and therefore stable.
For circuit 2, if you keep the local negative feedback then you need resizing.
But bottom line is there is only one main (+ve) loop with an inner -ve feedback loop that is useful for adjusting the loop gain

Hope this helps
Tosei

Title: Re: loopgain
Post by nobody on Apr 26^th, 2009, 7:56pm

If you did the problem set in Lee's book, you will know the loop gain @ dc in figure2 is large than one. In figure 1,sometimes it is not stable.
If you are interested in the loop gain @ dc or high frequencies, please see "Improvements in Biasing and Compensation of CMOS Opamps".