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Design >> Analog Design >> Feedback Ckt 3-dB Bandwidth (Fundamental question)
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Message started by hchanda on Oct 11^th, 2007, 2:26pm

Title: Feedback Ckt 3-dB Bandwidth (Fundamental question)
Post by hchanda on Oct 11^th, 2007, 2:26pm

All,

I am very confused how a 3-dB bandwidth is defined for a feedback circuit.

As we know closed-loop gain A(s)=a(s)/[ 1 + a(s)*f]

where a(s) is gain of the basic amplifier in feedback loop and 'f' is feeeback gain.

We define loop gain T(s)= a(s)*f

So the 3-dB bandwidth of the feedback circuit [A(s)] is the frequency where loop gain is 1 or 0dB. (page 636 in Grey Meyer, 4th edition)

But If you see the chapter 9 of Grey Meyer 4th edition page 631

There he calculates A(jw) = a(jw)/[1+ T(jw)]

|T(jw)|=|a(jw) *f|
if |T(jw)|=1 ====> |a(jw) =1/f

when |T(jw)|=1 , phase(T(jw))=-135 at w=w0 ; Then A(jw0)=1.3/f

when |T(jw)|=1 , phase(T(jw))=-120 at w=w0 ; Then A(jw0)=1/f

when |T(jw)|=1 , phase(T(jw))=-90 at w=w0 ; Then A(jw0)=0.7/f

From the above it looks like the closed loop 3-dB bandwidth is the frequency where |T(jw)=1 and phase(T(jw)) is -90

But why does author always says"3-dB bandwidth of the feedback circuit is at the frequency where loop gain is 0dB" but does not consider the phase margin at all?

Please provide your inputs on this topic.

Thank you,
hc

Title: Re: Feedback Ckt 3-dB Bandwidth (Fundamental quest
Post by tosei on Oct 14^th, 2007, 9:15pm

Hi,

The examples for loop gain=0dB with different phase shifts are examples of different phase margins systems, meaning that the second pole of your system is "close" enough to the ideal -3dB frequency (loop gain = 1) in such a way that the effect of the phase shift associated to it produces an attenuation different than -3dB. Therefore the BW is not the one for the loop gain = 0dB anymore.

I guess the correct way to state it is that the -3dB frequency is the frequency at which the loop gain is 1 only for a one-pole system or a system with a dominant pole whose second pole is at least 2 decades away from the 0dB loop gain frequency (this guarantees 90 phase at such frequency).

Regards
tosei

Title: Re: Feedback Ckt 3-dB Bandwidth (Fundamental quest
Post by hchanda on Oct 15^th, 2007, 10:30am

Thanks for clarifying Tosei.