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

Thanks for clarifying Tosei.