Hi Lily,
Quote:What is the relation between the bandwidtn of the filter and the unity gain bandwidth of the amplifier?
I agree with Buddypoor that there's no direct relation between filter BW & reqd. Opamp BW. But would like to add a few things :--
1.
A
∞ = -1/sRC = - w
0 / s
A(s) = V
out(s)/V
in(s) = A
∞ T(s) / ( 1+T(s) )
T(s) = -a(s) R/( R + 1/sC ) =
a0 / ( 1 + 1/w
p) *
s/w0 /
( 1 + s/w0 ) where w
p ≈ w
0 / s
....aah, that was a pain...to type it out...
Is from my notebook...had done this analysis sometime back...
So now you can see, there a magnitude fn A(s) which is close to desired function A
∞ as long as T(s) is large....
Ohh This eqn will make it more clear....
we can write from above --> A(s) = -w
0/s * 1/(1+w
0/w
u) * 1/(1+s/(w
0 + w
u))
The first term is the desired ideal term...
The second term shows magnitude error due to finite GBW
The Third term shows undesired shift in pole frequency(both mag+phase error) due to finite GBW..
I hope that makes it a bit more clear...through the mathematical analysis....
thanx,
Mayank.