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could you help me to find the band-pass gain of the following filter please?
The correct expression of pass-band gain hasn't the term \$ C_{B}R_{B} \$ to the numerator (said my professor), instead in my expression there is:
$$G_{PB}=\left(1+\frac {R_{4}}{R_{3}} \right)\left( 1+\frac {R_{2}}{R_{1}} \right)R_{B}C_{B}$$
Thank you for your help.
I only see one cap, Ca, not two Ca, Cb
The "unstated" assumption in this circuit is that the pulse width expected is much shorter than the time constant T=RaCa so for this condition, assume V(Ca) is a drifting DC voltage dependant on the duty cycle of the pulse and will always be between the pulse max~min levels, so the DC reference level Vlf will change with the signal and its gain is 1+|Av-| which for high gain 1+ can be neglected. Taking the difference between a signal and it's LPF signal yields the HPF response when both gains are the same (assuming Av>>1 of 2nd stage. This is an intuitive answer not mathematical such as yours which may be correct for Tpw>RaCa (low frequencies). When we want to simplify gain, we make these assumptions and state them e.g. for f>> 1/(2piRaCa) Av2= +R2/R1
You have two opamp buffers with gain totalling Av = (1 + R2/R1) * (1 + R4/R3) and two first order networks a lowpass RA/CA and a highpass RB/CB.
A first order LPF is G(w) = 1 / (1+jRaCaw)and a highpass is G(w) = jRbCbw/(1+jRbCbw)
Putting it all together I make the overall response (1/(1+jRaCaw)) * jRbCbw/(1+jRbCbw) * (1 + R2/R1) * (1 + R4/R3)
It might be worthwhile multiplying thru by a few complex conjugates to see if you can massage the thing into whatever form the prof wants.
Been a few years since I took this crap back in circuits and systems but it looks right to me.
