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could you help me to find the band-pass gain of the following filter please?

enter image description here enter image description here

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.

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    \$\begingroup\$ That photo hurts my eyes. Please find a way to upload an easier to read schematic. Or redraw it with the in build schematic tool. You might get more help that way. \$\endgroup\$
    – crowie
    Sep 25, 2016 at 15:24
  • \$\begingroup\$ Hi @crowie, please tell me what parts of photo aren't clear. \$\endgroup\$ Sep 25, 2016 at 15:26
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    \$\begingroup\$ Its all just very hard to read I'm just suggesting if you want to get help on this site make it clear and easy for people. \$\endgroup\$
    – crowie
    Sep 25, 2016 at 15:33
  • \$\begingroup\$ For starters, what is the symbol in parentheses after \$V_{IN}\$? \$\endgroup\$ Sep 26, 2016 at 9:56
  • \$\begingroup\$ Hi @Dmitry Grigoryev, I wrote $$V_{IN}\left(s\right)$$ where s is the Laplace's variable. \$\endgroup\$ Sep 26, 2016 at 12:20

2 Answers 2

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  • Gnd symbols are too close to parts.
  • contrast of grids is same as pencil so hard to read.
  • adding brightness and contrast to photo could help us.

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

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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.

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