I am assigned to design a circuit that peaks voltage at 10kHz and is less than half peak voltage at 3k and 30k. Only capacitors and resistors are allowed. The circuit I'm using is attached. I end up with(adsbygoogle = window.adsbygoogle || []).push({});

##I_0 = [\frac{-R_2\omega^2C_1C_2 + [C_1+C_2]R_1R_2\omega^3C_1C_2 - R_1\omega^2[C_1+C_2]^2 - R_2\omega^2C_2[C_1+C_2]}{(R_1R_2\omega^2C_1C_2-R_1\omega[C_1+C_2]-R_2C_2\omega)^2 +1} + \frac{-R_1R_2^2\omega^4C_1^2C_2^2 + R_1R_2\omega^3C_1C_2[C_1+C_2] +R_2^2\omega^3C_1C_2^2 + [C_1+C_2]\omega}{(R_1R_2\omega^2C_1C_2-R_1\omega[C_1+C_2]-R_2C_2\omega)^2 +1}i] V_{in}##

Which I just realized I have I naught and not I2 (running through R2), so I need to fix that.

I'm assuming there are some tricks to picking values to accomplish this? We're staying in the peco-micro range for caps and <1M for resistors, just for accessibility.

If I make a spreadsheet trying to capture all the variance, it's too huge. I'm already out to DZ and only have r1 + w, and r2 + w variance.

I don't think I'll even be able to solve for ##\frac{d}{d\omega} \text{Transfer} = 0 ##

Since the resistors don't seem to change much of the frequency response (I assumed they might have to do with the width of the peak, as in an RLC Q-factor), I should be able to simplify a little, but I think the key will be in my capacitance ratios.

Thanks.

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# Optimization Problem with an RC BP filter

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