I can get s-domain transfer functions, say for a AC coupled inverting amplifer. But I can't quite interpret it, especially when gains are in dB. I know what dB is and can interchange simple gains into dB.

But when there is a circuit involved, I get confused: how does transfer function map simple voltage gain to dB?

I was trying to solve a problem(5.25) from sedra and smith(5ed): R1 is 1k, R2 is 1M.(See attached figure)

Question is that what will be the value of coupling capacitor to ensure gain will be greater than 57dB down to 100Hz.

I am getting 10uF as answer, while the books says it's 1.6uF. I first found the transfer function, which was: Vo/Vin=(-R2/R1)*(s/(s+(1/R1C1)). I take 20 log on both sides, and solve for c1 putting s=100. Where am I wrong? Or my entire concept is botched?

Help!!

But when there is a circuit involved, I get confused: how does transfer function map simple voltage gain to dB?

I was trying to solve a problem(5.25) from sedra and smith(5ed): R1 is 1k, R2 is 1M.(See attached figure)

Question is that what will be the value of coupling capacitor to ensure gain will be greater than 57dB down to 100Hz.

I am getting 10uF as answer, while the books says it's 1.6uF. I first found the transfer function, which was: Vo/Vin=(-R2/R1)*(s/(s+(1/R1C1)). I take 20 log on both sides, and solve for c1 putting s=100. Where am I wrong? Or my entire concept is botched?

Help!!

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