An RC one-pole filter having some attention at dc is show below. The input is v1

Question

An RC one-pole filter having some attention at dc is show below. The input is v1 and the output is v2. Determine the transfer function H(f) = .

Explanation / Answer

considering the circuit in s-domain R1 and R2 doesnt change but capacitor C is 1/(Cs), v1-->V1(s),v2-->V2(s) R2 and C are parallel so [R2/(Cs)]/[R2+(1/Cs)] so V2(s)= I {[R2/(Cs)]/[R2+(1/Cs)]} and R1 is in series with resultant of parallel branches [R2/(Cs)]/[R2+(1/Cs)] so total equivalent impedance ={R1+ [R2/(Cs)]/[R2+(1/Cs) ] } so V1(s)= I {R1+ [R2/(Cs)]/[R2+(1/Cs) ] } so we find the V2(s) and V1(s) then V2(s)/V1(s) = I {[R2/(Cs)]/[R2+(1/Cs)]} / I {R1+ [R2/(Cs)]/[R2+(1/Cs) ] } BY SIMPLIFYING THE ABOVE EQUATION TRANSFER FUNCTION = [1/(R1C)]/[S+(1/R1C)+(1/R2C)] IF U WANT substitute s=jw = j 2(pi )*f

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