Question

Given the circuit below, determine the transfer function V (s)/V,(s) in terms of the parameters given. LE +? UD ok

Answer 1

Ans)

the circuit in frequency domain is

C1 HH 1/sC1 R2 R1 Vm(s) C3 V-V. 0 1/sC3 Vo(s) vs(s) OUT C2 1/sC2 V 0 V R4 0 circuit in frequency domain As it is in negative feedback inverting mode V.=V.=0

now node equation gives

Vm (s) Vm (s) V(s) Vm(s) 0 + R1 sC2 sC3

Vm (s) V(s) sC2Vm (s)sCa Vm(s) R1 R1

V,(s) s(C2+Ca))Vm (s) = R1 R1

(1s(C2C3) RI)Vm (s V(s) S

V(s) Vm (s) (1s(C2C3) R1) eq1

now node equation at other node i.e -ve input node of op-amp

0 V 0- Vo(s) 0- Vo(s) + 0 = R2 sC1 sCs

Vo(s) sC1 Vo(s) -sC3Vn(s) R2

sC1 )V(s)sC3Vm (s) R2

SC1R21 -Vo(s)sC3Vm (s) R2.

$V_{o}(s)=-\frac{sC_{3}R2}{(sC_{1}R2+1)}V_{m}(s)$

using eq1

V(s) sC3 R2 (sC1 R21) Vo(s) (1s(C2C) R1)

$\frac{V_{o}(s)}{V_{s}(s)}=-\frac{sC_{3}R2}{(sC_{1}R2+1)(1+s(C_{2}+C_{3})R1)}$

$\frac{V_{o}(s)}{V_{s}(s)}=-\frac{sC_{3}R2}{(s^{2}(C_{2}+C_{3})R1*C_{1}R2+s(C_{2}+C_{3})R1+sC_{1}R2+1)}$

Vo(s) SC3R2 Vs(s (s2C1 (C2C3) R1R2 +s( (C2+ C3)R1 C R2)1) S