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Question

For the system shown in below figure, what is the transfer function Vo(s)Vi(s)?

(Given R1=R2=C1=C2=1 unit)

A
Vo(s)Vi(s)=ss2+3s+1
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B
Vo(s)Vi(s)=1s2+3s+1
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C
Vo(s)Vi(s)=s2s2+2s+1
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D
Vo(s)Vi(s)=s+1s2+2s+1
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Solution

The correct option is A Vo(s)Vi(s)=ss2+3s+1
After taking Laplace transform, the series combination of R1 and C1 gives:
R1+1sC1

Similarly, the parallel combination of R2 and C2 gives:
R2sC2R2+1sC2

Substituting, R1=R2=C1=C2=1 makes the above combinations 1+1/s and 1/s1+1/s

On applying the voltage divider rule, we get

Vo(s)=1/s1+1/s1+1s+1/s1+1/sVi(s)

Vo(s)Vi(s)=1s+1s(s+1)+(s+1)+ss(s+1)

Vo(s)Vi(s)=ss2+3s+1

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