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Question

# An open loop transfer function of a unity negative feedback control system is given by, G(s)=Ks(s+a)(s+b) If the gain margin of the system is 32 dB for K = 2, then the value of K required to get the gain margin of 25 dB will be

A
4.48
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B
38.1
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C
1.12
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D
6.38
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Solution

## The correct option is A 4.48The gain margin of the system can be given as, GM=20log101|G(jωpc)| ωpc is independent of the value of K. So, GM=C−20log10(K) Where, C is a term independent of "K". For K = 2, GM=32 dB So, C=32+20log10(2) When GM = 25 dB, 25=C−20log10(K) 25=32+20log10(2)−20log10(K) 20log10(K)=7+20log10(2)=13.02 K=10(13.02/20)=4.48

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