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The asymptotic approximation of the log-magnitude vs frequency plot of a system containing only real poles and zeros is shown in the figure given below. Its transfer function is
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10(s + 5) s(s + 2)(s + 25) -
1000(s + 5) s2(s + 2)(s + 25) -
100(s + 5) s(s + 2)(s + 25) -
80 (s + 5) s2 (s + 2)(s + 25)
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Correct Option: B
| At ω = 0.1, | 2 poles |
| At ω = 2, | 1 pole |
| At ω = 5 , | 1 zero |
| At ω = 25 , | 1 pole |
So, transfer function,
| T(s) = | ||
| s(s + 2)(s + 25) |
| ∴ 80 = 20 log | ||
| (0.1)2 × 2 × 25 |
| ⇒ 4 = log | ||
| 0.5 |
⇒ 10k = 104
⇒ k = 103 = 1000
| ∴ T(s) = | ||
| s2(s + 2)(s + 25) |
