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The asymptotic approximation of the log-magnitude versus frequency plot of a minimum phase system with real poles and one zero is shown in the figure. Its transfer function is
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20(s + 5) s(s + 2)(s + 25)
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10(s + 5) (s + 2) s2 (s + 25)
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20(s + 5) s2 (s + 2)(s + 25)
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50(s + 5) s2 (s + 2)(s + 25)
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Correct Option: D
Since at ω = 2 and ω = 25, slope changes from 40dB/dec to – 60 dB/dec at both the value. So there are poles at ω = 2 and ω = 25.
Also at ω = 0.1, slope is – 40 dB/dec, i.e. there are two poles at origin.
Hence transfer function, should be of the form
| T(s) = | ||
| s2(s + 2)(s + 25) |
| Now , 54 = 20 log | ||
| (0.1)2 × 50 |
⇒ K = 50
| ∴ T(s) = | ||
| s2(s + 2)(s + 25) |
