GATE 2023 EC – Question 57
The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $G(s)=\dfrac{k(s+z)^a}{s^b(s+p)^c}$, where $k,z,p,a,b$ and $c$ are positive constants. The value of $(a+b+c)$ is ________ (rounded off to the nearest integer).
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Correct answer: 4
Explanation
The plot starts with a slope of $-20$ dB/decade, so there is one pole at the origin: $b=1$. At $\omega_1$ the slope rises by 20 dB/decade to 0, so there is one zero: $a=1$. At $\omega_2$ the slope falls by 40 dB/decade to $-40$ dB/decade, which is a repeated pole: $c=2$. So $a+b+c=1+1+2=4$.