GATE 2023 EC – Question 25
The open loop transfer function of a unity negative feedback system is $G(s)=\dfrac{k}{s(1+sT_1)(1+sT_2)}$, where $k$, $T_1$ and $T_2$ are positive constants. The phase cross-over frequency, in rad/s, is
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Correct answer: (A) $\dfrac1{\sqrt{T_1T_2}}$
Explanation
The phase is $-90^\circ-\tan^{-1}(\omega T_1)-\tan^{-1}(\omega T_2)$. Setting it to $-180^\circ$ gives $\tan^{-1}(\omega T_1)+\tan^{-1}(\omega T_2)=90^\circ$, so $\omega T_1\cdot\omega T_2=1$ and $\omega_{pc}=\dfrac1{\sqrt{T_1T_2}}$.