Question

For Nyquist contour, the size of radius is ____ .

• A. 25
• B. 0
• C. 1
• D. \(\infty\)

Hint:

Nyquist Contour. Used for Nyquist stability analysis. It encloses the entire right-half of the s-plane. Consists of the imaginary axis (\(j\omega\)) and a semi-circular arc of infinite radius in the right-half plane.

Answer 1

The Correct Option is D

The Nyquist stability criterion involves mapping a specific contour from the s-plane (Laplace domain) through the open-loop transfer function G(s)H(s) onto the G(s)H(s)-plane (Nyquist plot)
The standard Nyquist contour is chosen to enclose the entire right-half of the s-plane, as stability requires that the closed-loop poles (zeros of 1+G(s)H(s)) lie in the left-half plane
This contour typically consists of:
(1) The entire imaginary axis (\(s = j\omega\), from \(\omega = -\infty\) to \(+\infty\))

(2) A large semi-circular arc in the right-half plane, connecting \(+j\infty\) to \(-j\infty\)
The radius of this semi-circle is taken to be infinitely large (\(R \to \infty\)) to ensure that all possible right-half plane poles and zeros of the characteristic equation are enclosed
Therefore, the size of the radius for the semi-circular part of the Nyquist contour is infinite