**Nyquist Stability Criterion MCQ**

**1. Which principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q(s) plane contour?**

a) Argument

b) Agreement

c) Assessment

d) Assortment

**Answer:** a

**Explanation:** Argument principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q(s) plane contour.

**2. If a Nyquist plot of G (jω) H (jω) for a closed loop system passes through (-2, j0) point in GH plane, what would be the value of gain margin of the system in dB?**

a) 0 dB

b) 2.0201 dB

c) 4 dB

d) 6.0205 dB

**Answer:** d

**Explanation:** Gain Margin is calculated by taking inverse of the gain where the Nyquist plot cuts the real axis.

**3. For Nyquist contour, the size of radius is _______**

a) 25

b) 0

c) 1

d) ∞

**Answer:** d

**Explanation:** For Nyquist contour, the size of radius is ∞.

**4. Consider a feedback system with gain margin of about 30. At what point does Nyquist plot crosses negative real axis?**

a) -3

b) -0.3

c) -30

d) -0.03

**Answer:** b

**Explanation:** Gain Margin is always inverse of the point which cuts the Nyquist on the real axis.

**5. According to Nyquist stability criterion, where should be the position of all zeros of q(s) corresponding to s-plane?**

a) On left half

b) At the center

c) On right half

d) Random

**Answer:** a

**Explanation:** According to Nyquist stability criterion zeroes must lie on the left half on the s plane.

**6. If the system is represented by G(s) H(s) = k (s+7) / s (s +3) (s + 2), what would be its magnitude at ω = ∞?**

a) 0

b) ∞

c) 7/10

d) 21

**Answer:** a

**Explanation:** On calculating the magnitude of the system and putting the value of frequency one gets the magnitude as 0.

**7. Consider the system represented by the equation given below. What would be the total phase value at ω = 0? ****200/[s3 (s + 3) (s + 6) (s + 10)].**

a) -90°

b) -180°

c) -270°

d) -360°

**Answer:** c

**Explanation:** The phase can be calculated by the basic formula for calculating phase angle.

**8. Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0 ?**

a) -45°

b) -60°

c) -90°

d) -180°

**Answer:** c

**Explanation:** Addition of pole causes instability to the system.

**9. In polar plots, if a pole is added at the origin, what would be the value of the magnitude at Ω = 0?**

a) Zero

b) Infinity

c) Unity

d) Unpredictable

**Answer:** b

**Explanation:** Addition of pole causes instability to the system.

**10. In polar plots, what does each and every point represent w.r.t magnitude and angle?**

a) Scalar

b) Vector

c) Phasor

d) Differentiator

**Answer:** c

**Explanation:** Each and every point on the polar plot is the phasor where value of frequency varies.

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