**All-pass & Minimum-phase Systems**

**1. A minimum phase unity feedback system has a bode plot with a constant slope of -20dB/decade for all frequencies. What is the value of the maximum phase margins of the system?**

a) 0°

b) 90°

c) -90°

d) 180°

**Answer:** b

**Explanation:** For given Bode plot, G(s) H(s) =K/jw

As H(s) =1

PM (maximum) =90°.

**2. The range of K for the stability of system is 0<K<100. For K =10, The gain Margin of the system**

a) 10

b) 5

c) 0.1

d) 0.5

**Answer:** a

**Explanation:** Gain margin of the system is 10.

**3. The frequency at which the Nyquist diagram cuts the unit circle is known as:**

a) Gain crossover frequency

b) Phase crossover frequency

c) Damping frequency

d) Corner frequency

**Answer:** a

**Explanation:** The frequency at which the Nyquist diagram cuts the unit circle is known as gain cross over frequency.

**4. The forward path transfer function of a unity feedback system is given by G(s) = 1/(1+s) ^{^}2. What is the phase margin of the system?**

a) –π rad

b) 0 rad

c) π/2 rad

d) π rad

**Answer:** d

**Explanation:** Magnitude at gain cross over frequency is 1 and PM is π rad.

**5. Consider the following statements:**

**1. The delay time is the time required to reach 50% of the final value in the first time.**

**2. The rise time is the time required for the response to rise from 10% to 90% of its final value for underdamped systems.**

**3. The rise time is the time required for the response to rise from 0 to 100% for the underdamped systems.**

**Which of these statements are correct?**

a) 1,2 and 3 only

b) 1 and 2 only

c) 1 and 3 only

d) 2 and 3 only negative real axis

**Answer:** c

**Explanation:** The rise time is the time required for the response to rise from 10% to 90% of its final value for overdamped systems.

**6. For minimum phase systems:**

a) Pole must lie on left plane

b) Zeroes must lie on left plane

c) Poles and zeroes must lie on left plane

d) Both must lie on right plane

**Answer:** c

**Explanation:** For minimum phase systems poles and zeroes must lie on the right s-plane.

**7. For non-minimum phase systems:**

a) Poles and zeroes must lie on the right s-plane

b) Zeroes must lie on right of s-plane

c) Both lie on left of s-plane

d) Poles must be on the left and zeroes can be on the right s –plane.

**Answer:** d

**Explanation:** For non-minimum phase systems poles must be on the left and zeroes can be on the right s –plane.

**8. For all-pass systems:**

a) Poles must lie on right of the s-plane

b) Zeroes must lie on the left of s-plane

c) Poles must lie on the left and zeroes on the mirror image of the pole can be on the right

d) None of the mentioned

**Answer:** c

**Explanation:** For all-pass systems poles must lie on the left and zeroes on the mirror image of the pole can be on the right.

**9. All pass system and minimum phase system constitute_________________**

a) Pole must lie on left plane

b) Minimum phase system

c) Non-minimum phase system

d) Both must lie on right plane

**Answer:** c

**Explanation:** All pass system and minimum phase system constitute non-minimum phase system.

**10. Minimum phase systems have unique relationship between its phase and magnitude curves**

a) True

b) False

**Answer:** a

**Explanation:** Minimum phase system has the least phase angle range for a given magnitude curve.