The frequency response of a linear system G(jw) is provided in the tubular form below

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The phase cross-over frequency of the transfer function is

**A. ** √3

**B. ** 1/√3

**C. ** 3

**D. ** 3√3

**Answer : ****Option A**

**Explaination / Solution: **

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Consider the feedback system shown in the figure. The Nyquist plot of G (s) is
also shown. Which one of the following conclusions is correct ?

**A. ** G (s) is an all pass filter

**B. ** G (s) is a strictly proper transfer function

**C. ** G (s) is a stable and minimum phase transfer function

**D. ** The closed-loop system is unstable for sufficiently large and positive k

**Answer : ****Option D**

**Explaination / Solution: **

Given the feedback system and the Nyquist plot of G (s)is

Given the feedback system and the Nyquist plot of G (s)is

For the given system, we have the open loop transfer function as

G (s) = KG (s)

Considering the open loop system G (s) is stable, we have no open loop poles in
right half plane

P = 0

From Nyquist theorem, we know that

N = P - Z

Where N is the number of encirclements of (-1 + j0), P is number of open loop
poles in right half plane, Z is number of closed loop poles in right half plane. For
stability, we must have

Z = 0

N = 0, if closed loop system is stable

N ≠ 0, if closed loop system is unstable

observing the Nyquist plot, we conclude that the plot of KG(s) encircles (-1 + j0)

if K> 1

Hence, N ≠ 0 for sufficient large and positive value of K . Thus, the closedsystem
is unstable for sufficiently large and positive K .

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The unilateral Laplace transform of f (t) is . The unilateral Laplace transform of
t f (t)
is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option D**

**Explaination / Solution: **

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The transfer function of a compensator is given as

G_{c}(s) is a lead compensator if

both option (A) and (C) satisfier but option (C) will pot polar and zero as RHS of s-plane thus not possible option (A) is right

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The root locus plot for a system is given below. The open loop transfer function
corresponding to this plot is given by

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option B**

**Explaination / Solution: **

For given plot root locus exists from -3 to ∞, So there must be odd number of poles and zeros. There is a double pole at s = - 3

For given plot root locus exists from -3 to ∞, So there must be odd number of poles and zeros. There is a double pole at s = - 3

Now poles = 0, -2, -3, -3

zeros = - 1

Thus transfer function

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The signal flow graph for a system is given below. The Transfer function, Y(s)/U(s) for the system is

**A. **

**B. **

**C. **

**D. **

**Answer : ****Option A**

**Explaination / Solution: **

No Explaination.

No Explaination.

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The input-output transfer function of a plant The plant is
placed in a unity negative feedback configuration as shown in the figure below. **A. ** 0 dB

**B. ** 20 dB

**C. ** 26 dB

**D. ** 46 dB

**Answer : ****Option C**

**Explaination / Solution: **

The gain margin of the system under closed loop unity negative feedback is

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The asymptotic approximation of the log-magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function is

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If the closed-loop transfer function of a control system is given as then It is

**A. ** an unstable system

**B. ** an uncontrollable system

**C. ** a minimum phase system

**D. ** a non-minimum phase system

**Answer : ****Option D**

**Explaination / Solution: **

In a minimum phase system, all the poles as well as zeros are on the left half of the s −plane. In given system as there is right half zero (s = 5), the system is a non-minimum phase system.

In a minimum phase system, all the poles as well as zeros are on the left half of the s −plane. In given system as there is right half zero (s = 5), the system is a non-minimum phase system.

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**Preparation Study Material**- Circuit Analysis (Study/Preparation)
- Digital Electronics (Study/Preparation)
- Signals and Systems (Study/Preparation)
- Communication Theory (Study/Preparation)
- Basic Electrical and Instrumentation Engineering (Study/Preparation)
- Electrical Engineering and Instrumentation (Study/Preparation)
- Electronic Devices (Study/Preparation)
- Linear Integrated Circuits LIC (Study/Preparation)
- Electronic Circuits I (Study/Preparation)
- Electronic Circuits II (Study/Preparation)
- Control System Engineering (Study/Preparation)
- Digital Communication (Study/Preparation)
- Digital Signal Processing (Study/Preparation)
- Microprocessors and Microcontrollers (Study/Preparation)
- Electromagnetic Theory (Study/Preparation)