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Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Test  >  GATE Mock Test Series 2027  >  Test: Frequency - Domain Analysis - Electrical Engineering (EE) MCQ

GATE Electrical Engineering (EE) Test: Frequency - Domain Analysis Free


MCQ Practice Test & Solutions: Test: Frequency - Domain Analysis (20 Questions)

You can prepare effectively for Electrical Engineering (EE) GATE Electrical Engineering (EE) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Frequency - Domain Analysis". These 20 questions have been designed by the experts with the latest curriculum of Electrical Engineering (EE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 60 minutes
  • - Number of Questions: 20

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Test: Frequency - Domain Analysis - Question 1
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An under damped second order system having a transfer function of the form

has a frequency response plot shown in fig.

 

Q. The system gain K is

Detailed Solution: Question 1



From the fig. P6.5.1-2, |T(j0)| = 1

Test: Frequency - Domain Analysis - Question 2
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An under damped second order system having a transfer function of the form

has a frequency response plot shown in fig.

 

Q. The damping factor ξ is approximately

Detailed Solution: Question 2

The peak value of T(jω) occurs when the denominator of function |T(jω)|2 is minimum i.e. when


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Test: Frequency - Domain Analysis - Question 3
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Consider the Bode plot of a ufb system shown in fig.

Q. The steady state error corresponding to a rampinput is

Detailed Solution: Question 3

The Bode plot is as shown in fig.


Test: Frequency - Domain Analysis - Question 4
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Consider the Bode plot of a ufb system shown in fig.

The damping ratio is

Detailed Solution: Question 4

From Fig.:

Test: Frequency - Domain Analysis - Question 5
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The Nyquist plot of a open-loop transfer function G(jω)H(jω) of a system encloses the (-1, j0) point. The gain margin of the system is

Detailed Solution: Question 5

If Nyquist plot encloses the point (-1, j0), the system is unstable and gain margin is negative.

Test: Frequency - Domain Analysis - Question 6
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Consider a ufb system

The angle of asymptote, which the Nyquist plotapproaches as ω → 0 is

Detailed Solution: Question 6


Hence, the asymptote of the Nyquist plot tends to an angle of -90° as ω→ 0.

Test: Frequency - Domain Analysis - Question 7
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If the gain margin of a certain feedback system isgiven as 20 dB, the Nyquist plot will cross the negativereal axis at the point

Detailed Solution: Question 7


Since system is stable, it will cross at s = -0.1

Test: Frequency - Domain Analysis - Question 8
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The transfer function of an open-loop system is

The Nyquist plot will be of the form

Detailed Solution: Question 8




Hence (B) is correct option.

Test: Frequency - Domain Analysis - Question 9
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Consider a ufb system whose open-loop transfer function is

The Nyquist plot for this system is

Detailed Solution: Question 9





Due to s there will be a infinite semicircle. Hence (C) is correct option. 

Test: Frequency - Domain Analysis - Question 10
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The open loop transfer function of a system is

The Nyquist plot for this system is

Detailed Solution: Question 10

∠GH(jw) = -270°+ 2 tan-1ω 
For ω = 0, GH(jω) = ∞∠ -270°
For ω = 1 , ∠GH(jω) =  -180°
For ω = ∞, GH(jω) = 0 ∠ - 90°
As ω increases from 0 to ∞, phase goes -270° to -90°.
Due to s3 term there will be 3 infinite semicircle. 

Test: Frequency - Domain Analysis - Question 11
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For the certain unity feedback system

The Nyquist plot is

Detailed Solution: Question 11


∠GH(j(ω) = -90 °- tan-1 ω - tan-1 2ω - tan -1 3ω,
For ω = 0, GH(jω) = ∞∠ - 90°,
For ω = ∞, GH(jω) = 0∠- 360°,
Hence (A) is correct option. 

Test: Frequency - Domain Analysis - Question 12
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The Nyquist plot of a system is shown in fig. The open-loop transfer function is

The no. of poles of closed loop system in RHP are

Detailed Solution: Question 12

The open-loop poles in RHP are P = 0. Nyquist path enclosed 2 times the point (-1 + j0). Taking clockwise encirclements as negative N = -2.
N = P - Z, -2 = 0 -Z , Z = 2 which implies that two poles of closed-loop system are on RHP. 

Test: Frequency - Domain Analysis - Question 13
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The open-loop transfer function of a feedback control system is

Q. The Nyquist plot for this system is

Detailed Solution: Question 13



Test: Frequency - Domain Analysis - Question 14
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If the damping of the system becomes equal to zero, which condition of the resonant frequency is likely to occur?

Test: Frequency - Domain Analysis - Question 15
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A unity feedback system has the open loop transfer function G(s)=1/((s−1)(s+2)(s+3))
The Nyquist plot of GG encircle the origin

Test: Frequency - Domain Analysis - Question 16
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The open-loop transfer function of a feedback system is

Q. The Nyquist plot of this system is

Detailed Solution: Question 16



Test: Frequency - Domain Analysis - Question 17
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The open-loop transfer function of a feedback system is

The system is stable for K

Detailed Solution: Question 17

RHP poles of open-loop system P = 1, Z = P - N .
For closed loop system to be stable, Z = 0, 0 =1 -  N ⇒N = 1
There must be one anticlockwise rotation of point (-1+ j0). It is possible when K > 1.

Test: Frequency - Domain Analysis - Question 18
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A unity feedback system has open-loop transfer function

Q. The Nyquist plot for the system is

Detailed Solution: Question 18





The intersection with the real axis can be calculated as {GH(jω)} = 0, The condition gives ω(2ω2 -1) = 0 

With the above information the plot in option (C) is correct. 

Test: Frequency - Domain Analysis - Question 19
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A unity feedback system has open-loop transfer function

Q. The phase crossover and gain crossover frequenciesare

Detailed Solution: Question 19

The Nyquist plot crosses the negative real axis

Hence phase crossover frequency is 

The frequency at which magnitude unity is

Test: Frequency - Domain Analysis - Question 20
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A unity feedback system has open-loop transfer function

The gain margin and phase margin are

Detailed Solution: Question 20


∠GH(jω) = -90°- tan-1 ω- tan-1 2ω ,
At unit gain ω1 = 0.57 rad/sec,
Phase at this frequency is ∠GH(jω1) = -90°- tan-1 0.57 -tan-1 2(0.57) = -168.42°
Phase margin = -168.420+180° = 11.6°
Note that system is stable. So gain margin and phase margin are positive value. Hence only possible option is (D). 

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About this Electrical Engineering (EE) Practice Test

This test contains 20 MCQs on Frequency - Domain Analysis with detailed solutions for each question. It is part of the GATE Electrical Engineering (EE) Mock Test Series 2027 course on EduRev, designed to align with the current Electrical Engineering (EE) syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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