JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (August/September - 2024 - R16)

B. Tech | III | III-II | R16 | August/September - 2024

Answer PaperPaper Code: 136CJMaximum Marks: 75Time: 3 Hours

Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.

Part A

125 marks

Why is the choice of state variables in State Variable Analysis is crucial for achieving a simplified and efficient representation of the system dynamics.

2 marks

Answer

The choice of state variables determines the structure of the system matrices (A, B, C, D). A judicious selection, such as choosing variables that correspond to physical energy-storing elements, leads to a diagonal or Jordan canonical form, which simplifies the computation of the state transition matrix and decouples the system equations, making analysis and control design more efficient.

Obtain the State Variable representation of the system

G(s) = 2 / ((s+1)(s+2))

3 marks

Answer

Given G(s) = 2 / (s^2 + 3s + 2). The differential equation is y''(t) + 3y'(t) + 2y(t) = 2u(t). Defining state variables x1 = y and x2 = y', the state-space representation is:

[x1'] = [0 1] [x1] + [0] u

[x2'] = [-2 -3] [x2] + [2] u

y = [1 0] [x1 x2]^T

Obtain the relation between Fourier Transform and Laplace Transform.

2 marks

Answer

What is the Fourier Transform of Dirac Delta Function?

3 marks

Answer

List the properties of positive real functions.

2 marks

Answer

State Sturm’s theorem.

3 marks

Answer

What is Guard Band?

2 marks

Answer

What is Power Spectral Density?

3 marks

Answer

What is the Z-transform of unit ramp sequence?

2 marks

Answer

State the differences between Laplace and Z-transform.

3 marks

Answer

Part B

210 marks

Obtain the state variable model for a system described by the differential equation

10 d^3y/dt^3 + 5 d^2y/dt^2 + 2 dy/dt + 3y = 20 dx/dt + 10x

5 marks

Answer

Discuss the Network Topological Method in State Variable Analysis. How does this method help in formulating state equations for complex electrical networks?

5 marks

Answer

310 marks

A system matrix is given by

A = [[-1/2, -5/2], [1/2, -7/2]]

. Obtain the state transition matrix.

5 marks

Answer

Describe the Equivalent Source Method used in State Variable Analysis for electrical networks. How is this method applied to simplify the analysis process?

5 marks

Answer

410 marks

Find the exponential fourier series coefficient of the signal

x(t) = 2 + cos(2πt/3) + 4sin(5π/3 t)

5 marks

Answer

What is meant by Fourier series of a non-sinusoidal periodic waveform? Explain the significance of the term “Half wave symmetry” used in determining the Fourier series of a given waveform.

5 marks

Answer

510 marks

State and prove the properties of Fourier Transform.

5 marks

Answer

Find the fourier transform of a square wave form of duration two seconds and an amplitude of 10 volts given to a RC circuit where R=2 Ohms, C = 10 micro farads, frequency = 50 Hz. Also derive the expression for 5th harmonic current, average power, power factor.

5 marks

Answer

610 marks

Find the current i(t) in a series circuit comprising R = 1 Ohm, C = 0.2 F when it is fed by ramp voltage of 3r(t-1).

6 marks

Answer

State and prove convolution theorem.

4 marks

Answer

710 marks

Check whether given polynomial

H(S) = 2S^4 + 5S^3 + 6S^2 + 2S + 1

is Hurwitz or not.

4 marks

Answer

Given the driving point admittance function

Y(s) = (S(S^2+1)(S^2+4)) / (S(S^2+2))

. Synthesize ladder network of the first Cauer form.

6 marks

Answer

810 marks

With neat diagram, explain the reconstruction of signal from its samples.

5 marks

Answer

A signal

x(t) = e^(-2t)u(t)

is passed through an ideal low pass filter with cutoff frequency of 1 rad/sec. Test whether the input signal is an energy signal. Also find the input and output energy.

5 marks

Answer

910 marks

State and prove the properties of Cross Correlation of Power Signals.

5 marks

Answer

Find the autocorrelation of the signal

x(t) = A sin(ωot + θ)

5 marks

Answer

1010 marks

Determine the z-transform and ROC of

(1/2)^n u(-n) - 2^n u(-n-1)

5 marks

Answer

Simplify x(t) if its bilateral Laplace transform is given

X(S) = (2s-3) / ((S-2)(S+3)), -3 < Re(s) < 2

5 marks

Answer

1110 marks

Find the inverse Z-transform of

X(z) = (2+z)(3+3z^-4) / (z^2+4z+3)

; ROC; |Z| > 0.

5 marks

Answer

Make use of the properties and find the Z-transform of

x(n) = 1/3 (n^2 + n) (1/2)^(n-1) u(n-1)

5 marks

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (August/September - 2024 - R16)

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Part B

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