JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (May - 2019 - R16)
Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit.
Part A
Answer all questions:
Define state variables.
Answer
State variables are the smallest set of linearly independent variables that completely describe the dynamic behavior of a system at any time instant t. If the state of a system is known at t = t0, and the inputs for t ≥ t0 are known, the future state and output of the system can be uniquely determined.
Briefly explain the concept of state space.
Answer
A State Space is an n-dimensional Euclidean space where the axes are defined by the state variables of the system. Each point in this space represents a specific state of the system. The evolution of the system over time is represented by a trajectory within this space, providing a comprehensive mathematical framework to analyze multi-input multi-output (MIMO) systems in the time domain.
State time shift property of continuous time Fourier series.
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State and prove frequency shift of Fourier transform.
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Find Laplace transform of the ramp function.
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Write properties of positive real function.
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Define Flat Top Sampling.
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What are the effects of under sampling?
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What is the significance of region of convergence (ROC) in Z-transform?
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Determine Z-transform of x(t)= u(t-2).
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Unit I
Find the state equations for the network shown in the figure 1. Choose iL1, iL2 and Vc as state variables.
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For the network shown in figure 2 obtain the state equations in matrix form using equivalent source method.
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Unit II
Find the exponential Fourier series and plot the magnitude and phase spectrum for the sawtooth wave form of figure 3.
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The voltage v(t) = 10 + 20 sin(314t) + 40sin(942t+30°) is applied to an RL circuit with R=10Ω and L=0.0318 H. Obtain:
- Expression for current in the RL circuit.
- Effective values of voltage and currents.
- Power factor of the circuit.
Answer
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Unit III
Answer the following parts:
Obtain the Laplace transform of the square wave train shown in the figure 4.
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Test whether the given polynomial P(s)=s³+2s²+4s+2 is Hurwitz.
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Synthesize the Foster-I and Foster-II forms of LC driving point impedance.
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Unit IV
Answer the following parts:
Determine and sketch the auto correlation function of given exponential pulse f(t)=e⁻ᵃᵗ u(t).
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Give physical interpretation of power density spectrum.
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Answer the following parts:
State and prove sampling theorem.
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Write comparisons between energy spectral density and power spectral density.
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Unit V
Answer the following parts:
State and explain four properties of Z-transform.
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Determine inverse Z-transform of X(z) = [2z²] / [(z-1)(z-2)]
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Answer the following parts:
State and prove initial value theorem of Z-transform.
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Determine inverse Z-transform of X(z) = [z] / [(z-1)(z+1)]
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