Q1.Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response
As shown in Figure (b). The output of the lowpass filter is Y(t ).
Let E be the expectation operator and consider the following statements.
Q2.A half wavelength dipole is kept in the x-y plane and oriented along 450 from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ (0 ≤ θ ≤ π) is measured from the z-axis, and the angle ϕ (0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.
Answer : Option AExplaination / Solution:
The null occurs along axis of the antenna which is θ = 900and ϕ= 450
Q4.A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size Δ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is
Answer : Option AExplaination / Solution:
For preventing slope overload, we should have
Q5.The time domain behavior of an RL circuit is represented by For an initial current of
For an initial current of the steady state value of the current is given by
Answer : Option AExplaination / Solution:
Steady state all transient effect die out and inductor act as short circuits and forced response acts only. It doesn’t depend on initial current state. From the given time domain behavior we get that circuit has only R and L in series with v0 Thus at steady state
The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression The cross-sectional dimensions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
Answer : Option CExplaination / Solution:
We have the expression,
and the cross sectional dimension is
a = 0.08 m, b = 0.033m
Now, we compare the equation for TEm,n mode whose Hz is given as
Q7.Consider a system whose input x and output y are related by the equation where h(t) is shown in the graph.
Which of the following four properties are possessed by the system ? BIBO : Bounded input gives a bounded output. Causal : The system is causal, LP : The system is low pass. LTI : The system is linear and time-invariant.
Answer : Option BExplaination / Solution:
Here h(t) ! 0 for t < 0. Thus system is non causal. Again any bounded input x(t) gives bounded output y(t). Thus it is BIBO stable.
Q8.For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in
Answer : Option BExplaination / Solution: No Explaination.
A communication channel with AWGN operating at a signal to noise ration SNR >> 1 and bandwidth B has capacity C1. If the SNR is doubled keeping constant, the resulting capacity C2 is given by
A transmission line terminates in two branches, each of length as shown. The branches are terminated by 50W loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source.
Answer : Option DExplaination / Solution:
The transmission line are as shown below. Length of all line is
Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0