Question 1 |

Consider the following statements regarding the complex Poynting vector \vec{P} for the power radiated by a point source in an infinite homogeneous and lossless medium. Re(\vec{P}) denotes the real part of \vec{P}, S denotes a spherical surface whose centre is at the point source, and \hat{n}
denotes the unit surface normal on S. Which of the following statements is TRUE?

Re(\vec{P}) remains constant at any radial distance from the source | |

Re(\vec{P}) increases with increasing radial distance from the source | |

\oint \oint_{S}Re(\vec{P}).\hat{n} dS remains constant at any radial distance from the source | |

\oint \oint_{S}Re(\vec{P}).\hat{n} dS decreases with increasing radial distance form the source |

Question 1 Explanation:

Power density of any point source decreases with
distance i.e. the density decreases and area of
cross-over increases with the product being
constant.

Question 2 |

A transmission line of characteristic impedance 50 W is terminated by a 50 \Omega load. When excited by a sinusoidal voltage source at 10 GHz, the phase
difference between two points spaced 2 mm apart on the line is found to \frac{\pi }{4} radians. The phase velocity of the wave along the line is

0.8 \times 10^{8} m/s | |

1.2 \times 10^{8} m/s | |

1.6 \times 10^{8} m/s | |

3 \times 10^{8} m/s |

Question 2 Explanation:

\begin{aligned} \text { Phase difference }&=\frac{2 \pi}{\lambda} \text { (path difference) } \\ \Rightarrow \frac{\pi}{4}&=\frac{2 \pi}{\lambda}\left(2 \times 10^{-3}\right) \\ \therefore \quad &=8 \times 2 \times 10^{-3} \\ &=16 \times 10^{-3} \mathrm{m} \\ f&= 10 \mathrm{GHz}=10 \times 10^{9} \mathrm{Hz} \end{aligned}

Hence the phase velocity of wave along the line is,

\begin{aligned} & v=f \lambda=10 \times 10^{9} \times 16 \times 10^{-3} \mathrm{m} / \mathrm{sec} \\ \therefore \quad v &=1.6 \times 10^{8} \mathrm{m} / \mathrm{s} \end{aligned}

Hence the phase velocity of wave along the line is,

\begin{aligned} & v=f \lambda=10 \times 10^{9} \times 16 \times 10^{-3} \mathrm{m} / \mathrm{sec} \\ \therefore \quad v &=1.6 \times 10^{8} \mathrm{m} / \mathrm{s} \end{aligned}

Question 3 |

An analog signal is band-limited to 4 kHz, sampled at the Nyquist rate and
the samples are quantized into 4 levels. The quantized levels are assumed to be
independent and equally probable. If we transmit two quantized samples per
second, the information rate is ________ bits / second.

1 | |

2 | |

3 | |

4 |

Question 3 Explanation:

Quantized levels are equiprobable; hence

\begin{aligned} H&=\log _{2} 4=2 \text { bits/sample }\\ r&=2 \text{samples/sec} \\ \end{aligned}

Hence information rate R=r \cdot H=2 \text{ samples/sec}

\times 2\text{ bits/sample}

\Rightarrow R=4 \mathrm{bits} / \mathrm{sec}

\begin{aligned} H&=\log _{2} 4=2 \text { bits/sample }\\ r&=2 \text{samples/sec} \\ \end{aligned}

Hence information rate R=r \cdot H=2 \text{ samples/sec}

\times 2\text{ bits/sample}

\Rightarrow R=4 \mathrm{bits} / \mathrm{sec}

Question 4 |

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

G(S)H(S)=k\frac{s(s+1)}{(s+2)(s+3)} | |

G(S)H(S)=k\frac{(s+1)}{(s+2)(s+3)^{2}} | |

G(S)H(S)=k\frac{1}{s(s-1)(s+2)(s+3)} | |

G(S)H(S)=k\frac{(s+1)}{(s+2)(s+3)} |

Question 4 Explanation:

From plot we can observe that one pole terminates
at one zero at position -1 and three poles
terminates to \infty. It means there are four poles and
1 zero. Pole at -3 goes on both sides. It means
there are two poles at -3.

Question 5 |

A system is defined by its impulse response h(n) =2^{n} u(n - 2). The system is

stable and causal | |

causal but not stable | |

stable but not causal | |

unstable and non-causal |

Question 5 Explanation:

h(n)=2^{n} u(n-2)

For causal system h(n)=0 for n \lt 0

Hence given system is causal.

For stability:

\sum_{n=2}^{\infty} 2^{n}=\infty, so given system is not stable.

For causal system h(n)=0 for n \lt 0

Hence given system is causal.

For stability:

\sum_{n=2}^{\infty} 2^{n}=\infty, so given system is not stable.

There are 5 questions to complete.