# Electronics and Communication Engg - GATE 2011 Paper Solution

The modes in a rectangular waveguide are denoted by TEmn/TMmn where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

The Column-1 lists the attributes and the Column-2 lists the modulation systems. Match the attribute to the modulation system that best meets it

 Column-1 Column-2 P.  Power efficient transmission of signals I.   Conventional AM Q. Most bandwidth efficient transmission of voice signals II.   FM R. Simplest receiver structure III.  VSB S.  Bandwidth efficient transmission of signals with Significant dc component IV.  SSB-SC

The differential equation $100\frac{{d}^{2}y}{d{t}^{2}}-20\frac{dy}{dt}+y=x\left(t\right)$  describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

For the transfer function $G\left(\mathrm{j\omega }\right)=5+\mathrm{j\omega },$ the corresponding Nyquist plot for positive frequency has the form

The trigonometric Fourier series of an even function does not have the

When the output Y in the circuit below is "1", it implies that data has

The logic function implemented by the circuit below is (ground implies a logic "0")

The circuit below implements a filter between the input current ii and the output voltage vo. Assume that the opamp is ideal. The filter implemented is a

A silicon PN junction is forward biased with a constant current at room temperature. When the temperature is increased by 10oC, the forward bias voltage across the PN junction

In the circuit shown below, the Norton equivalent current in amperes with respect to the terminals P and Q is

In the circuit shown below, the value of RL such that the power transferred to RL is maximum is

The value of the integral $\underset c{\oint\;}\frac{-3z+4}{\left(z^2+4z+5\right)}dz$ where c is the circle $\left|z\right|=1$ is given by

A transmission line of characteristic impedance 50Ω is terminated by a 50 Ω load. When excited by a sinusoidal voltage source at 10GHz, the phase difference between two points spaced 2mm apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is

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

 (A)  $\mathbf{Re}\mathbf{\left(}\stackrel{\mathbf{\to }}{\mathbf{P}}\mathbf{\right)}$ remains constant at any radial distance from the source (B)  $\mathbf{Re}\mathbf{\left(}\stackrel{\mathbf{\to }}{\mathbf{P}}\mathbf{\right)}$ increases with increasing radial distance from the source (C) (D)

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

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

A system is defined by its impulse response h(n) = 2n u(n − 2). The system is

If the unit step response of a network is ${\left(1-{e}^{-\alpha t}\right)}^{}$ then its unit impulse response is

The output Y in the circuit below is always "1" when

In the circuit shown below, capacitors C1 and C2 are very large and are shorts at the input frequency. vi is a small signal input. The gain magnitude |vo/vi| at 10Mrad/s is