GATE ECE 2012 PYQ

The voltage gain of the circuit shown below is

The current through the base of a silicon npn transistor is mA. At 300 K, the in the small signal model of the transistor is

In the CMOS circuit shown, electron and hole mobilities are equal, and M1 and M2 are equally sized. The device M1 is in the linear region if

The circuit shown is a

The diodes and capacitors in the circuit shown are ideal. The voltage across the diode D1 is

The power spectral density of a real process X(t) for positive frequencies is shown below. The values of and |E[X(t)]|, respectively, are

A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount and decreases tha

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0) = 9/10, then the probability of error for an optimum receiver will be

The signal m(t) as shown is applied both to a phase modulator (with as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency The ratio (in ra

In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible sig

Two independent random variables X and Y are uniformly distributed in the interval [-1,1]. The probability that max[X,Y] is less than 1/2 is

A BPSK scheme operating over an AWGN channel with noise power spectral density of , uses equiprobable signals and over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahe

A system with transfer function is excited by sin( t). The steady-state output of the system is zero at

The feedback system shown below oscillates at 2 rad/s when

The transfer function of a compensator is given as is a lead compensator if

The transfer function of a compensator is given as The phase of the above lead compensator is maximum at

The state variable description of an LTI system is given by where y is the output and u is the input. The system is controllable for

The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is

The state transition diagram for the logic circuit shown is

In the sum of products function f (X, Y, Z) = (2, 3, 4, 5), the prime implicants are

Consider the given circuit. In this circuit, the race around

In the circuit shown

A plane wave propagating in air with V/m is incident on a perfectly conducting slab positioned at 0 x. The E field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive direction, is given by . The frequency and polarization of the wave, respectively, are

An infinitely long uniform solid wire of radius a carries a uniform dc current of density . A hole of radius is now drilled along the length of the wire at a distance d from the center of the wire as

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given , the characteristic impedance of the cable is

The magnetic field along the propagation direction inside a rectangular waveguide with the crosssection shown in the figure is The phase velocity of the wave inside the waveguide satisfies

A transmission line with a characteristic impedance of 100 is used to match a 50 section to a 200 section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line

The source of a silicon ( per ) n-channel MOS transistor has an area of 1 sq m and a depth of 1 m. If the dopant density in the source is , the number of holes in the source region with the above volu

In the three dimensional view of a silicon n-channel MOS transistor shown below, =20nm. The transistor is of width 1 m. The depletion width formed at every p-n junction is 10 nm. The relative permitti

The i-v characteristics of the diode in the circuit given below are The current in the circuit is

The average power delivered to an impedance (4 - j3) by a current 5cos(100 t +100) A is

In the circuit shown below, the current through the inductor is

The impedance looking into nodes 1 and 2 in the given circuit is

With 10 V dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: (i) 1 connected at port B draws a current of 3 A (ii) 2.5 connected at port B dr

If =6V, then is

Assuming both the voltage sources are in phase, the value of R for which maximum power is transferred from circuit A to circuit B is

In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current for all is

If , then the region of convergence (ROC) of its Z-transform in the Z-plane will be

T he input and output of a system are related as . The system is

Let y[n] denote the convolution of h[n] and g[n], where and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

The unilateral Laplace transform of is . The unilateral Laplace transform of is

The Fourier transform of a signal h(t) is H(j ) = (2cos )(sin2 ) / . The value of h(0) is