GATE ECE 1990
GATE ECE
1
The CMRR of the differential Amplifier of the fig is equal to
2
The Op-Amp of fig has a very poor open loop voltage gain of 45 but is otherwise ideal. The gain of the Amplifier equals:
3
If the input to the circuit of figure is a sine wave the output will be.
4
For good stabilized biasing of the transistor of the CE Amplifier of fig, we should have
5
Which of the following statements are correct for basic transistor Amplifier configurations?
6
An image uses $$512\, \times \,512$$ picture elements. Each of the picture elements can take any of the 8 distinguishable intersity levels. The maximum entropy in the above image will be
7
In a BPSK signal detector, the local oscillator has a fixed phase error of 200. This phase error deteriorates the SNR at the output by a factor of
8
A system is characterized by the following state-space equations:
a) Find the transfer function of the system
b) Compute the state-transition matrix/p>
a) Solve the state equation for a unit-step input under zero initial conditions
9
The transfer function of a simple RC network functioning as a controller is:
$${G_c}(s) = {{s + {z_1}} \over {s + {p_1}}}$$
The condition for the RC network to act as a phase lead controller is:
10
An electromechanical closed-loop control system has the following characteristic equation $$s^3+6Ks^2+\left(K+2\right)s+8\;=\;0$$, where K is the forward gain of the system.The condition for closed loop stability is
11
The steady state error of a stable 'type 0' unity feedback system for a unit step function is
12
Which of the resistance networks of figure can be used as 3 bit R-2R ladder DAC. Assume $${V_0}$$ corresponds to LSB.
13
A 4 bit modulo-16 ripple counter uses JK flip-flops. If the propagation delay of each FF is 50ns, the maximum clock frequency that can be used is equal to:
14
The minimum function that can detect a "divisible by 3" 8421 BCD code digit (representation is D8 D4 D2 D1) is given by:
15
The number of Boolean functions that can be generated by n variable is equal to:
16
Two isotropic antennas are separated by a distance of two wavelengths. If both the antennas are fed with currents of equal phase and magnitude, the number of lobes in the radiation pattern in the horizontal plane are
17
A 300 MHz plane E.M. wave is propagating in free space. The wave is incident normally on an infinite copper slab. For the transmitted wave in the copper slab, calculate the following
(a) Attenuation constant
(b) Phase constant
(c) Skin depth
(d) Phase velocity and
(e) Group velocity
for copper assume the following values
Conductivity $$\sigma = 5.8 \times {10^7}$$ $$mho/m$$
Permeability $$\mu = 4\pi \times {10^{ - 7}}$$ $$H/m$$
Permeability $$\varepsilon = {1 \over {36\pi }} \times {10^{ - 9}}$$ $$F/m$$
18
Choose the correct statements.
For a wave propagating in an air filled rectangular wave guide
For a wave propagating in an air filled rectangular wave guide
19
Which of the following field equations indicate that the free magnetic charges do not exits?
20
A 200 volt (r. m. s) generator having an internal resistance of 200 ohm is feeding a loss-less transmission line. The characteristic impedance and the length of the line are 200 ohm and 10 m respectively. The line is terminated in a resistive load of 100 ohm. If the operating frequency is 37.5 MHz calculate the
Current drawn from the generator.
Magnitude and phase of the current flowing in the load.
Power delivered to the load.
Current drawn from the generator.
Magnitude and phase of the current flowing in the load.
Power delivered to the load.
21
The incoming solar radiation at a place on the surface of the earth is 1.2 KW/m2.The amplitude of the electric field corresponding to this incident power is nearly equal to
22
In a junction diode
23
The transfer function of simple RC network functioning as a controller is
$$$G\,{}_c\left( s \right)\,\,\,\,{{s + {z_1}} \over {s + {p_1}}}$$$
The condition for the RC network to act as a phase lead controller is
24
The resonant frequency of this series circuit shown in figure is
25
The switch $$S$$ in figure is thrown to position $$'a'$$ at $$t = 0$$. At $$t = 1$$ second, the switch is thrown to position $$'b'$$. Find the current through $${R_2}$$ for $$ t > 1$$ sec.
26
If the Laplace transform of the voltage across a capacitor of value of $$\frac12\;\mathrm F$$ is $$V_C\;\left(s\right)\;=\;\frac{s\;+\;1}{s^3\;+\;s^2\;+\;s\;+\;1}$$ , the value of the current through the capacitor at t = 0+ is
27
A 4 GHz carrier is DSB-SC modulated by a low pass message signal with maximum frequency of 2 MHz. The resultant signal is to be ideally sampled. The minimum frequency of the sampling impulse train should be:
28
The magnitude and phase transfer functions for a distortionless filter should respectively be:
29
The impulse response and the excitation function of a linear time invariant casual system are shown in Fig. a and b respectively. The output of the system at t = 2 sec. is equal to
30
The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to a unit step function will be:
31
The Z-transform of the following real exponential sequence:
x(nT) = $${a^n}$$, nT $$ \ge $$ 0
=0, nT<0, a> 0
gives us by
x(nT) = $${a^n}$$, nT $$ \ge $$ 0
=0, nT<0, a> 0
gives us by