GATE ECE 1998
GATE ECE
1
The circuit of Fig. is an example of feedback of the following type
2
From a measurement of the rise time of the output pulse of an amplifier whose
input is a small amplitude square wave, one can estimate the following parameter of the amplifier:
3
For full wave rectification, a four diode bridge rectifier is claimed to have the
following advantages over a two diode circuit:
(1) less expensive transformer
(2) smaller size transformer, and
(3) suitability for higher voltage application.
Of these,4
The emitter coupled pair of BJT’s gives a linear transfer relation between the
differential output voltage and the differential input voltage Vid only. When the
magnitude of Vid is less than '$$\alpha$$' times the thermal voltage, where '$$\alpha$$' is
5
One input terminal of high gain comparator circuit is connected to ground and a
sinusoidal voltage is applied to the other input. The output of comparator will be
6
In a shunt-shunt negative feedback Amplifier, as compared to the basic Amplifier,
7
In a differential Amplifier, CMRR can be improved by using an increased
8
Implement a monostable multivibrator using the timer circuit shown, in Fig. Also determine an expression for ON time T of the o/p pulse.
9
In the MOSFET amplifier of the figure the signal output V1 and V2 obey the relationship
10
In the circuit of fig. Determine the resistance Ro seen by the output terminals, ignore the effects of R1 and R2.
11
Find the value of $${R^1}$$ in the circuit of fig. For generating sinusoidal Oscillations. Find the frequency of oscillations. 
12
The $${f_T}$$ of a BJT is related to its $${g_{m,}}\,\,{C_\pi }$$ and $${C_\mu }$$ as follows
13
In a series regulated power supply circuit, the voltage gain Av of the ‘pass’
transistor satisfies the condition:
14
Compression in PCM refers to relative compression of
15
For a given data rate, the bandwidth Bp of a BPSK signal and the band width B0 of the OOK signal are related as
16
Quadrature multiplexing is
17
In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by a factor of
18
The ACF of a rectangular pulse of duration T is
19
The probability density function of the envelope of narrow band Gaussian noise is
20
The amplitude spectrum of a Gaussian pulse is
21
A DSB-SC signal is generated using the carrier $$\cos\left(\omega_ct\;+\;\theta\right)$$ and modulating singal
x(t). The envelope of the DSB-SC signal is
22
The image channel selectivity of super heterodyne receiver depends upon
23
If $$F\left(s\right)\;=\;\frac\omega{s^2\;+\;\omega^2}$$, then the value of $$\underset{t\rightarrow\infty}{\lim\;}f\left(t\right),\;\left\{where\;F\left(s\right)\;is\;the\;L\left[f\left(t\right)\right]\right\}$$
24
The unit impulse response of a linear time invariant system is the unit step
function u(t). For t>0, the response of the system ot an excitation e-at u(t), a > 0 will be
25
Consider a unity feedback control system with open-loop transfer function
$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)}$$ .
The steady state error of the system due to a unit step input is
26
The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are
27
The loop transfer function of a single loop control system is given by
$$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$
Using Nyquist criterion, find the condition for the closed loop system to be stable.
28
The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. The gain margin of the system is
29
The transfer function of a phase lead controller is $${\textstyle{{1 + 3Ts} \over {1 + Ts}}}.$$
The maximum value of phase provided by this controller is
30
In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The phase margin of the system is
31
The open loop transfer function of a unity feedback open-loop system is $$\frac{2s^2+6s+5}{\left(s+1\right)^2\left(s+2\right)}$$. The characteristic equation of the closed loop system is
32
The transfer function of a tachometer is of the form
33
The characteristic equation of a feedback control system is
$$$s^4+20s^3+15s^2+2s+K\;=\;0$$$
(i) Determine the range of K for the system to be stable.
(ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation.
(i) Determine the range of K for the system to be stable.
(ii) Can the system be marginally stable? If so, find the required value of K and the frequency of sustained oscillation.
34
Consider the system shown in Fig. Determine the value of 'a' such that the
damping ratio is 0.5. Also obtain the values of the rise time 'tr' and maximum
overshoot 'Mp' in its step response.
35
Draw a signal flow graph for the following set of algebraic equations:
$$$\begin{array}{l}y_2=ay_1-\;gy_3\\y_3=ey_2+\;cy_4\\y_4=by_2-dy_4\end{array}$$$
Hence, find the gains $$\frac{y_2}{y_1}$$ and $$\frac{y_3}{y_1}$$.
36
Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+2s\right)}$$$
The type of the closed loop system is
37
In figure, A = 1 and B = 1. The input B is now replaced by a sequence 101010 ___, the outputs x and y will be
38
The noise margin of a TTL gate is about
39
The threshold voltage for each transistor in Fig.2.5, is 2V. For this circuit to work as an inverter, Vi must take the values
40
For an ADC, match the following : if
List 1
A. Flash converter
B. Dual slope converter
C. Successive approximation Converter List 2
1. requires a conversion time of the order of a few seconds
2. requires a digital- to- analog converter
3. minimizes the effect of power supply interference.
4. requires a very complex hardware.
5. It is a tracking A/D converter.
List 1
A. Flash converter
B. Dual slope converter
C. Successive approximation Converter List 2
1. requires a conversion time of the order of a few seconds
2. requires a digital- to- analog converter
3. minimizes the effect of power supply interference.
4. requires a very complex hardware.
5. It is a tracking A/D converter.
41
The mod-5 counter shown in figure counts through states Q2 Q1 Q0 = 000, 001, 010, 011 and 100.
(a) Will the counter lockout if it happens to be in any one of the unused states?
(b) Find the maximum rate at which the counter will operate satisfactorily. Assume the propagation delays of flip-flop and AND gate to be tF and tA
42
The advantage of using a dual slope ADC in a digital voltmeter is that
43
Figure shows a mod-K counter, Here K is equal to
44
The K-map for a Boolean function is shown in figure. The number of essential prime implicants for this function is
45
An equivalent 2’s complement representation of the 2’s complement number
1101 is
46
Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function.
47
The electric field vector of a wave is given as
$$$\vec E = {E_0}{\mkern 1mu} {e^{j\left( {\omega t + 3x - 4y} \right)}}{\mkern 1mu} {{8{{\vec a}_x} + 6{{\vec a}_y} + 5{{\vec a}_z}} \over {\sqrt {125} }}\,\,V/m$$$
Its frequency is 10 GHz.
(i) Investigate if this wave is a plane wave.
(ii) Determine its propagation constant, and
(iii) Calculate the phase velocity in $$y$$-direction.
48
A rectangular waveguide with inner dimensions 6 cm $$ \times $$ 3 cm has been designed for a single mode operation. Find the possible frequency range of operation such that the lowest frequency is 5% above the cut off and the highest frequency is 5% below the cut off of the next higher mode.
49
The region between a pair of parallel perfectly conducting planes of infinite extent in the y and z directions is partially filled with a dielectric as shown in Figure. A 30 GHz $$T{E_{10}}$$ wave is incident on the air dielectric interface as shown. Find the
VSWR at the interface.
50
The far field of an antenna varies with distance r as
51
The vector $$\mathop H\limits^ \to $$ in the far field of an antenna satisfiels
52
An antenna in free space receives 2$$\mu $$ W of power when the incident electric field is 20 m V/m rms. The effective aperture of the antenna is
53
The radiation resistance of a circular loop of one turn is 0.01 $$\Omega $$. The radiation resistance of five turns of such a loop will be
54
A plane wave with $$\overrightarrow E = 10\,{e^{j\left( {\omega t - \beta z} \right)\,}}\,\,{\overrightarrow a _{_y}}$$ is incident normally on a thick plane conductor lying in the $$X - Y$$ plane. Its conductivity is $$6 \times {10^6}\,\,\,S/m\,\,\,$$ and surface impedance is $$5 \times {0^{ - 4}}\,\angle {45^0}\Omega $$. Determine the propagation constant and the skin depth in the conductor.
55
The time averaged Poynting vector, in W/m2, for a wave with $$\vec E = 24{e^{j\left( {\omega t + \beta z} \right)}}{\mkern 1mu} {\overrightarrow a _y}$$ V/m in free space is
56
The wavelength of a wave with propagation constant $$\left( {0.1\,\pi + j\,0.2\pi } \right){m^{ - 1}}$$ is
57
The depth of penetration of a wave in a lossy dielectric increases with increasing
58
The intrinsic impedance of copper at high frequencies is
59
All transmission line sections shown in Fig. have characteristic impedance $${R_0}\, + \,j0$$. The input impedance $${Z_{in}}$$ equals
60
The polarization of a wave with electric field vector $$\overrightarrow E = {E_0}\,{e^{j\left( {\omega t - \beta z} \right)}}\left( {\overrightarrow {{a_x}} + \overrightarrow {{a_y}} } \right)$$ is
61
The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\partial t}$$ is based on
62
A loop is rotating about the y-axis in a magnetic field $$$\overrightarrow B\;=\;B_0\cos\left(\mathrm{ωt}\;+\;\mathrm\phi\;\right)\;{\overrightarrow a}_x\;\mathrm T .$$$
The
voltage in the loop is
63
For small signal a.c. operation, a practical forward biased diode can be modeled
as
64
The static characteristic of an adequately forward biased p-n junction is a straight
line, if the plot is of
65
If $$\,\,\,L\,\,\left\{ {f\left( t \right)} \right\} = {w \over {{s^2} + {w^2}}}$$ then the value of
$$\mathop {Lim}\limits_{t \to \infty } f\left( t \right) = $$ ____________.
$$\mathop {Lim}\limits_{t \to \infty } f\left( t \right) = $$ ____________.
66
The eigen values of the matrix $$A = \left[ {\matrix{
0 & 1 \cr
1 & 0 \cr
} } \right]$$ are
67
An instruction used to set the carry flag in a computer can be classified as
68
An I/O processor control the flow of information between
69
The parallel $$RLC$$ circuit shown in figure is in resonance. In this circuit
70
Determine the frequency of resonance and the resonant impedance of the parallel circuit shown in figure. What happens when $$L = C{R^2}$$?
71
A voltage source of internal impedance $${\mathrm R}_\mathrm s\;+\;{\mathrm{jX}}_\mathrm s$$ supplies power to a load of impedance $${\mathrm R}_\mathrm L\;+\;{\mathrm{jX}}_\mathrm L$$ in which only $${\mathrm R}_\mathrm L$$ is variable. Determine the value of $${\mathrm R}_\mathrm L$$ for maximum power transfer from the source to the load. Also, find the numerical value of $${\mathrm R}_\mathrm L$$ if the source impedance is 3.0 Ω (purely resistive) and $${\mathrm X}_\mathrm L$$ is 4.0 Ω.
72
The short-circuit admittance matrix of a two-port network is $$$\begin{bmatrix}0&-\frac12\\\frac12&0\end{bmatrix}$$$
The two port network is
73
A network has 7 nodes and 5 independent loops. The number of branches in the
network is
74
The Nodal method of circuit analysis is based on
75
The voltage across the terminals a and b in Fig. is
76
Superposition theorem is NOT applicable to networks containing
77
If L$$\left[ {f\left( t \right)} \right]$$ = $$\omega /\left( {{s^2} + {\omega ^2}} \right),$$ then the value of $$\matrix{
{Lim\,f\,\left( t \right)} \cr
{t \to \infty } \cr
} $$
78
The ACF of a rectangular pulse of duration T is
79
Flat top sampling of low pass signals
80
The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is
81
The amplitude spectrum of a Gaussian pulse is
82
The transfer function of a zero - order - hold system is
83
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e-at u(t), a>0 will be
84
Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse obtained by convolving g(t) with itself. The Fourier transform of g(t) is a sinc function. Write down the Fourier transform of the pulse obtained by the above convolution.
85
The Fourier transform of a voltage of a voltage signal x(t) is X(f). The unit of |X(f)| is
86
The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be
87
The trigonometric Fourier series of a periodic time function can have only