GATE 1998 Electronics & Communication
71 questions across 1 session
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 voltag...
The Maxwell's equation $$\nabla\times\overrightarrow H\;=\;\overrightarrow J\;+\;\frac{\partial\overrightarrow D}{\partial t}$$ is based on
The intrinsic impedance of copper at high frequencies is
Superposition theorem is NOT applicable to networks containing
The noise margin of a TTL gate is about
The Nodal method of circuit analysis is based on
A voltage source of internal impedance $${\mathrm R}_\mathrm s\;+\;{\mathrm{jX}}_\mathrm s$$ supplies power to a load of impedance $${\mathrm R}_\mathrm L\;+\;{\mathrm{jX}}_\mathrm...
If $$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[...
The short-circuit admittance matrix of a two-port network is $$$\begin{bmatrix}0&-\frac12\\\frac12&0\end{bmatrix}$$$ The two port network is
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 uni...
A network has 7 nodes and 5 independent loops. The number of branches in the network is
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
The number of roots of $$s^3\;+\;5s^2\;+\;7s\;+\;3\;=\;0$$ in the left half of the s-plane are
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 tra...
An equivalent 2’s complement representation of the 2’s complement number 1101 is
The emitter coupled pair of BJT’s gives a linear transfer relation between the differential output voltage and the differential input voltage V id only. When the magnitude of V id...
The transfer function of a tachometer is of the form
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 $$\fra...
Consider a feedback control system with loop transfer function $$$G\left(s\right)H\left(s\right)=\frac{K\left(1+0.5s\right)}{s\left(1+s\right)\left(1+2s\right)}$$$ The type of the...
The open loop transfer function of a unity feedback open-loop system is $$\frac{2s^2+6s+5}{\left(s+1\right)^2\left(s+2\right)}$$. The characteristic equation of the closed loop sys...
The characteristic equation of a feedback control system is $$$s^4+20s^3+15s^2+2s+K\;=\;0$$$ (i) Determine the range of K for the system to be stable. (ii) Can the system be margin...
The transfer function of a phase lead controller is $${\textstyle{{1 + 3Ts} \over {1 + Ts}}}.$$ The maximum value of phase provided by this controller is
The advantage of using a dual slope ADC in a digital voltmeter is that
The Nyquist plot of a loop transfer function G$$(j\omega )$$ H$$(j\omega )$$, of a system encloses the (-1, j0) point. The gain margin of the system is
If $$\,\,\,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) = $$ ____________.
Two 2' s complement numbers having sign bits x and y added and the sign bit of the result is z. Then, the occurrence of overflow is indicated by the Boolean function.
In a differential Amplifier, CMRR can be improved by using an increased
The $${f_T}$$ of a BJT is related to its $${g_{m,}}\,\,{C_\pi }$$ and $${C_\mu }$$ as follows
In the Bode-plot of a unity feedback control system, the value of phase of G($$j\omega $$) at the gain cross over frequency is $$ - 125^\circ $$. The phase margin of the system is
A plane wave with $$\overrightarrow E = 10\,{e^{j\left( {\omega t - \beta z} \right)\,}}\,\,{\overrightarrow a _{_y}}$$ is incident normally on a thick plane conductor lying in the...
The probability density function of the envelope of narrow band Gaussian noise is
From a measurement of the rise time of the output pulse of an amplifier whose input is a small amplitude square wave, one can estimate the following parameter of the amplifier:
In a series regulated power supply circuit, the voltage gain A v of the ‘pass’ transistor satisfies the condition:
The amplitude spectrum of a Gaussian pulse is
The vector $$\mathop H\limits^ \to $$ in the far field of an antenna satisfiels
For a given data rate, the bandwidth B p of a BPSK signal and the band width B 0 of the OOK signal are related as
The loop transfer function of a single loop control system is given by $$G(s)H(s) = {{100} \over {s\left( {1 + 0.01s} \right)}}{e^{ - ST}}$$ Using Nyquist criterion, find the condi...
In a PCM system with uniform quantization, increasing the number of bits from 8 to 9 will reduce the quantization noise power by a factor of
One input terminal of high gain comparator circuit is connected to ground and a sinusoidal voltage is applied to the other input. The output of comparator will be
The depth of penetration of a wave in a lossy dielectric increases with increasing
The electric field vector of a wave is given as $$$\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}...
The ACF of a rectangular pulse of duration T is
The wavelength of a wave with propagation constant $$\left( {0.1\,\pi + j\,0.2\pi } \right){m^{ - 1}}$$ is
The time averaged Poynting vector, in W/m 2 , 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
The far field of an antenna varies with distance r as
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 low...
An instruction used to set the carry flag in a computer can be classified as
The polarization of a wave with electric field vector $$\overrightarrow E = {E_0}\,{e^{j\left( {\omega t - \beta z} \right)}}\left( {\overrightarrow {{a_x}} + \overrightarrow {{a_y...
Compression in PCM refers to relative compression of
The radiation resistance of a circular loop of one turn is 0.01 $$\Omega $$. The radiation resistance of five turns of such a loop will be
For an ADC, match the following : if List 1 A. Flash converter B. Dual slope converter C. Successive approximation Converter List 2 1. requires a conversion time of the order of a...
The eigen values of the matrix $$A = \left[ {\matrix{ 0 & 1 \cr 1 & 0 \cr } } \right]$$ are
In a shunt-shunt negative feedback Amplifier, as compared to the basic Amplifier,
Flat top sampling of low pass signals
The trigonometric Fourier series of a periodic time function can have only
For small signal a.c. operation, a practical forward biased diode can be modeled as
The static characteristic of an adequately forward biased p-n junction is a straight line, if the plot is of
The Fourier transform of a voltage of a voltage signal x(t) is X(f). The unit of |X(f)| is
Consider a rectangular pulse g(t) existing between $$t = \, - {T \over 2}\,and\,{T \over 2}$$. Find and sketch the pulse obtained by convolving g(t) with itself. The Fourier transf...
The ACF of a rectangular pulse of duration T is
The z - transform of the time function $$\sum\limits_{k = 0}^\infty {\delta \left( {n - k} \right)} $$ is
If L$$\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 } $$
The amplitude spectrum of a Gaussian pulse is
The Fourier transform of a function x(t) is X(f). The Fourier transform of $${{dx(t)} \over {dt}}$$ will be
The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e -at u(t), a>0 will be
The transfer function of a zero - order - hold system is
An antenna in free space receives 2$$\mu $$ W of power when the incident electric field is 20 m V/m rms. The effective aperture of the antenna is
Quadrature multiplexing is
An I/O processor control the flow of information between
The image channel selectivity of super heterodyne receiver depends upon
A DSB-SC signal is generated using the carrier $$\cos\left(\omega_ct\;+\;\theta\right)$$ and modulating singal x(t). The envelope of the DSB-SC signal is