GATE 1996 Electronics & Communication
29 questions across 1 session
A lossless transmission line having 50 $$\Omega $$ characteristic impedance and lenght $$\lambda /4$$ is short ciruited at one end and connected to an ideal voltage sourec of 1 V a...
The number of independent loops for a network with n nodes and b branches is
An npn transistor has a beta cut-off frequency $${f_\beta }$$ of 1MHz and Common Emitter short circuit low frequency current gain $${\beta _o}$$ of 200. The unity gain frequency $$...
A system having an open loop transfer function $$G\left(s\right)=\frac{K\left(s+3\right)}{s\left(s^2+2s+2\right)}$$ is used in a control system with unity negative feedback. Using...
Obtain a state space representation in diagonal form for the following system $$${{{d^3}y} \over {d{t^3}}} + 6{{{d^2}y} \over {d{t^2}}} + 11{{dy} \over {dt}} + 6y = 6u\left( t \rig...
The open circuit impedance matrix $${Z_{OC}}$$ of a three-terminal two-port network with A as the input terminal, B as the output terminal, and C as the common terminal, is given a...
Each cell of a static Random Access Memory Contains
The inverse laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is _______________.
The total number of memory accesses involved (inclusive of the op-code fetch) when an 8085 processor executes, the instruction LDA 2003 is
A metal sphere with 1 m radius and a surface charge density of 10 Coulombs/m 2 is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of...
Given the Boolean function F in three variables R, S and T as F=$$\,\overline R \,S\overline T + R\overline {S\,} T + RST$$ (a) Express F in the minimum sum-of-products from. (b) E...
The number of bits in a binary PCM system is increased from n to n+1. As a result, the signal to quantization noise ratio will improve by a factor
The following sequence of instructions are executed by an 8085 microprocessor: 1000: LXI SP< 27FF 1003: CALL 1006 1006: POP H The contents of the stack pointer (SP) and the HL regi...
A uniform plane wave in air is normally incident on an infinitely thick slab. If the reflective index of the glass slab is 1.5, then the percentage of the incident power that is re...
In an air-filled rectangular waveguide, the vector electric field is given by $$\mathop E\limits^ \to = \cos \,(20\,\pi \,y)\,\exp \,\,\left[ { - j\left( {{{40\,\,\pi } \over 3}} \...
A 1 km long microwave link uses two antennas each having 30dB gain. If the power transmitted by one antenna is 1 W at 3 GHz, the power received by the other antenna is approximatel...
Some unknown material has a conductivity of $${10^{ 6}}$$ $$mho/m$$ and a permeability of $$4\pi \times {10^{ - 7}}\,\,\,\,\,H/m.$$ The skin depth for the material at $$1GHz$$ is
A transverse electromagnetic wave with circular polarization is received by a dipole antenna. Due to polarization mismatch, the power transfer efficiency from the wave to the anten...
A 12-bit ADC is operating with a 1$$\mu $$ sec clock period and the total conversion time is seen to be 14 $$\mu $$ sec. The ADC must br of the
Match the following. Group - I (a)Cascode amplifier (b)Differential Amplifier (c)Darlington pair common-collector Amplifier Group - II (1)does not provide current gain (2)is a wide...
The trigonometric Fourier series of an even function of time does not have the
The Fourier transform of a real valued time signal has
The inverse Laplace transform of the function $${{s + 5} \over {\left( {s + 1} \right)\left( {s + 3} \right)}}$$ is
A signal 3 sin $$\left( {\pi \,\,{f_0}t} \right) + \,5\,\,\cos \,\,\,(3\pi \,\,{f_0}t)$$ is applied to an RC low pass filter of 3 dB cutoff frequency $${f_0}$$. Determine and plot...
A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a
The autocorrelation function of an energy signal has
An input signal A exp $$\left( { - \alpha \,t} \right)$$ u(t) with $$\alpha > 0$$ is applied to a causal filter, the impulse response of which is A exp $$\,( - \alpha \,\,t)$$. Det...
A system having a unit impulse response $$h\left( n \right)$$ = $$u\left( n \right)$$ is excited by a signal $$x\left( n \right)$$ $$ = \,{\alpha ^n}\,\,u\left( n \right).\,$$ Dete...
The capacitance per unit length and the characteristic impedance of a lossless transmission line are C and $$Z_0$$ respectively. The velocity of a traveling wave on the transmissio...