GATE 1999 Electronics & Communication

A transmitting antenna radiates 251 W isotropically. A receiving antenna, located 100m away from the transmitting antenna, has an effective aperture of 500 cm 2 . The total power r...

In a twin-wire transmission line in air, the adjacent voltage maxima are at 12.5 cm and 27.5. The operating frequency is

If $$\,\,L\left\{ {f\left( t \right)} \right\} = F\left( s \right)$$ then $$\,\,\,L\left\{ {f\left( {t - T} \right)} \right\}$$ is equal to

Consider the points s 1 = −3 + j4 and s 2 = −3 − j2 in the s-plane. Then, for a system with the open loop transfer function $$$G\left(s\right)H\left(s\right)=\frac K{\left(s+1\righ...

A dc power supply has a no-load voltage of 30V, and a full-load voltage of 25 V at a full-load current of 1A. Its output resistance and load regulation, respectively are

For a second-order system with the closed-loop transfer function $$$T\left(s\right)=\frac9{s^2+4s+9}$$$ the settling time for 2% band in seconds is

If the closed-loop transfer function T(s) of a unity negative feedback system is given by $$$T\left(s\right)=\frac{a_{n-1}s+a_n}{s^n+a_1s^{n-1}+.....+a_{n-1}s+a_n}$$$ then the stea...

The loop transfer function of a feedback control system is given by $$$G\left(s\right)H\left(s\right)=\frac{K\left(s+1\right)}{s\left(1+Ts\right)\left(1+2s\right)},\;K>0$$$ Using R...

Crossover distortion behavior is characteristic of

The first dominant pole encountered in the frequency response of a compensated op-amp is approximately at

The Logical expression $$Y = A + \overline A B$$ is equivalent to

The circuit diagram of a synchronous counter is shown in the figure. Determine the sequence of states of the counter assuming that the initial state is ‘000’. Give your answer in a...

For a binary half-subtractor having two inputs A and B, the correct set of Logical expressions for the output D(=Aminus B) and X(=Borrow) are

An amplifier has an open loop gain of 100, an input impedance of 1 k$$_\Omega $$, and an output impedance of 100 $$_\Omega $$ . A feedback network with a feedback factor of 0.99 is...

An amplifier is assumed to have a single pole high frequency transfer function. The rise time of its output response to a step function input is 35 nsec. The upper 3 dB frequency (...

Consider a feedback system with the open loop transfer function given by $$G(s)H(s) = {K \over {s\left( {2s + 1} \right)}}.$$ Examine the stability of the closed-loop system using...

For a binary half-sub-tractor having two inputs A and B, the correct set of logical expressions for the outputs D (=A minus B) and X (=borrow) are

In certain application, four inputs A, B, C, D (both true and complement forms available)are fed to logic circuit, producing an output F which operates a relay. The relay turns on...

The system mode described by the state equations $$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right)x + \left( {\matrix{ 0 \cr 1 \cr } } \right)u,y = \left[ {\matrix{ 1 &...

A coil with a quality factor $$(Q)$$ of $$10$$ is put in series with a capacitor $${C_1}$$ of $$10\,\,\mu F,$$ and the combination is found to draw maximum current when a sinusoida...

Indicate which one of the following modes do NOT exist in a rectangular resonant cavity.

Four independent messages have bandwidths of 100Hz, 100 Hz, 200Hz and 400Hz respectively. Each is sampled at the Nyquist rate, and the samples are time division multiplexed (TDM) a...

If $$CS\;=\overline{A_{15}}\;A_{14}\;A_{13}$$ is used as the chip select logic of a 4K RAM in an 8085 system, then its memory range will be

The peak-to-peak input to an 8-bit PCM coder is 2 volts . The signal power - to -quantization noise power ratio (in dB) for an input of 0.5 $$\cos \left( {{\omega _m}t} \right)$$ i...

Identify which one of the following will NOT satisfy the wave equation.

A 100 m section of an air-filled rectangular wave-guide operating in the $$T{E_{10}}$$ mode has a cross-sectional dimension of 1.071 cm $$ \times $$ 0.5 cm. Two pulses carriers of...

The input to a matched filter is given by $$$S\left( t \right) = \left\{ {\matrix{ {10\sin \left( {2\pi \times {{10}^6}t} \right),} & {0 < 1 < {{10}^{ - 4}}\sec } \cr {0\,\,\,\,\,\...

The average power of an omni-directional antenna varies as the magnitude of cos($$\theta $$) where $$\theta $$ is the azimuthal angle. Calculate the maximum Directive Gain of the a...

Assuming perfect conductors of a transmission line, pure TEM propagation is NOT possible in

The resolution of a 4-bit counting ADC is 0.5 Volts. For an analog input of 6.6 Volts, the digital output of the ADC will be

A Darlington Emitter follower circuit is sometimes used in the output stage of a TTL gate in order to

Commercially available ECL gates use two ground lines and one negative supply in order to

An NPN transistor (with $${C_\pi }\,\, = \,\,0.3\,\,$$ pf) has a unity gain cutoff frequency $${f_T}$$ of 400 MHz at a DC-bias current I c = 1mA. The value of its $${C_\mu }$$ (in...

The phase margin (in degrees) of a system having the loop transfer function is $$G(s)H(s) = {{2\sqrt 3 } \over {s(s + 1)}}$$

The gain margin of a system having the loop transfer function G(s)H(s) =$${{\sqrt 2 } \over {s(s + 1)}}$$ is

For the system described by the state equation $$$\mathop x\limits^ \bullet = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr {0.5} & 1 & 2 \cr } } \right]x + \left[ {\matrix{ 0 \cr 0...

The minimized form of the logical expression ($$\overline A \,\overline B \,\overline C + B\overline C + \overline A B\overline C + \overline A BC + AB\overline C )$$

Negative feedback in an amplifier

An n-channel JEFT has I DSS = 2 mA and V p = −4 V. It's transconductance g m (in mA/V) for an applied gate-to-source voltage V GS of –2V is:

A signal x(t) has a Fourier transform X ($$\omega $$). If x(t) is a real and odd function of t, then X($$\omega $$) is

The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{ - 4}}\sec } \cr 0 & {Otherwise} \cr } } \ri...

The z-transform of a signal is given by c(z)=$${1 \over 4}{{{z^{ - 1}}(1 - {z^{ - 4}})} \over {{{(1 - {z^{ - 1}})}^2}}}$$. Its final value is

The z-transform F(z) of the function f(nT) = $${a^{nT}}$$ is

The input to a channel is a band pass signal. It is obtained by linearly modulating a sinusoidal carrier with a signal- tone signal. The output of the channel due to this input is...

A modulated signal is given by s(t)= $${e^{ - at}}$$ cos $$\left[ {({\omega _c} + \Delta \omega )t} \right]$$ u (t), where a, $${\omega _c}$$ and $${\Delta \omega }$$ are positive...

The Nyquist sampling frequency (in Hz) of a signal given by $$16 \times {10^{4\,}}\,\sin {c^2}(400t)*{10^6}\,\sin {c^3}(100t)$$ is

$$If\,\,L\left[ {f\left( t \right)} \right]\, = \,F\left( s \right),$$ then $$L\left[ {f\left( {t - T} \right)} \right]$$ is equal to

A modulated signal is given by, $$s\left(t\right)=m_1\left(t\right)\cos\left(2{\mathrm{πf}}_\mathrm c\mathrm t\right)\;+m_2\left(t\right)\sin\left(2{\mathrm{πf}}_\mathrm c\mathrm t...

An electric field on a plane is described by its potential V = $$20\left(r^{-1}\;+\;r^{-2}\right)$$ where r is the distance from the source. The field is due to