2004|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

Choose the correct one from among the alternatives A, B, C, D, after matching an item from Group 1 most appropriate item in Group 2.
Group 1 Group 2
P. Shift register 1. Frequency division
Q. Counter 2. Addressing in memory chips
R. Decoder 3. Serial to parallel data conversion

Consider the sequence of 8085 instructions given below:
LXI H, 9258
MOV A, M
CMA
MOV M, A

Which one of the following is performed by this sequence?

A Boolean function f of two variables x and y is defined as follows :
F(0,0) = f(0,1) = f(1,1) = 1; f(1,0)
Assuming complements of x and y are not available, a minimum cost solution for realizing f using only 2-
input NOR gates and 2- input OR gates (each having unit cost) would have a total cost of

A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from minimum to a maximum in 100 increments. The minimum number of bits required to encode, in straight binary, is

In the modulo-6 ripple counter shown in the figure below, the output of the 2- input gate is used to clear the J-K flip-flop. The 2-input gate is

It is desired to multiply the numbers 0AH by 0BH and store the result in the accumulator. The numbers are available in registers B and C respectively. A part of the 8085 program for this purpose is given below :
MVI A, 00H
LOOP ------

HLT
END
The sequence of instructions to complete the program would be

A parallel plate air-filled capacitor has plate area of 10^-4 m² and plate separation of 10^-3 m. It is connected to a 0.5 V, 3.6 GHz source. The magnitude of the displacement current is ($\epsilon$= $\dfrac{1}{36\pi} 10^{-9}$F/m)

Consider the following statements S₁ and S₂.
S₁ : The ^$\beta$ of a bipolar transistor reduces if the base width is increased.
S₂ : The ^$\beta$ of a bipolar transistor increases if the doping concentration in the base is increased.

Which of the following statements is correct?

In an abrupt p – n junction, the doping concentrations on the p − side and n − side are N_D = 10¹⁶/cm³ and N_A = 9 x 10¹⁶/cm³ respectively. The p – n junction is reverse biased and the total depletion width is 3 ^_$\mu$m. The depletion width on the p −side is

Consider a 300 $\Omega$, quarter - wave long (at 1 GHz) transmission line as shown in figure. It is connected to a 10 V, 50 $\Omega$ source at one end and is left open circuited at the other end. The magnitude of the voltage at the open circuit end of the line is

A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is 2. The percentage of the power that is reflected back is

If for a silicon npn transistor, the base-to-emitter voltage (V_BE) is 0.7 V and the collector-to-base voltage (V_CB) is 0.2 V, then the transistor is operating in the

Consider an abrupt p - n junction. Let V_bi be the built-in potential of this junction and V_R be the applied reverse bias. If the junction capacitance (C_j) is 1 pF for V_bi + V_R = 1 V, then for V_bi + V_R = 4 V, C_j will be

The drain of an n-channel MOSFET is shorted to the gate so that V_GS = V_DS. The threshold voltage (V_T) of the MOSFET is 1 V. If the drain current (I_D) is 1 mA for V_GS = 2 V, then for V_GS = 3 V, I_D is

The longest wavelength that can be absorbed by silicon, which has the bandgap of 1.12 eV, is 1.1 $\mu$m. If the longest wavelength that can be absorbed by another material is 0.87 $\mu$m, then bandgap of this material is

The resistivity of a uniformly doped n −type silicon sample is 0.5 ظ - mc. If the electron mobility ($\mu_0$) is 1250 cm² / V-sec and the charge of an electron is 1.6 x 10^-19 Coulomb, the donor impurity concentration (N_D) in the sample is

Consider the following statements S1 and S2
S1 : At the resonant frequency, the impedance of a series RLC circuit is zero.
S2 : In a parallel GLC circuit, increasing the conductance G results in increase in its Q factor.
Which one of the following is correct?

In a PCM system, if the code word length is increased from 6 to 8 bits, the signal to quantisation noise ratio improves by the factor

An AM signal is detected using an envelop detector. The carrier frequency and modulating signal frequency are 1 MHz and 2 kHz respectively. An appropriate value for the time constant of the envelop detector is

An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of 0.1 are added together. The resultant signal can be closely approximated by

Consider the signal x (t) shown in Fig. Let h (t) denote the impulse response of the filter matched to x (t), with h (t) being non-zero only in the interval 0 to 4 sec. The slope of h (t) in the interval 3 < t < 4 sec is

In the output of a DM speech encoder, the consecutive pulses are of opposite polarities during time interval t₁ ^$\le$ t ^$\le$ t₂. This indicates that during this interval,

Two sinusoidal signals of same amplitude and frequencies 10 kHz and 10.1 kHz are added together. The combined signal is given to an ideal frequency detector. The output of the detector is

Match the following:

A random variable X with uniform density in the interval 0 to 1 is quantized as follows :
If 0$\le$x$\le$ 0.3, x_q = 0
If 0.3 < X$\le$1, x_q = 0.7
where xq is the quantized value of X.
The root-mean square value of the quantization noise is

Consider a system shown in the figure. Let X (f) and Y( f) denote the Fourier transforms of x (t) and y (t) respectively. The ideal HPF has the cutoff frequency 10 kHz.

The positive frequencies, where Y (f) has spectral peaks are

Three analog signals, having bandwidths 1200 Hz, 600 Hz and 600 Hz, are sampled at their respective Nyquist rates, encoded with 12 bit words, and time division multiplexed. The bit rate for the multiplexed signal is

A causal LTI system is described by the difference equation
2y[n] = $\alpha$y[n-2] -2x [n] + $\beta$x[n-1]
The system is stable only if

The impulse response h [n] of a linear time-invariant system is given by h[n]= u[n+3] + u [n-2)-2n[n-7] where u[n] is the unit step sequence. The above system is

The impulse response H [n] of a linear time invariant system is given as
$h[n] =
\begin{cases}
-2\sqrt 2 & n=1, -1 \\
4\sqrt 2 & n=2, -2 \\
0 & otherwise
\end{cases}

$
If the input to the above system is the sequence e^j$\pi$n/4, then the output is

The circuit shown in the figure has initial current i_L (0^-) = 1 A through the inductor and an initial voltage v_C(0^-) = -1 V across the capacitor. For input = v(t) = u (t), the Laplace transform of the current i(t) for t $\ge$0 is

The circuit shown in the figure, with R = $\dfrac{1}{3}$$\Omega$, L = $\dfrac{1}{3}$H and C = 3 F has input voltage v (t) = sin 2t. The resulting current i(t) is

For the circuit shown in the figure, the time constant RC = 1 ms. The input voltage is v₁ (t) = ^{$\sqrt 2$}sin 10³t. The output voltage v₀ (t) is equal to

For the lattice shown in the figure, Z_a = j2^$\Omega$ and Z_b = 2^$\Omega$. Calculate the values of the open circuit impedance parameter [z] = ^{$\left[
\begin{array}
\ Z_{11} & Z_{12} \\
Z_{21} & Z_{22}
\end{array}
\right]$}.

The transfer function H(s) = $\dfrac{V_0 (s)}{V_i (s)}$ of an RLC circuit is given by
H(s) = $\dfrac{10^6}{s^2 + 20s + 10^6}$
The Quality factor (Q-factor) of this circuit is

Consider the following statements Sq and S2.
S1 : The threshold voltage (V_T) of MOS capacitor decreases with increase in gate oxide thickness.
S2 : The threshold voltage (V_T) of a MOS capacitor decreases with increase in substrate doping concentration.
Which one of the following is correct?

Assuming 0.2 V_CEsat = V and $\beta$= 50, the minimum base current (I_B) required to drive the transistor in the figure to saturation is

Consider a lossless antenna with a directive gain of 6 + dB. If 1 mW of power is fed to it, the total power radiated by the antenna will be

A system described by the following differential equation $\frac{d^2y}{dt^2} + 3 \frac{dy}{dt} + 2y = x(t)$is initially at rest. For input x(t) = 2u(t), the output y(t) is

A rectangular pulse train s(t) as shown in the figure is convolved with the signal cos²(4p x 10³t). The convolved signal will be a

A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low-pass filter with cut-off frequency 800 Hz. The output signal has the frequency

Consider an impedance Z = R + jX marked with point P in an impedance Smith chart as shown in figure. The movement from point P along a constant resistance circle in the clockwise direction by an angle 45c is equivalent to

_If ^{$\overrightarrow{E}$}₌ ^{$(\hat{a}+ j \hat{a_y}) e^{jkz - kwt}$}_and ^{$\overrightarrow{H}$}_{= (k/w^$\mu$)} ^{$(\hat{a_y}+ k \hat{a_x}) e^{jkz - jwt}$}_{, the time - averaged Poynting vector is}

A bipolar transistor is operating in the active region with a collector current of 1 mA. Assuming that the $\beta$ of the transistor is 100 and the thermal voltage (V_T) is 25 mV, the transconductance (g_m) and the input resistance ($r_x$)the transistor in the common emitter configuration, are

In a full-wave rectifier using two ideal diodes, V_dc and V_m are the dc and peak values of the voltage respectively across a resistive load. If PIV is the peak inverse voltage of the diode, then the appropriate relationships for this rectifier are

In the voltage regulator shown in the figure, the load current can vary from 100 mA to 500 mA. Assuming that the Zener diode is ideal (i.e., the Zener knee current is negligibly small and Zener resistance is zero in the breakdown region), the value of R is

A causal system having the transfer function H(s) = 1 /(s+2) is excited with 10u(t) . The time at which the output reaches 99% of its steady state value is

A system has poles at 0.1 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz.
The approximate phase of the system response at 20 Hz is

The open-loop transfer function of a unity feedback system is

G(s) ^{$\dfrac{K}{s(s^2+s+2)(s+3)}$}

The range of K for which the system is stable is