2006|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

Following is the segment of a 8085 assembly language program:
LXI SP, EFFF H
CALL 3000 H
:
:
3000 H : LXI H, 3CF4 H
PUSH PSW
SPHL
POP PSW
RET
On completion of RET execution, the contents of SP is

The number of product terms in the minimized sum-of-product expression obtained through the following K-map is (where “d” denotes don't care states)

An I/O peripheral device shown in the figure below is to be interfaced to an 8085 microprocessor. To select the I/O device in the I/O address range D4 H - D7 H, its chip-select (^{$\overline {CS}$}) should be connected to which output of the decoder?

A 4-bit D/A converter is connected to a free-running 3-bit UP counter, as shown in the following figure. Which of the following waveforms will be observed at V₀?

For the circuit shown in figure below, two 4-bit parallel-in serial-out shift registers loaded with the data shown are used to feed the data to a full-adder. Initially, all the flip-flops are in clear state. After applying two clock pulses, what will be the outputs of the full-adder?

Two D-flip-flops, as shown below, are to be connected as a synchronous counter that goes through the following Q₁ Q₀ sequence
00 ^{_{$\rightarrow$}} 01 ^{_{$\rightarrow$}} 11 ^{_{$\rightarrow$}} 10 ^{_{$\rightarrow$}} 00 ^{_{$\rightarrow$}}.........
The inputs D₀ and D₁ respectively should be connected as

The electric field of an electromagnetic wave propagating in the positive z - direction is given by

$E = \widehat a_x sin(\omega t - \beta z) + \widehat a_y sin(\omega t - \beta z + \pi / 2)$

The wave is

When a plane wave traveling in free-space is incident normally on a medium having $\epsilon_r$ = 4.0 the fraction of power transmitted into the medium is given by

A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is

A mast antenna consisting of a 50 metre long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of 600 kHz. The radiation resistance of the antenna in Ohms is

A medium is divided into regions I and II about x = 0 plane, as shown in the figure below. An electromagnetic wave with electric field E₁ = 4$\widehat a$_x + 3$\widehat a$_y + 5$\widehat a$_z is incident normally on the interface form region-I. The electric field E₂ in region-II at the interface is

In the circuit shown below, the switch was connected to position 1 at t < 0 and at t = 0, it is changed to position 2. Assume that the diode has zero voltage drop and a storage time t_s For 0 < t$\le$ t_s , v_R is given by (all in Volts)

Find the correct match between Group 1 and Group 2:

A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as

The diagonal clipping in Amplitude Demodulation (using envelope detector) can be avoided if RC time-constant of the envelope detector satisfies the following condition, (here W is message bandwidth and c w is carrier frequency both in rad/sec)

Let g (t) = p (t) * p (t), where * denotes convolution and p (t) = u (t) − u (t − 1) with u (t) being the unit step function

The impulse response of filter matched to the signal s (t) = g (t) − ^_$\delta$ (t − 2) * g (t) is given as:

A low-pass filter having a frequency response H (j^_$\omega$) = A (^_$\omega$)^{_{$e^{j \phi (\omega)}$}} does not produce any phase distortion if

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal is
x (t ) = 125t (u (t ) − u (t − 1)) + (250 − 125t ) (u (t − 1) − u (t − 2)). (Here u (t) is the unit-step function.)
So that slope-overload is avoided, would be

A uniformly distributed random variable X with probability density function
f_x (x) = $\dfrac{1}{10}$(u (x + 5) - u (x - 5))
Where u (.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be

A zero-mean white Gaussian noise signal is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period 0.03 m. The samples so obtained would be

In the following figure, the minimum value of the constant “C”, which is to be added to y₁ (t) such that y₁ (t) and y₂ (t) are different, is

A signal m(t )with bandwidth 500 Hz is first multiplied by a signal g (t ) where
g (t) = $\displaystyle \sum_{R = - \infty}^\infty (-1)^k \delta (t - 0.5 \times O^{-4}k )$
The resulting signal is then passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be

A message signal with bandwidth 10 kHz is Lower-Side Band SSB modulated with carrier frequency f_c1 = 10⁶ Hz. The resulting signal is then passed through a Narrow-Band Frequency Modulator with carrier frequency f_c2 = 10⁹ Hz.
The bandwidth of the output would be

The minimum sampling frequency (in samples/sec) required to reconstruct the following signal x (t) = 5 ^{$\left(
\dfrac{sin2\pi 1000 t}{\pi t}
\right) ^ 3
$} + 7^{$\left(
\dfrac{sin2\pi 1000 t}{\pi t}
\right) ^ 2
$} from its samples without distortion would be

Consider the following Amplitude Modulated (AM) signal, where fm < B :
$X_{AM}(t) = 10 (1+0.5 sin 2\pi f_m t) cos2\pi f_ct$

The average side band power for the AM signal given above is:

Consider the following Amplitude Modulated (AM) signal, where fm < B:

$X_{AM}(t) = 10 (1+0.5 sin 2\pi f_m t) cos2\pi f_ct$

The AM signal gets added to a noise with Power Spectral Density S_n (f) given in the figure below. The ratio of average sideband power to mean noise power would be

The unit-step response of a system starting from rest is given by

c (t) = 1 - e^-2t for t ^$\ge$ 0

The transfer function of the system is

Let x (t) ^{_{$\leftrightarrow$}} X (j^_$\omega$) be Fourier Transform pair. The Fourier Transform of the signal x (5t − 3) in terms of X (j^_$\omega$) is given as

Consider the function f(t) having Laplace transform
F (s) = ^{$\dfrac{\omega_0}{s^2 + \omega^2_0}$} Re [s] > 0

The final value of f(t) would be

If the region of convergence of x₁ [n] + x₂ [n] is ^{$\dfrac{1}{3} \lt |z| \lt \dfrac{2}{3}$}, then the region of convergence of x_n [n] - x₂ [n] includes

The unit impulse response of a system is
h (t) = e^-t , t$\ge$ 0
For this system, the steady-state value of the output for unit step input is equal to

A negative resistance R_neg is connected to a passive network N having driving point impedance Z₂ (s) as shown below. For Z₁ (s) to be positive real,

A 2 mH inductor with some initial current can be represented as shown below, where s is the Laplace Transform Variable. The value of initial current is

In the figure shown below, assume that all the capacitors are initially uncharged. If v_i (t) = 10u (t ) Volts, v₀ (t) is given by

A two port network is represented by ABCD parameters given by
$\left[
\begin{array}
\ V_1 \\
I_1
\end{array}
\right]
$$\left[
\begin{array}
\ A & B\\
C & D
\end{array}
\right]
$$\left[
\begin{array}
\ V_2 \\
-I_2
\end{array}
\right]
$
If port-2 is terminated by R_L, the input impedance seen at port-1 is given by

The first and the last critical frequencies (singularities) of a driving point impedance function of a passive network having two kinds of elements, are a pole and a zero respectively. The above property will be satisfied by

The open-loop transfer function of a unity-gain feedback control system is given by

G (s) = ^{$$\dfrac{k}{(s+1)(s+2)}$$}

The gain margin of the system in dB is given by

For the function of a complex variable W = ln Z
(where, W = u + jv and Z = x + jy), the u = constant lines get mapped in Z-plane as

Three companies, X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below.

Given that a computer is defective, the probability that it was supplied by Y is

For the matrix $\begin{bmatrix}
\ 4 & 2 \
\ 2 & 4 \
\end{bmatrix}$, the eigen value corresponding to the eigenvector$\begin{bmatrix}
\ 101\
\ 101 \
\end{bmatrix}$ is

The eigen values and the corresponding eigen vectors of a 2 × 2 matrix are given by

<blockquote |||="" |---|---|="" |="" eigen="" value|="" vector|="" |<sup="">$\lambda_1$ = 8| V₁ = ^{$\begin{bmatrix}
\ 1\
\ 1 \
\end{bmatrix}$}|
|^$\lambda_2$ = 4| V₁ = ^{$\begin{bmatrix}
\ 1\
\ -1 \
\end{bmatrix}$}|

For the differential equation $\frac{d^2y}{dx^2}$+ k²y = 0 the boundary conditions are
(i) y = 0 for x = 0 and
(ii) y = 0 for x = a
The form of non-zero solutions of y (where m varies over all integers) are

The majority carriers in an n-type semiconductor have an average drift velocity v in a direction perpendicular to a uniform magnetic field B. the electric field E induced due to Hall effect acts in the direction

The values of voltage (V_D) across a tunnel-diode corresponding to peak and valley currents are V_P and V_V respectively. The range of tunnel-diode voltage V_D for which the slope of its I − V_D characteristics is negative would be

Consider two transfer functions:

G₁ (s) = ^{$\dfrac{1}{s^2 + as +b}$} and G₂ (s) = ^{$\dfrac{1}{s^2 + as +b}$}

The 3 dB bandwidths of their frequency responses respectively are

For the circuit shown below, assume that the zener diode is ideal with a breakdown voltage of 6 Volts. The waveform observed across R is

An n-channel depletion MOSFET has following two points on its I_D -V_GS curve:
(i) V_GS = 0 at I_D = 12 mA and
(ii) V_GS = - 6 volts at I_D = 0

Which of the following Q-points will give the highest trans-conductance gain for small signals?

The input impedance (Z_i) and the output impedance (Z₀) of an ideal trans - conductance (voltage controlled current source) amplifier are

The Nyquist plot of G (j$\omega$) H (j$\omega$) for a closed loop control system, passes through (- 1, j0) point in the GH-plane. The gain margin of the system in dB is equal to

The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are

The transfer function of a phase-lead compensator is given by G_c = ^{$\dfrac{1+3T_s}{1+T_s}$}, where T > 0. What is the maximum phase shift of the compensator?

A linear system is described by the following state equation:

X(t) = AX (t) + BU (t), A =^{$\left[
\begin{array}
\ 0 & 1 \\
-1 & 0
\end{array}
\right]$}

The state-transition matrix of the system is

A rectangular waveguide having 10 TE mode as dominant mode is having a cutoff frequency of 18-GHz for the TE₃₀ mode. The inner broad-wall dimension of the rectangular waveguide is: