GATE 2005 Electronics and Communication Engineering Previous Year Paper

The transistors used in a portion of the TTL gate shown in figure have ^_$\beta$ = 100 ,the base-emitter voltage is 0.7 V for a transistor in active region and 0.75 V for a transistor in saturation. If the sink current I = 1 mA and the output is at logic 0, then the current I_R will be equal to

Consider an 8085 microprocessor system.
The following program starts at location 0100H.
LXI SP, 00FF
LXI H, 0701
MVI A, 20H
SUB M

The content of accumulator when the program counter reaches 0109H is

Consider an 8085 microprocessor system.
If in addition following code exists from 0109H onwards.
ORI 40H
ADD M
What will be the result in the accumulator after the last instruction is executed?

What memory address range is NOT represented by chip #1 and chip #2 in figure? A₀ to A₁₅ in this figure are the address lines and CS means Chip Select.

The Boolean expression for the truth table shown is

Figure shows a ripple counter using positive edge triggered flip-flops. If the present state of counter is Q₂Q₁Q₀ = 011, then its next state (Q₂Q₁Q₀) will be

Which one of the following represents the electric field lines for the TE₀₂ mode in the cross-section of a hollow rectangular metallic waveguide?

The magnetic field intensity vector of a plane wave is given by $\bar H (x,y,z,t)$ = 10 sin (50000t + 0.004x + 30)$\widehat a_y$ where $\widehat a_y$denotes the unit vector in y direction. The wave is propagating with a phase velocity

Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of 10¹⁴ Hz in glass. Assume velocity of light is 3 × 10⁸ m/s in vacuum.

Characteristic impedance of a transmission line is 50$\Omega$. Input impedance of the open circuited line is Z_oc = 100 + j150$\Omega$. When the transmission line is short-circuited, the value of the input impedance will be

Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $\Omega$ and a resistive load is shown in figure.

The reflection coefficient is given by

Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $\Omega$ and a resistive load is shown in figure.

The value of the load resistance is

A silicon sample A is doped with 10¹⁸ atoms/cm³ of Boron. Another sample B of identical dimensions is doped with 10¹⁸ atoms/cm³ of Phosphorus. The ratio of electron to hole mobility is 3. The ratio of conductivity of the sample A to B is

A MOS capacitor is made using p-type substrate in the accumulation mode. The dominant charge in the channel is due to the presence of

A Silicon PN junction at a temperature of 20°C has a reverse saturation current of 10 pico-Amperes (pA). The reverse saturation current at 40°C for the same bias is approximately

Match the following:

Noise with uniform power spectral density of N_oW/Hz is passed through a filter ^{_{$H(\omega) = 2 \ exp(-j\omega t_d)$}} followed by an ideal low-pass filter of bandwidth B Hz. The output noise power in Watts is

An output of a communication channel is a random variable $\nu$ with the probability density function as shown in figure. The mean square value of $\nu$ is

A carrier is phase modulated (PM) with frequency deviation of 10 kHz by a single tone frequency of 1 kHz. If the single tone frequency is increased to 2 kHz, assuming that phase deviation remains unchanged, the bandwidth of the PM signal is

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

The quantization noise power for the quantization region between -a and +a in the figure is

A device with input x(t) and output y(t) is characterized by: y(t) = x²(t). An FM signal with frequency deviation of 90 kHz and modulating signal bandwidth of 5 kHz is applied to this device. The bandwidth of the output signal is

A symmetric three-level midtread quantizer is to be designed assuming equiprobable occurrence of all quantization levels.

If the input probability density function is divided into three regions as shown in figure, the value of a in the figure is

A sequence x(n) has non-zero values as shown in figure.

The sequence
$y(n) =
\begin{cases}
x\left( \dfrac{n}{2} -1 \right) & \text{for n even} \\
0 & \text{for n odd}
\end{cases}
$
will be

A signal $x(n) = sin(\omega_on + \phi)$ is the input to a linear time invariant system having a frequency response $H(e^{j\omega})$. If the output of the system is $Axn - n_0$, then the most general form of $\angle H (e^{j\omega})$ will be

The output y(t) of a linear time invariant system is related to its input x(t) by the following equation: $y(t) = 0.5 \times (t-t_d + T) + x(t-t_d) + 0.5 \times (t-t_d-T)$. The filter transfer function $H(\omega)$ of such a system is given by

Let $x(n) = \left( \dfrac{1}{2} \right) ^ n u(n), \ y(n) = x^2(n)$ and $Y (e^{j\omega})$ be the Fourier transform of y(n)  Then $Y(e^{j0})$ is

The ABCD parameters of an ideal n : 1 transformer shown in figure are $
\left[
\begin{array}
\ n & 0 \\
0 & x
\end{array}
\right]

$. The value of X will be

A square pulse of 3 volts amplitude is applied to C - R circuit shown in figure. The capacitor is initially uncharged. The output voltage v₀ at time t = 2 sec is

If R₁ = R₂ = R₄ and R₃ = 1. 1R in the bridge circuit shown in figure, then the reading in the ideal voltmeter connected between a and b is

A linear system is equivalently represented by two sets of state equations; ^{$\bar X = AX + BU$} and W = CW + DU. The eigen values of the representations are also computed as ^$[\lambda]$ and ^$[\mu]$. Which of the following statements is true?

Let $A = \begin{bmatrix}
\ 2 & -0.1 \
\ 0 & 3 \
\end{bmatrix} \hspace{0.2cm} and \hspace{0.2cm} A^{-1}\begin{bmatrix}
\ \frac{1}{2} & a \
\ 0 & b \
\end{bmatrix}$, then (a + b) =

Given an orthogonal matrix ^{$\begin{bmatrix}
\ 1 & 1 & 1 & 1 \
\ 1 & 1 & -1 & -1 \
\ 1 & -1 & 0 & 0 \
\ 0 & 0 & 1 & -1
\end{bmatrix}$$\begin{bmatrix}
\ AA^T \
\end{bmatrix}^{-1}$} is

For an npn transistor connected as shown in figure, V_BE = 0.7 Volts. Given that reverse saturation current of the junction at room temperature 300°K is 10^-13 A, the emitter current is

The circuit using a BJT with $\beta$ = 50 and V_BE = 0.7 V is shown in figure. The base current I_B and collector voltage V_C are respectively

In the derivation of expression for peak percent overshoot, ^{$M_p = exp
\left(
\dfrac{-\pi\xi}{\sqrt{1-\xi^2}}
\right) \times 100 %
$}, which of the following conditions is not required?

The polar diagram of a conditionally stable system for open loop gain K = 1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for

A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are respectively

Both transistors T₁ and T₂ in figure have a threshold voltage of 1 Volt. The device parameters K₁ and K₂ of T₁ and T₂ are, respectively, 36 A/V² and 9 A/V². The output voltage V₀ is

The Zener diode in the regulator circuit shown in figure has a Zener voltage of 5.8 Volts and a Zener knee current of 0.5 mA. The maximum load current drawn from this circuit ensuring proper functioning over the input voltage range between 20 and 30 Volts, is

Given the ideal operational amplifier circuit shown in figure indicate the correct transfer characteristics assuming ideal diodes with zero cut-in voltage.

A Silicon PN junction diode under reverse bias has depletion region of width 10 m. The relative permittivity of Silicon, $\epsilon_r = 11.7$ and the permittivity of free space ^{$\epsilon_0 = 8.85 \times 10^{-12} F/m$}. The depletion capacitance of the diode per square metre is

A double integrator plant, ^{$G(s) = \dfrac{k}{s^2} \ H(s) = 1$} is to be compensated to achieve the damping ratio _^$\xi$ = 0.5, and an undamped natural, _{^{$\omega_n = 5\ rad/s$}}. Which one of the following compensator G_c(S) will be suitable?

Two identical and parallel dipole antennas are kept apart by a distance of ^{$\frac{\lambda}{4}$} in the H-plane. They are fed with equal current but the right most antenna has a phase shift of + 90^o. The radiation pattern is given as

Given, r_d = 20 k$\Omega$, I_DSS = 10 mA, V_p = -8 V

Transconductance in milli-Siemens (mS) and voltage gain of the amplifier are respectively

The open loop transfer function of a unity feedback is given by
$G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

The gain and phase crossover frequencies in rad/sec are respectively

The open loop transfer function of a unity feedback is given by
$G(s) = \dfrac{3e^{-2s}}{s(s+2)}$

Based on the above results, the gain and phase margins of the system will be

The region of convergence of Z-transform of the sequence $\bigg(\frac{5}{6}\bigg)^n u(n) - \bigg(\frac{6}{5}\bigg)^n u(n - 1)$ must be