2011|Electronics and Comm (GATE Exam)-Previous Question Paper Solution

Two D flip-flops are connected as a synchronous counter that goes through the following Q_BQ_A sequence 00^{_{$\rightarrow$}}11^{_{$\rightarrow$}}01^{_{$\rightarrow$}}10^{_{$\rightarrow$}}00^{_{$\rightarrow$}}…
The combination to the inputs D_A and D_B are

The output of a 3-stage Johnson (twisted ring) counter is fed to a digital-to analog (D/A) converter as shown in the figure below. Assume all the states of the counter to be unset initially. The waveform which represents the D/A converter output V_o is

An 8085 assembly language program is given below. Assume that the carry flag is initially unset. The content of the accumulator after the execution of the program is

A transmission line of characteristic impedance 50W is terminated in a load impedance Z_L. The VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a distance of $\dfrac{\lambda}{4}$from the load. The value of Z_L is

A silicon PN junction is forward biased with a constant current at room temperature. When the temperature is increased by 10^oC, the forward bias voltage across the PN junction

A transmission line of characteristic impedance 50 Ω is terminated by a 50 Ωload.
When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $\dfrac{2\pi}{\lambda}$ radians. The phase velocity of the wave along the line is

The modes in a rectangular waveguide are denoted by where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM signal, then the coefficient of the term $\cos[2\pi(1008 \times 10^3t)] $ in the FM signal (in terms of the Bessel coefficients) is

An analog signal is band-limited to 4kHz, sampled at the Nyquist rate and the samples are quantized into 4 levels. The quantized levels are assumed to be independent and equally probable. If we transmit two quantized samples per second, the information rate is

A four-phase and an eight-phase signal constellation are shown in the figure below

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

A four-phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r₁, and r₂ of the circles are

X(t) is a stationary random process with autocorrelation function R_x(^_$\tau$) = exp ^{$(\pi r^2)$}. This process is passed through the system shown below. The power spectral density of the output process Y(t) is

The first six points of the 8-point DFT of a real valued sequence are 5, 1 - j3,0,3 - j4, 0 and 3 + j4. The last two points of the DFT are respectively

Two systems H₁ (z) and H₂ (z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H₂ (z) is

The differential equation 100$\dfrac{d^2 y}{dt^2}$- 20$\dfrac{dy}{dt}$ + y = x(t) describes a system with an input x(t) and an output y(t). The system, which is initially relaxed, is excited by a unit step input. The output y(t) can be represented by the waveform

In the circuit shown below, the initial charge on the capacitor is 2.5 mC, with the voltage polarity as indicated. The switch is closed at time t = 0. The current i(t) at a time t after the switch is closed is

In the circuit shown below, the network N is described by the following Y matrix:

Y = $\left[
\begin{array}
\ 0.1S & -0.01S \\
0.01S & 0.1S
\end{array}
\right]$. The voltage gain $\dfrac{V_2}{V_1}$is

In the circuit shown below, capacitors C₁ and C₂ are very large and are shorts at the input frequency. v_i is a small signal input. The gain magnitude $|\frac{v_0}{v_i}|$ at 10 M

The circuit below implements a filter between the input current ii and the output voltage v_o. Assume that the opamp is ideal. The filter implemented is a

Consider a closed surface S surrounding volume V. If $\overrightarrow{r}$is the position vector of a point inside S, with $\hat{n}$ the unit normal on S, the value of the integral $\oint_s 5 \hat{r} . \overrightarrow{n} dS$is

In the circuit shown below, for the MOS transistors, $\mu_n C - {ox}$ = 100$\mu A/V^2$and the threshold voltage V_T = 1V. The voltage V_x at the source of the upper transistor is

For a BJT the common base current gain $\alpha$ = 0.98 and the collector base junction reverse bias saturation current I_CO 0.6$\mu A$. This BJT is connected in the common emitter mode and operated in the active region with a base drive current I_B = 20XA. The collector current I_C for this mode of operation is

A numerical solution of the equation f(x) = x + ^{$\sqrt{x - 3}$} = 0 can be obtained using Newton Raphson method. If the starting value is x = 2 for the iteration, the value of x that is to be used in the next step is

The input-output transfer function of a plant H(x) = $\dfrac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The signal flow graph that DOES NOT model the plant transfer function H(s) is

The input-output transfer function of a plant H(x) = $$\dfrac{100}{s(s+10)^2}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The gain margin of the system under closed loop unity negative feedback is

For the BJT Q_L in the circuit shown below,
$\beta = \infty$, $V_{B Eon - 0.7, V_{cEsat}}$0.7V. The switch is initially closed. At time t = 0, the switch is opened. The time t at which Q₁ leaves the active region is

In the circuit shown below, assume that the voltage drop across a forward biased diode is 0.7 V. The thermal voltage V_t = kT / q = 25mV. The small signal input v_i = V_p cos $(\omega t)$ where V_p = 100 mV.

The bias current I_DC through the diodes is

The system of equations
x + y + z = 6
x + 4y + 6z = 20
x + 4y + ^{_{$\lambda z$}} = ^_$\mu$
has NO solution for values of ^_$\lambda$ and ^_$\mu$ given by

In the circuit shown below, assume that the voltage drop across a forward biased diode is 0.7 V. The thermal voltage V_t = kT/q = 25 mV and small signal input v_i = V_p cos $(\omega t)$ where V_p = 100 mV.

The ac output voltage v_ac is