GATE EC question library

A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form $$\sum_{k=1}^{3} a_k\cos(k\omega_0t) ,\text{where } \thinspace a_k\neq 0, \omega_0\neq0$$ The source has nonzero impedance. Which one of the following is a possible form of …

A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$ with the corresponding time responses for $t \geq 0$: …

An AC voltage source $V = 10 \sin(t)$ volts is applied to the following network. Assume that $R_1 = 3 k\Omega$, $R_2 = 6 k\Omega$ and $R_3 = 9k\Omega$, and that the diode is ideal. RMS current $I_{rms}$(in mA) through the diode is _______

In the circuit shown in the figure, the maximum power (in watt) delivered to the resistor $R$ is _______

Consider the signal $$x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$$ If $X(e^{jw})$ is the discrete-time Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{-\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______

Consider a silicon $p-n$ junction with a uniform acceptor doping concentration of $10^{17} cm^{-3}$ on the $p$-side and a uniform donor doping concentration of $10^{16}cm^{-3}$ on the $n$-side. No external voltage is applied to the diode. Given: $kT/q = 26 \: mV$, $n_i = 1.5 \times 10^{10} cm^{-3}$ , $\epsilon_{Si} = 12 \varepsilon_0$, …

Consider an $n$-channel metal oxide semiconductor field effect transistor (MOSFET) with a gate-to-source voltage of $1.8$ V. Assume that $\frac{W}{L}=4$, $\mu_NC_{ox}= 70 \times 10^{-6} AV^{-2}$, the threshold voltage is $0.3$V, and the channel length modulation parameter is $0.09 \: V^{-1}$. In the saturation region, the drain conductance (in …

The figure below shows the doping distribution in a $p$-type semiconductor in log scale. The magnitude of the electric field (in $kV/cm$) in the semiconductor due to non uniform doping is _________

Consider a silicon sample at $T = 300 \: K$, with a uniform donor density $N_d = 5 \times 10 ^{16} cm^{-3}$ , illuminated uniformly such that the optical generation rate is $G_{opt}=1.5 \times 10^{20} cm^{-3}s^{-1}$ throughout the sample. The incident radiation is turned off at $t=0$. Assume low-level injection to be valid and ignore surface effects. …

An ideal opamp has voltage sources $V_1, V_3, V_5, \dots, V_{N-1}$ connected to the non-inverting input and $V_2, V_4, V_6, \dots, V_N$ connected to the inverting input as shown in the figure below $(+V_{CC}= 15$ volt, $– V_{CC} = – 15$ volt). The voltages $V_1, V_2, V_3, V_4, V_5, V_6, \dots$ are $1, -1/2, 1/3, -1/4, 1/5, -1/6, \dots$ volt, …

A $p-i-n$ photodiode of responsivity $0.8 \: A/W$ is connected to the inverting input of an ideal opamp as shown in the figure, $+V_{CC}= 15 V, \: – V_{CC} = – 15 V$, Load resistor $R_L=10k\Omega$. If $10 \mu W$ of power is incident on the photodiode, then the value of the photocurrent(in $\mu A$) through the load is _________

Identify the circuit below.

The functionality implemented by the circuit below is

In an $8085$ system, a PUSH operation requires more clock cycles than a POP operation. Which one of the following options is the correct reason for this?

The open-loop transfer function of a unity-feedback control system is $$G(s)= \frac{K}{s^2+5s+5}$$. The value of $K$ at the breakaway point of the feedback contol system’s root-locus plot is _________

The open-loop transfer function of a unity feedback control system is given by $$G(s)= \frac{K}{s(s+2)}$$. For the peak overshoot of the closed-loop system to a unit step input to be $10 \%$, the value of $K$ is _________

The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s -2$. The number of zeroes in the right half of the $s$-plane is _________

Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \bigg\}$. The entropy of the source (in bits) is _________

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times ($0$ is transmitted as $000$, and $1$ is transmitted as $111$). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three …

An analog pulse $s(t)$ is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is $r(t) = s(t) + n(t)$, where $n(t)$ is additive white Gaussian noise with power spectral density $\frac{N_0}{2}$. The received signal is passed through a filter with impulse response $h(t)$. Let $E_s$ and $E_h$ denote the energies …