GATE EC question library

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 …

The current density in a medium is given by $${\overrightarrow J= \frac{400 \sin\theta}{2\pi(r^2+4)} \hat {a}_r \: Am^{-2}}$$ The total current and the average current density flowing through the portion of a spherical surface $r = 0.8 \: m$, $\frac{\pi}{12} \leq \theta \leq \frac{\pi}{4}$, $0 \leq \phi \leq 2\pi$ are given, respectively, by

An antenna pointing in a certain direction has a noise temperature of $50 \: K$. The ambient temperature is $290 \: K$. The antenna is connected to a pre-amplifier that has a noise figure of $2$ dB and an available gain of $40$ dB over an effective bandwidth of $12$ MHz. The effective input noise temperature $T_e$ for the amplifier and the noise …

Two lossless X-band horn antennas are separated by a distance of $200 \lambda$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are $0.15$ and $0.18$,respectively. The maximum directives of the transmitting and receiving antennas (over the isotropic antenna) are $18$ dB and $22$ dB, respectively. …

The electric field of a uniform plane wave traveling along the negative $z$ direction is given by the following equation: $${\overrightarrow {E}^i_w= ( \hat {a}_x+ j\hat {a}_y)E_0e^{jkz}}$$ This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation: …

The far-zone power density radiated by a helical antenna is approximated as: $${\overrightarrow W_{rad}= \overrightarrow W_{average} \approx \hat {a_r}C_0\frac{1}{r^2}\cos^4\theta}$$ The radiated power density is symmetrical with respect to $\phi$ and exists only in the upper hemisphere: $0\leq\theta\leq\frac{\pi}{2}; \: 0\leq\phi\leq 2\pi$; $C_0$ is a …