GATE EC question library

A one-sided abrupt $pn$ junction diode has a depletion capacitance $C_{D}$ of $50$ $\text{pF}$ at a reverse bias of $0.2 V$. The plot of $1/C^{2}_{D}$ versus the applied voltage $V$ for this diode is a straight line as shown in the figure below. The slope of the plot is ___________ $\times 10^{20}F^{-2}V^{-1}$.

The band diagram of a $p$-type semiconductor with a band-gap of $1$ eV is shown. Using this semiconductor, a $\text{MOS}$ capacitor having $V_{TH}$ of $-0.16 V$, ${C}'_{ox}$ of $100\:nF/cm^{2}$ and a metal work function of $3.87 \: eV$ is fabricated. There is no charge within the oxide. If the voltage across the capacitor is $V_{TH}$, the …

The base of an $\text{npn BJT T1}$ has a linear doping profile $N_{B}\left ( x \right )$ as shown below. The base of another $\text{npn BJT T2}$ has a uniform doping $N_{B}$ of $10^{17}cm^{-3}$. All other parameters are identical for both the devices. Assuming that the hole density profile is the same as that of doping, the common-emitter current …

A $pn$ junction solar cell of area $1.0\:cm^{2}$, illuminated uniformly with $100\:mW\:cm^{-2}$, has the following parameters: Efficiency $= 15\%$, open circuit voltage $= 0.7\:V$, fill factor $= 0.8$, and thickness $=200 \mu m$. The charge of an electron is $1.6\times 10^{-19}C$. The average optical generation rate (in $cm^{-3} s^{-1}$) is

For the $\text{BJT}$ in the amplifier shown below, $V_{BE}=0.7V,\:kT/q=26\:mV$. Assume that $\text{BJT}$ output resistance $(r_{o})$ is very high and the base current is negligible. The capacitors are also assumed to be short circuited at signal frequencies. The input $v_{i}$ is direct coupled. The low frequency voltage gain $v_{o}/v_{i}$ of the …

An enhancement $\text{MOSFET}$ of threshold voltage $3\:V$ is being used in the sample and hold circuit given below. Assume that the substrate of the $\text{MOS}$ device is connected to $-10\:V$. If the input voltage $V_{1}$ lies between $\pm 10\:V,$ the minimum and the maximum values of $V_{G}$ required for proper sampling and holding …

Using the incremental low frequency small-signal model of the $\text{MOS}$ device, the Norton equivalent resistance of the following circuit is

$P, Q$, and $R$ are the decimal integers corresponding to the $4$-bit binary number $1100$ considered in signed magnitude, $1$’s complement, and $2$’s complement representations, respectively. The $6$-bit $2$’s complement representation of $(P+Q+R)$ is

The state diagram of a sequence detector is shown below. State $S_{0}$ is the initial state of the sequence detector. If the output is $1$, then

The characteristic equation of a system is $$s^{3}+3s^{2}+\left ( K+2 \right )s+3K=0.$$ In the root locus plot for the given system, as $K$ varies from $0$ to $\infty$, the break-away or break-in points(s) lie within

The components in the circuit given below are ideal. If $R=2\:k \Omega$ and $C=1$ $\mu F$, the $-3$ dB cut-off frequency of the circuit in Hz is

For the modulated signal $x\left ( t \right )=m\left ( t \right )\cos\left ( 2\pi f_{c}t \right )$, the message signal $m\left ( t \right )=4\cos\left ( 1000\pi t \right )$ and the carrier frequency $f_{c}$ is $1\: MHz$. The signal $x(t)$ is passed through a demodulator, as shown in the figure below. The output $y(t)$ of the demodulator is

For an infinitesimally small dipole in free space, the electric field $E_{\theta }$ in the far field is proportional to $e^{-jkr/r}\sin\theta$, where $k=2\pi /\lambda$. A vertical infinitesimally small electric dipole $\left (\delta l \ll \lambda \right )$ is placed at a distance $h\left ( h> 0 \right )$ above an infinite ideal conducting plane, …

In the voltage regulator shown below, $V_{1}$ is the unregulated imput at $15\:V$. Assume $V_{BE}=0.7\:V$ and the base current is negligible for both the $\text{BJTs}$. If the regulated output $V_{O}$ is $9\:V$, the value of $R_{2}$ is ___________$\Omega$

The magnetic field of a uniform plane wave in vacuum is given by $$\overrightarrow{H}\left ( x,y,z,t \right )=(\hat{a_{x}}+2\hat{a_{y}}+b\hat{a_{z}})\cos\left ( \omega t+3x-y-z\right ).$$ The value of $b$ is ___________.

For a $2$-port network consisting of an ideal lossless transformer, the parameter $S_{21}$ (rounded off to two decimal places) for a reference impedance of $10 \Omega$, is __________.

$S_{PM}(t)$ and $S_{FM}(t)$ as defined below, are the phase modulated and the frequency modlated waveforms, respectively, corresponding to the message signal $m(t)$ shown in the figure. …

In a digital communication system, a symbol $S$ randomly chosen from the set $\left \{ s_{1},s_{2},s_{3},s_{4} \right \}$ is transmitted. It is given that $s_{1}=-3,s_{2}=-1,s_{3}=+1$ and $s_{4}=+2$. The received symbol is $Y=S+W$ . $W$ is a zero-mean unit-variance Gaussian random variable and is independent of $S$. $P_{i}$ is the conditional …

A system with transfer function $G\left ( s \right )=\dfrac{1}{\left ( s+1 \right )\left ( s+a \right )},\:\:a> 0$ is subjected to an input $5 \cos3t$. The steady state output of the system is $\dfrac{1}{\sqrt{10}}\cos\left ( 3t-1.892 \right )$. The value of $a$ is _______.

For the components in the sequential circuit shown below, $t_{pd}$ is the propagation delay, $t_{\text{setup}}$ is the setup-time, and $t_{\text{hold}}$ is the hold time. The maximum clock frequency (rounded off to the nearest integer), at which the given circuit can operate reliably, is _________$\text{MHz}$.