GATE EC question library

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t = 0, then the magnitude of the current (in mA) through the $4k \Omega$ resistor at $t= 0^{+}$ is ________.

A silicon bar is doped with donor impurities $N_{D}= 2.25 \times 10^{15} \text{atoms} / cm^{3}$. Given the intrinsic carrier concentration of silicon at $T = 300 \: K$ is $n_{i}= 1.5 \times 10^{10} cm^{-3}.$ Assuming complete impurity ionization, the equilibrium electron and hole concentrations are

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

The feedback topology in the amplifier circuit ( the base bias circuit is not shown for simplicity) in the figure is

In the differential amplifier shown in the figure, the magnitude of the common-mode and differential-mode gains are $A_{CM}$ and $A_{d},$ respectively. If the resistance $R_{E}$ is increased, then

A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ for A1 and A2 are as follows: $A1: A_{V0} = 10, R_{in} = 10k \Omega, R_{o} = 1k\Omega$ $A2: A_{V0} = 5, R_{in} = 5k \Omega, R_{o} =200\Omega$ The approximate overall voltage …

For an $n$-variable Boolean function, the maximum number of prime implicants is

The number of bytes required to represent the decimal number $1856357$ in packed BCD (Binary Coded Decimal) form is ___________.

In a half-subtractor circuit with $X$ and $Y$ as inputs, the Borrow $(M)$ and Difference $(N = X – Y)$ are given by

As FIR system is described by the system function $$H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2}z^{-2}$$. The system is

Let $x[n] = x[-n]$. Let $X(z)$ be the $z$-transform of $x[n]$. If $0.5 + j 0.25$ is a zero of $X(z)$, which one of the following must also be a zero of $x(z)$

Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harmonic to the power in the $5^{th}$ harmonic for this waveform is closest in value to ________.

The natural frequency of an undamped second-order system is $40$ rad/s. If the system is damped with a damping ratio $0.3$, the damped natural frequency in $rad/s$ is ___________.

For the following system, when $X_{1} (s) = 0$, the transfer function $\frac{Y(s)}{X_{2}(s)}$ is

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), where $W$ is the channel bandwidth, $P$ is the average power received and $\sigma ^{2}$ is the one-sided power spectral density of the AWGN. For a fixed …

Consider sinusoidal modulation in an AM system. Assuming no overmodulation, the modulation index ($\mu$) when the maximum and minimum values of the envelope, respectively, are $3$ V and $1$ V, is ___________.

To maximum power transfer, a lossless transmission line is to be matched to a resistive load impedance via a $\lambda/4$ transformer as shown. The characteristic impedance (in $\Omega$) of the $\lambda$/4 transformer is ___________.

Which one of the following field patterns represents a TEM wave travelling in the position $x$ direction?