GATE EC Electromagnetics questions

A $16$ – bit ripple carry adder is realized using $16$ identical full adders (FA) as shown in the figure. The carry-propagation delay of each FA is $12$ ns and the sum-propagation delay of each FA is $15$ ns. The worst case delay (in ns) of this $16$-bit adder will be _______

The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, respectively. The value of $\psi _B – \psi _A$ in Volts is ____________

If $\overrightarrow{E} = -(2y^3 – 3yz^2)\hat{x} – (6xy^2-3xz^2) \hat{y}+(6xyz) \hat{z}$ is the electric field in a source free region, a valid expression for the electrostatic potential is

In a voltage-voltage feedback as shown below, which one of the following statements is TRUE if the gain $k$ is increased?

A source $v_{s}(t) = V\cos100\:\pi t$ has an internal impedance of $(4 + j3)\:\Omega.$ If a purely resistive load connected to this source has to extract the maximum power out of the source, its value in $\Omega$ should be

A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\:25x}$. The frequency and polarization of the wave, respectively, are

The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is

A coaxial cable with an inner diameter of $1\:mm$ and outer diameter of $2.4\:mm$ is filled with a dielectric of relative permittivity $10.89$. Given $\mu_0=4\pi\times10^{-7}\:H/m$, $\varepsilon_0=\frac{10^{-9}}{36\pi}\:F/m$, the characteristic impedance of the cable is

The radiation pattern of an antenna in spherical co-ordinates is given by $$F(\theta)=\cos^4\theta\:\:\:;\:\:\:0\le \theta\le \frac{\pi}{2}$$ The directivity of the antenna is

The impedance looking into nodes $1$ and $2$ in the given circuit is

A trasmission line with a characteristic impedance of $100\:\Omega$ is used to match a $50\:\Omega$ section to a $200\:\Omega$ section. If the matching is to be done both at $429\:MHz$ and $1\:GHz$, the length of the transmission line can be approximately

The magnetic field along the propagation direction inside a rectangular waveguide with the cross-section shown in the figure is $$H_Z=3\:\cos(2.094\times10^2x)\:\cos(2.618\times10^2y)\:\cos(6.283\times10^{10}t-\beta z)$$ The phase velocity $v_p$ of the wave inside the waveguide satisfies

For a Hertz dipole antenna, the half power beam width $\text{(HPBW)}$ in the $\text{E}$-plane is

The electric field of an electomagnetic wave propagating in the positive $z$-direction is given by $$\left.\text{E}=\hat{a_x} \sin (\omega t-\beta z\right)+\hat{a_y} \sin \left(\omega t-\beta z+\frac{\pi}{2}\right)$$ The wave is

A transmission line is feeding $1 \mathrm{Watt}$ of power to a horn antenna having a gain of $10 \mathrm{~dB}$. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is

A medium of relative permittivity $\varepsilon_{r 2}=2$ forms an interface with free-space. A point source of electronagnetic energy is located in the medium at a depth of $1$ meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the …

A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \hat{a}_{y}+5 \hat{a}_{z}$ is incident normally on the interface from region-I. The electric field $E_{2}$ in region-II at the interface is

When a plane wave travelling in free-space is incident normally on a medium having $\varepsilon_{t}=4.0$, then fraction of power transmitted into the medium is given by

A rectangular waveguide having $\mathrm{TE}_{10}$ mode as dominant mode is having a cutoff frequency of $18-\mathrm{GHz}$ for the $\mathrm{TE}_{w,}$ mode. The inner broad-wall dimension of the rectangular waveguide is