GATE EC Electromagnetics questions

For a parallel plate transmission line, let $v$ be the speed of propagation and $Z$ be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results in

The input impedance of a $\dfrac{\lambda}{8}$ section of a lossless transmission line of characteristic impedance $50\: \Omega$ is found to be real when the other end is terminated by a load $Z_{L} (=R + jX)\Omega.$ If $X$ is $30\:\Omega ,$ the value of $R ( \text{in} \:\Omega )$ is _______.

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 …

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 ________.

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?

If the electric field of a plane wave is $$\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega t-kz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$$ the polarization state of the plane wave is

In the transmission line shown, the impedance $Z_{\text{in}}$ (in ohms) between node A and the ground is _________.

For a rectangular waveguide of internal dimension $a\times b \: (a> b)$, the cut-off frequency for the $TE_{11}$ mode is the arithmetic mean of the cut-off frequencies for $TE_{10}$ mode and $TE_{20}$ mode. If $a= \sqrt{5}$ cm, the value of $b$ (in cm) is ______.

Let $x(t)= \cos(10\pi t)+\cos(30\pi t)$ be sampled at $20 Hz$ and reconstructed using an ideal low-pass filter with cut-off frequency of $20 Hz$. The frequency/frequencies present in the reconstructed signal is/are

The phase response of a passband waveform at the receiver is given by $$\varphi (f)= -2\pi \alpha (f-f_{c})-2\pi \beta f_{c}$$ where $f_{c}$ is the centre frequency, and $\alpha$ and $\beta$ are positive constants. The actual signal propagation delay from the transmitter to receiver is

Consider an air filled rectangular waveguide with a cross-section of $5 \: cm \times 3 \: cm$. For this waveguide, the cut-off frequency (in MHz) of $TE_{21}$ mode is __________.

In the following figure, the transmitter $Tx$ sends a wideband modulated $RF$ signal via a coaxial cable to the receiver $Rx$. The output impedance $Z_{T}$ of $Tx$, the characteristic impedance $Z_{0}$ of the cable and the input impedance $Z_{R}$ of $Rx$ are all real. Which one of the following statements is TRUE about the distortion of the …

In the circuit shown in the figure, the angular frequency $\omega$ (in rad/s), at which the Norton equivalent impedance as seen from terminals $b-b'$ is purely resistive, is ________.

Assume that a plane wave in air with an electric field $\overrightarrow{E}= 10\cos ( \omega t-3x-\sqrt{3}z )\hat{a_{y}}V/m$ is incident on a non-magnetic dielectric slab of relative permittivity $3$ which covers the region $z > 0$. The angle of transmission in the dielectric slab is _________ degrees.

At $T=300 \:K$, the band gap and the intrinsic carrier concentration of GaAs are $1.42$ eV and $10^6 \: cm^{-3}$, respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength $(\lambda_C)$ ranges of incident radiation, is most suitable? (Given that: Plank’s constant is $6.62 \times 10^{-34} \: J-s$, velocity of light …

If the emitter resistance in a common-emitter voltage amplifier is not bypassed, it will

For an antenna radiating in free space, the electric field at a distance of $1$ km is found to be $12 \: mV/m$. Given that intrinsic impedance of the free space is $120 \pi \: \Omega$, the magnitude of average power density due to this antenna at a distance of $2$ km from the antenna (in $nW/m^2$) is _________.

Match column A with column B. $\begin{array}{ll} \textbf{Column A} & \textbf{Column B} \\ \text{1. Point electromagnetic source} & \text{P. Highly directional} \\ \text{2. Dish antenna} & \text{Q. End fire} \\ \text{3. Yagi-Uda antenna} & \text{R. Isotrophic} \end{array}$

For the two-port network shown in the figure, the impedance (Z) matrix (in $\Omega$) is