GATE EC Transmission Lines questions

Consider the Friis' transmission equation $P_{R}=\left(P_{T} G_{T} G_{R} \lambda^{2}\right) /(4 \pi D)^{2}$, where $P_{R}$ and $P_{T}$ are the received and the transmitted powers, respectively. $G_{T}$ and $G_{R}$ are the gain of transmitting and receiving antennas, respectively, $D$ is the distance between the transmitting and receiving …

The cutoff frequency ( $\text{in GHz}$ ) for the dominant $\mathrm{TE}_{10}$ mode of an air-filled rectangular waveguide of inner dimension $0.28$ inch $\times 0.14$ inch is $\_\_\_\_$ . (rounded off to two decimal places).

A complex load (in $\Omega$ ) is represented as $\Gamma_{L}=0.5 \angle 30^{\circ}$ on the Smith chart. A co-axial cable with a characteristic impedance of $50 ~\Omega$ is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same $\Gamma$ circle on the Smith chart. Which option is the nearest …

A $50 \Omega$ lossless transmission line is terminated with a load $\mathrm{Z}_{\mathrm{L}}$ of $(50-\mathrm{j} 75) \Omega$. If the average incident power on the line is $10 \: \mathrm{mW}$, then the average power delivered to the load (in $\mathrm{mW}$, rounded off to one decimal place) is $\_\_\_\_\_\_\_$.

​​​​Consider a lossless transmission line terminated with a short circuit as shown in the figure below. As one moves towards the generator from the load, the normalized impedances $z_{\text{inA }}, z_{i n B}, z_{i n C}$, and $z_{i n D}$ (indicated in the figure) are $\_\_\_\_\_\_.$

A lossless transmission line with characteristic impedance $\mathrm{Z}_{0}=50 \Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma|=0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$ ) is $\_\_\_\_\_\_.$

The $S$-parameters of a two-port network is given as $$[S]=\left[\begin{array}{ll} S_{11} & S_{12} \\ S_{21} & S_{22} \end{array}\right]$$ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1=\beta l_1$ and $\theta_2=\beta l_2$ are added to the input and output ports for measurement purposes, …

The standing wave ratio on a $50 \; \Omega$ lossless transmission line terminated in an unknown load impedance is found to be $2.0$. The distance between successive voltage minima is $30 \mathrm{~cm}$ and the first minimum is located at $10 \mathrm{~cm}$ from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance …

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4} \; \text{cm},$ with air as the dielectric. Assume the speed of light in air to be $3 \times 10^{8} \; \text{m/s}.$ The frequency/frequencies of $\text{TM}$ waves which can propagate in this waveguide is/are _________.

The refractive indices of the core and cladding of an optical fiber are $1.50$ and $1.48$, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is _____ degree.

The impedance matching network shown n the figure is to match a lossless line having characteristic impedance $Z_{0}= 50 \:\Omega$ with a load impedance $Z_{L}$. A quarter-wave line having a characteristic impedance $Z_1=75\:\Omega$ is connected to $Z_{L}$. Two stubs having characteristic impedance of $75\:\Omega$ each are connected to this …

A standard air-filled rectangular waveguide with dimensions $\text{a=8 cm, b=4 cm}$, operates at $\text{3.4 GHz}$. For the dominant mode of wave propagation, the phase velocity of the signal in $v_{p}$. The value (rounded off to two decimal places) of $v_{p}/c$, where $c$ denotes the velocity of light, is ________________________

An antenna with a directive gain of $6\text{ dB}$ is radiating a total power of $\text{16 kW}$. The amplitude of the electric field in free space at a distance of $\text{8 km}$ from the antenna in the direction of $\text{6 dB}$ gain (rounded off to three decimal places) is ____________________ $\text{V/m}$.

The impedances $Z=jX,$ for all $X$ in the range $\left ( -\infty ,\infty \right )$, map to the Smith chart as

A transmission line of length $3\lambda /4$ and having a characteristic impedance of $50$ $\Omega$ is terminated with a load of $400 \Omega$. The impedance (rounded off to two decimal places) seen at the input end of the transmission line is __________ $\Omega$.

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, …

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 __________.

Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change in the radiation resistance, rounded off to two decimal places, is ________ $\%.$

The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is $$k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{\circ}^{2}}$$ where the speed of light $c= 2 \times 10^{8}\: m/s$ and $\omega_{\circ}$ is a constant . If the group velocity is $2 \times 10^{8}\: m/s$, then the phase velocity is