GATE EC Transmission Lines questions

A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to two decimal places , is _______.

A good transimpedance amplifier has

The points $\text{P, Q, and R}$ shown on the Smith chart (normalized impedance chart) in the following figure represent:

A lossy transmission line has resistance per unit length $R=0.05\:\Omega/m.$ The line is distortionless and has characteristic impedance of $50\:\Omega.$ The attenuation constant (in $\text{Np/m}$, correct to three decimal places) of the line is ________.

The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated at a frequency which is $25\%$ higher than the cutoff frequency of the dominant mode, the guide …

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is $V(l)= e^{-\gamma l +j\omega t }$ Volts, where $l$ is the distance along the length of the cable in meters, $\gamma=(0.1+j40)m^{-1}$ is the complex propagation constant, and $\omega=2 \pi \times 10^{9}$ rad/s is the angular frequency. The …

Consider a wireless communication link between a transmitter and a receiver located in free space, with finite and strictly positive capacity. If the effective areas of the transmitter and the receiver antennas, and the distance between them are all doubled, and everything else remains unchanged , the maximum capacity of the wireless link

An optical fiber is kept along the $\hat{z}$ direction. The refractive indices for the electric fields along $\hat{x}$ and $\hat{y}$ directions in the fiber are $n_{x}=1.5000$ and $n_{y}=1.5001$, respectively ($n_{x} \neq n_{y}$ due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber …

A half wavelength dipole is kept in the $x-y$ plane and oriented along $45^{\circ}$ from the $x$-axis. Determine the direction of null in the radiation pattern for $0\leq \phi \leq \pi$. Here the angle $\theta (0\leq \theta \leq \pi )$ is measured from the $z$-axis and the angle$\phi (0\leq \theta \leq 2\pi )$ is measured from the $x$-axis in …

A two-wire transmission line terminates in a television set. The VSWR measured on the line is $5.8$. The percentage of power that is reflected from the television set is _________

Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02$ cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $TE_{10}$ mode with the operating frequency at least $25 \%$ above the cutoff frequency of the $TE_{10}$ mode but not higher than $95 \%$ of the next higher …

The propagation constant of a lossy transmission line is $(2+j5) m^{-1}$ and its characteristic impedance is $(50+j0) \Omega$ at $\omega = 10^6 rad \: s^{-1}$. The values of the line constants L,C,R,G are,respectively,

An antenna pointing in a certain direction has a noise temperature of $50 \: K$. The ambient temperature is $290 \: K$. The antenna is connected to a pre-amplifier that has a noise figure of $2$ dB and an available gain of $40$ dB over an effective bandwidth of $12$ MHz. The effective input noise temperature $T_e$ for the amplifier and the noise …

Two lossless X-band horn antennas are separated by a distance of $200 \lambda$. The amplitude reflection coefficients at the terminals of the transmitting and receiving antennas are $0.15$ and $0.18$,respectively. The maximum directives of the transmitting and receiving antennas (over the isotropic antenna) are $18$ dB and $22$ dB, respectively. …

The far-zone power density radiated by a helical antenna is approximated as: $${\overrightarrow W_{rad}= \overrightarrow W_{average} \approx \hat {a_r}C_0\frac{1}{r^2}\cos^4\theta}$$ The radiated power density is symmetrical with respect to $\phi$ and exists only in the upper hemisphere: $0\leq\theta\leq\frac{\pi}{2}; \: 0\leq\phi\leq 2\pi$; $C_0$ is a …

Light from free space is incident at an angle $\theta _{i}$ to the normal of the facet of a step-index large core optical fibre. The core and cladding refractive indices are $n _{1}=1.5$ and $n _{2}=1.4$, respectively. The maximum value of $\theta _{i}$ (in degrees) for which the incident light will be guided in the core of the fibre is _________

A lossless microstrip transmission line consists of a trace of width $w$. It is drawn over a pratically infinite ground plane and is separated by a dielectric slab of thickness $t$ and relative permittivity $\varepsilon _{r}> 1.$ The inductance per unit length and the characteristic impedance of this line are $L$ and $Z_{0}$, respectively. Which …

A microwave circuit consisting of lossless transmission lines $T_{1}$ and $T_{2}$ is shown in the figure. The plot shows the magnitude of the input reflection coefficient $\Gamma$ as a function of frequency $f$. The phase velocity of the signal in the transmission lines is $2\times 10^{8}$ $m/s$. The length $L$ (in meters) of $T_{2}$ is …

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. At $10 \:GHz$ operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. The increasing order of the cut-off frequencies for different modes is