GATE EC Transmission Lines questions

A radar operating at $5\:GHz$ uses a common antenna for transmission and reception. The antenna has a gain of $150$ and is aligned for maximum directional radiation and reception to a target $1\:km$ away having radar cross-section of $3\:m^2$. If it transmits $100\:kW$, then the received power (in $\mu W)$ is _______

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $$H_z (x,y,z,t) = 0.1 \: cos(25 \pi x) \: \: \cos(30.3 \: \pi y) \: \: \cos(12 \pi \times 10^9 t- \beta z) \: \: (A/m)$$ The cross-sectional dimensions of the waveguide are give as …

An air-filled rectangular waveguide of internal dimensions $a\: cm \times b\: cm\:(a>b)$ has a cutoff frequency of $6\:GHz$ for the dominant $TE_{10}$ mode. For the same waveguide, if the cutoff frequency of the $TM_{11}$mode is $15\: GHz,$ the cutoff frequency of the $TE_{01}$ mode in $GHz$ is __________.

The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

Consider the $3\:m$ long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of $120\pi\: \Omega,$ is terminated by a short circuit, and is excited with a frequency of $37.5\: MHz.$ What is the nature of the input impedance $(Z_{in})?$

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_{1}$ of the first section to the input impedance $Z_{2}$ of the second section is

A good current buffer has

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 …

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 ___________.

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

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 ________.

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