GATE EC Transmission Lines questions

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

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 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

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 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

A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. The radiation resistance of the antenna in ohms is

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure represent

Characteristic impedance of a transmission line is $50 \Omega$. Input impedance of the open-circuited line is $Z_{a^{-}}=100+j 150 \Omega$. When the transmission line is short- circuited, then value of the input impedance will be

Statement of Linked Answer Questions 84a and 84b: Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{~W}$ and a resistive load is shown in the figure. The value of the load resistance is

The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode is

Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be