GATE EC 2026 Set 1 Q23 — Transmission Lines

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 …

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, …