GATE EC 2023 Question Paper (05-Feb-2023) (Shift 2)

The S-parameters of a two port network is given as

$[\mathrm{S}]=\left[\begin{array}{cc}{S}_{11}& S_{12}\\ S_{21}& S_{22}\end{array}\right]$

with reference to 𝑍₀. Two lossless transmission line sections of electrical lengths 𝜃₁ = 𝛽𝑙₁ and 𝜃₂ = 𝛽𝑙₂ are added to the input and output ports for measurement purposes, respectively. The S-parameters [𝑆′] of the resultant two port network is

The standing wave ratio on a 50 Ω lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. 𝑍${}_{\text{L}}$ can be replaced by an equivalent length 𝑙${}_{\text{m}}$ and terminating resistance 𝑅${}_{\text{m}}$ of the same line. The value of 𝑅${}_{\text{m}}$ and 𝑙${}_{\text{m}}$, respectively, are

The electric field of a plane electromagnetic wave is

𝑬 = 𝒂${}_{\text{x}}$ 𝐶${}_{1\text{x}}$ cos(𝜔𝑡 − 𝛽𝑧) + 𝒂${}_{\text{y}}$ 𝐶${}_{1\text{y}}$ cos(𝜔𝑡 − 𝛽𝑧 + 𝜃) V/m.

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

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

The value of the integral${\iint }_{\mathrm{R}}\mathrm{xydxdy}$ over the region R, given in the figure, is _______ (rounded off to the nearest integer).