# GATE Questions & Answers of Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart

## What is the Weightage of Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart in GATE Exam?

Total 24 Questions have been asked from Transmission lines: equations, characteristic impedance, impedance matching, impedance transformation, S-parameters, Smith chart topic of Electromagnetics subject in previous GATE papers. Average marks 1.67.

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

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___________

The propagation constant of a lossy transmission line is (2+$j$5) m−1 and its characteristic impedance is (50+$j$0) Ω at $\omega ={10}^{6}$ rad s−1. The values of the line constants L,C,R,G are, respectively,

A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness t and relative permittivity ${\epsilon }_{r}>1$. The inductance per unit length and the characteristic impedance of this line are L and Z0, respectively.

Which one of the following inequalities is always satisfied?

A microwave circuit consisting of lossless transmission lines T1 and T2 is shown in the figure. The plot shows the magnitude of the input reflection coefficient $\mathrm{\Gamma }$ as a function of frequency f. The phase velocity of the signal in the transmission lines is 2×108 m/s.

The length L (in meters) of T2 is ________

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon (${\epsilon }_{r}$ = 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 $\bigtriangleup$z ?

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

A 200 m long transmission line having parameters shown in the figure is terminated into a load RL. The line is connected to a 400 V source having source resistance RS Through a switch, which is closed at t=0. The transient response of the circuit at the input of the line (z=0) is also drawn in the figure. The value of RL (in Ω) is_______.

A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172 pF/m. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length (in pF/m) is ________.

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 $\frac{\lambda }{8}$ section of a lossless transmission line of characteristic impedance 50Ω is found to be real when the other end is terminated by a load ${Z}_{L}\left(=R+jx\right)\Omega$ If X is 30Ω, the value of R (in Ω) is_________

To maximize 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 Ω) of the $\lambda /4$ transformer is _________.

In the transmission line shown, the impedance Zin (in ohms) between node A and the ground 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 ZT of Tx, the characteristic impedance Z0 of the cable and the input impedance ZR of Rx are all real.

Which one of the following statements is TRUE about the distortion of the received signal due to impedance mismatch?

A transmission 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

A transmission line of characteristic impedance 50Ω is terminated by a 50 Ω load. When excited by a sinusoidal voltage source at 10GHz, the phase difference between two points spaced 2mm apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is

A transmission line of characteristic impedance 50Ω is terminated in a load impedance ZL. The VSWR of the line is measured as 5 and the first of the voltage maxima in the line is observed at a distance of $\lambda }{4}$ from the load. The value of ZL is

A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1 Ω /m. if the line is distortion less, the attenuation constant (in Np/m) is

In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ration(VSWR) on the 60$\Omega$ line is

A transmission line terminates in two branches, each of length λ/4, as shown. The branches are terminated by 50Ω loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Zi as seen by the source

One of a loss-less transmission line having the characteristic impedance of 75Ω and length of 1cm is short-circuited. At 3GHz, the input impedance at the other end of the transmission line is

In the design of a single mode step index optical fiber close to upper cut-off, the single mode operations is NOT preserved if

The parallel branches of a 2-wire transmission line are terminated in 100Ω and 200Ω resistors as shown in the figure. The characteristic impedance of the line is Z0 = 50Ω and each section has a length of $\lambda }{4}$. The voltage reflection coefficient $\Gamma$ at the input is