DELHI TECHNOLOGICAL UNIVERSITY
Electronics and Communication Engineering Department
B.Tech-4th semester, AY 2020-21
2021-22
Electromagnetics EE-262, ASSIGNMENT-32
Transmission Lines
1. A transmission line operating at 500 MHz has Zo = 80 , a = 0.04 Np/m,
line parameters R, L, G, and C.
=1.5 rad/m. Find the
2. A telephone line has R = 30 /km, L = 100 mH/km, G = 0, and C = 20 µF/km. At f= 1 kHz, obtain:
(a) The characteristic impedance of the line
(b) The propagation constant
(c) The phase velocity
3. A lossless transmission line is 80 cm long and operates at a frequency of 600 MHz. The line
parameters are L=0.25 µH/m and C= 100 pF/m. Find the characteristic impedance, the phase
constant, the velocity of the line and the input impedance for ZL = 100 .
4. At an operating radian frequency of 500 Mrad/s, typical circuit values for a certain transmission
line are: R= 0.2 /m, L= 0.25 µH/m, C= 100 pF/m and G=10 µS/m. Find: , , , vp, Zo.
5. A 40-m-long transmission line shown in figure below has Vg = 15 0° Vrms, Zo =30 + j60
= 5 -48° Vrms. If the line is matched to the load, calculate:
(a) The input impedance Zin
(b) The sending-end current Iin and voltage Vin
(c) The propagation constant
6. A 70Zin.
lossless line has s = 1.6 and
, and VL
long, obtain (a) T, (b) ZL and (c)
7. A certain microstrip line has fused quartz ( r = 3.8) as a substrate. If the ratio of line width
to substrate thickness is w/h = 0.8, determine
(a) The effective relative permittivity of the substrate
(b) The characteristic impedance of the line
(c) The wavelength of the line at 10 GHz
8. Calculate the attenuation due to ohmic losses at 20 GHz for a microstrip line constructed
of copper conductor having a width of 2.5 mm on an alumina substrate. Take the characteristic
impedance of the line as 50 .
Wave guides
9.
A rectangular waveguide with dimensions a = 2.5 cm, b = 1 cm is filled with a medium
characterized by = 0, = 4 o, µr = 1. Calculate the phase constant, phase velocity and wave
impedance for TE10 and T11 modes at the operating frequency of 15 GHz.
10. In a rectangular waveguide for which a = 1.5 cm, b = 0.8 cm, = 0, µ = µo and = 4
Hx = 2 sin ( x/a) cos (3 y/b) sin ( x1011t - z) A/m
o.
Assuming TE13 mode, determine;
(a) The mode of operation
(b) The cutoff frequency
(c) The phase constant
(d) The propagation constant
(e) The intrinsic wave impedance
11. A standard air-filled rectangular waveguide with dimensions a = 8.636 cm, b = 4.318 cm is fed
by a 4-GHz carrier from a coaxial cable. Determine if a TE11 mode will be propagated. If so,
calculate the phase velocity and the group velocity.
12. An air-filled rectangular waveguide of dimensions a = 2 cm, b = 4 cm transports energy in the
dominant mode at a rate of 2 mW. If the frequency of operation is 10 GHz, determine the peak
value of the magnetic field in the waveguide.
13. A brass waveguide ( c = 1.1 x 107 mhos/m) of dimensions a = 4.2 cm, b=1.5 cm is filled with
Teflon ( r = 2.6, = 10-15 mhos/m). The operating frequency is 9 GHz. For the TE10 mode:
(a) Calculate d and c.
(b) What is the loss in decibels in the guide if it is 40 cm long?
14. An air-filled resonant cavity with dimensions a = 5 cm, b = 4 cm, and c = 10 cm is made of
copper ( c = 5.8 x 107 mhos/m) is filled with a lossless material (µr= 1, r = 3).
Find
(a) The resonant frequency
(b) The quality factor for TE101 mode
15. An air-filled rectangular waveguide has dimensions a= 2 cm and b= 1 cm. Determine the range of
frequencies over which the guide will operate single mode (TE10).