EC2008 Electromagnetic Waves JAN—MAY 2023
Tutorial 1
Jan 12, 2023
1. A 1m long USB 3.0 cable is connected between a laptop and a mobile phone. The
operating frequency of this cable is 2.5 GHz. The signal travels within this cable
at a speed of 2×108 m/s.
(a) Find the signal transit time in the cable
(b) Do we need to consider distributed analysis in this scenario? Justify.
2. A coaxial line operates at 10 kHz. It has the following parameters: L = 0.5 µH/m,
C = 20 pF/m, G = 0.5 S/m and R = 20 Ω/m
(a) Calculate attenuation, phase, propagation constants, wavelength and characteristic impedance.
(b) How long must be the line so that the receiver receives only 1% of the wave?
(c) If the wave travels a distance of 10 m down the line , what phase shift does
it accumulate?
3. A transmission line has Z0 = 65 + j5 Ω and γ = 1+ j 10 m−1 .
(a)Is the line lossless? Find the primary constants (R,L,G,C) of the line at 900
MHz.
q
q
√
(b) Show that for a lowloss line α = R2 CL + G2 CL and β = ω LC
(c) For the primary constants calculated in part (a) over what frequency range
can the line be treated as low loss line? (Assume α < 0.01β for low loss)
4. A co-axial cable of characteristic impedance 50 Ω is connected to an indoor television
set. The signal travels within the cable at a speed of 32 c m/s . Assuming the line
to be lossless, calculate its inductance and capacitance per unit length. (c is the
velocity of light, 3×108 m/s)
5. The condition for signal transmission to be distortionless in a transmission line is
given by RC = LG.
(a) Show that
the attenuation constant
√ in such a distortionless transmission line, √
is equal to RG and and the phase constant equal to ω LC.
(b) Is a lossless transmission line distortionless? Why or why not?
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