August 2012
Intermediate to advanced
360 pages
10h 14m
English
Content preview from RF and Microwave Engineering: Fundamentals of Wireless Communications
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2.7 Problems
2.1. Consider a two wire transmission line, where two parallel thin wires have a distance of d = 1 cm. Each conductor carries a steady current of I0 = 10 mA. The currents flow in opposite directions. The transmission line is located in the plane z = 0 and has an infinite extent in ±y-direction.
a. Draw the distribution of the magnetic field strength 
in a cross-sectional area (xz-plane).
in a cross-sectional area (xz-plane).
b. Calculate the magnitude of the magnetic field strength H along the x-axis.
2.2. An air-filled coaxial transmission line has a solid cylindrical inner conductor of R1 = 2 mm, an outer conductor with an inner radius of R2 = 4 mm and an outer radius R3 = 5 mm. The inner and outer conductor carry steady currents I in opposite directions.
a. Determine the magnetic field strength by applying Faraday's law in integral form.
b. Calculate the inductance per unit length L′DC = L/Δ
for DC conditions (f = 0 Hz).
for DC conditions (f = 0 Hz).
c. Calculate the inductance per unit length L′RF = L/Δ for RF conditions. (Assume that the current flows in a thin layer at the surface of the conductors (skin effect).)
for RF conditions. (Assume that the current flows in a thin layer at the surface of the conductors (skin effect).)
2.3. A plane wave propagates through a dielectric (εr ≠ 1, μr = 1). The time-variant electric and magnetic field ...
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