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Application: λ/2 dipole. A half-wavelength antenna is made of copper wire with conductivity σ = 5.7 x 107 S/m. The antenna is 3-mm thick and 1.5-m long.
(a) Calculate the impedance of the antenna and its efficiency when radiating in free space.
(b) In an attempt to reduce the impedance and increase efficiency, the antenna is made of a copper tube, 12-mm in diameter. What is the efficiency of the antenna? Assume current flows entirely within one skin depth, on the surface of the tube.
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Check your results by first expressing the given transform in partial-fractions form and then inverting using the standard results:
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