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The outputs from two collinear, closely spaced, half-wave dipoles are added together as indicated by a summing device in the figure below. The transmission lines from the antennas to the summer are of equal length. Write the pattern F_{a}(θ) of this antenna system using array techniques.
(b) Now consider a center-fed, full-wave dipole that is along the z-axis. Write its pattern expression F_{b}(θ).
(c) Now draw the current distributions Ia(z) and Ib(z) for both antennas. From these current distributions, can you make a statement about the patterns from the two antennas? Return to the pattern expressions and prove your statement mathematically.
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