HW1 - with I being a constant and α some real number(note...

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ECE 613 – Antennas and Propagation for Wireless Systems Fall 2010 Homework Set # 1 Problems: (1) In the far-zone, it can be shown that the nabla operator can always be approximated as . Using this relation, obtain the three components of the far-zone electric fieldand three magnetic field in terms of three components of the far-zone magnetic vector potential : A r , A θ , and A φ . (2) As we saw in class, the vector potential of an arbitrary linear wire antenna in the far-zone is given by . By noting that a Fourier transform of an arbitrary function f(t) is given by , (a) write the far-zone magnetic vector potential in terms of a Fourier transform of the current and (b) identify which variables play the role analogous to t and ϖ , respectively. (3) Consider a one-wavelength wire antenna where the current distribution is given by

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Unformatted text preview: with I being a constant and α some real number (note that this is not the usual current distribution). Find the far-zone electric and magnetic fields radiated by this antenna (in spherical coordinates). You may use the results of problem 1. (4) Find the far-zone electric field of a linear wire antenna l =30 cm long at two frequencies: f = 1 GHz and f = 1.5GHz. Plot the antenna power pattern at both frequencies in rectangular (not polar) form. By inspecting these plots, determine the sidelobe levels in negative dB and the half-power bandwidth (HPBW) in degrees. Indicate both quantities in the plots (Note: assume the usual sinusoidal current distribution given in class for a finite length wire antenna)....
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HW1 - with I being a constant and α some real number(note...

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