homework7

Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 7 Due Thursday, May 26 th in class 1. ( Retarded Vector Potential ) Problem from Engineering Electromagnetics by Hayt and Buck. In a region where µ R = ε R = 1 and σ = 0, the retarded potentials are given by V = x ( z-ct ) V and A = x ( z/c-t ) a z Wb/m, where c = 1/sqrt( 0 0 ). (a). Show that t V = µε A (b). Find B , H , E and D . (c). Show that these results satisfy Maxwell’s equations if J and ρ v are zero. 2. ( Dipole Antenna ) Problem from Engineering Electromagnetics by Hayt and Buck. A dipole antenna in free space has a linear current distribution. If the length d is 0.02 λ , what value of I 0 is required to: (a). provide a radiation field amplitude of 100mV/m at a distance of 1mi, at θ = 90 0 ; (b). radiate a total power of 1 W? 3. ( Antenna ) A square loop antenna, in which a time-harmonic current Ie j ω t is circling, is located in the x-z plane as shown in Figure below. Consider a point P (0,0,z) in the far field of the loop antenna.
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Unformatted text preview: Calculate the magnetic field H at P. Show that if d << , the strength of the H field in the far field is proportional to d 2 . 4. ( Antenna Array ) Consider an array of N dipole antennas (N being an odd number) spaced by a distance d from each other along the z-axis. r z n=0 N-1 2 n= N-1 n= - 2 d x Each dipole has length L, with L< so you can treat the dipole as being infinitesimal. Each dipole is fed with a current given by jn t j o n e e I I = n= 2 1 N ,..,0,. . 2 1 N and is a constant. Find the radiated field produced by the antenna array. Sketch the radiation pattern as a function of . 5. ( FEMLAB ) Use FEMLAB 2D In-Plane Waves model to simulate the radiation from a dipole antenna. Assume the working frequency is 1GHz ( = 0.3 meter). Plot the E field magnitude of the radiated wave for antenna length h = /2, 3 /2, 2 , 5 /2....
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This homework help was uploaded on 02/04/2008 for the course EE 151 taught by Professor Psaltis during the Spring '05 term at Caltech.

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homework7 - Calculate the magnetic field H at P. Show that...

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