ECE 450
Homework 1
Due: Tue, Sept 1, 2009, 5 PM
1. In the four gures below the planar media interface coincides with the plane z = 0.
Match the descriptions below to the gures. Justify your answer. a) There is a surface electric charge density of (1/18 )
ECE 450
Homework 14
Due: Tue, Dec 8, 2009, 5 PM
1. Even though dielectric slab waveguides are used for the transmission of optical frequencies, their application to the transmission of microwave and millimeter-wave frequencies has been exploited also. As
ECE 450
Homework 13
Due: Tue, Dec 1, 2009, 5 PM
1. Rectangular waveguides are being used to construct the feed network of antenna arrays. The picture on the left below depicts such a feed network for a Ka-band multi-beam antenna (courtesy Alenia Spazio).
ECE 450
Homework 12
Due: Tue, Nov 17, 2009, 5 PM
1. Rectangular waveguides are commonly used in X-band microwave circuitry. X-band is dened to be the 8.2 GHz f 12.4 GHz portion of the electromagnetic frequency spectrum. The standard X-band rectangular-wav
ECE 450
Homework 11
Due: Tue, Nov 10, 2009, 5 PM
1. The electric eld phasor of TEm mode in air-lled parallel-plate waveguides is given as E = 2j y Eo ejkz z sin(kx x) for 0 < x < a subject to constraints 2 m 2 2 and kz = k2 kx = kx . a c2 The guide consis
ECE 450: Spring 2009
Homework Set 9 Solutions Due on Friday, Apr 10, 2009
f=
1 2
m n l + + = 2GHz a b c
2
2
2
( 4 m ) + ( 5n ) + ( 2c )
2 2
2
The lowest 5 frequencies are: TE101 = 4.47GHz TE011 = 5.39 TE102 = 5.66GHz TE012 or TM110= 6.4GHz TE111 or TM11
ECE 450
Homework 10
Due: Tue, Nov 3, 2009, 5 PM
1. The propagation of ocean waves on the surface of deep water (depth much longer than a wavelength = 2k ) is governed by the dispersion relation = gk
where g represents gravitational acceleration and , k ar
ECE 450
Homework 9
Due: Tue, Oct 27, 2009, 5 PM
1. A uniform, time-harmonic plane wave with TM polarized electric eld phasor
+ x z j 2 x z V 2 Ei = e m 2
propagating in glass is impinging obliquely upon a planar glass-air interface at x = 0 plane. The mag
ECE 450
Homework 8
Due: Tue, Oct 20, 2009, 5 PM
1. A uniform, time-harmonic, circularly polarized plane wave propagating in air is impinging obliquely upon a planar air-dielectric interface. The wavelength of the wave in air is 1 m. The magnetic permeabil
ECE 450
Homework 7
Due: Tue, Oct 13, 2009, 5 PM
1. A uniform, time-harmonic plane wave propagating in air is impinging upon a planar air-dielectric interface. The angle of incidence with respect to the normal to the interface is 45o . The frequency of the
ECE 450
Homework 5
Due: Tue, Sept 29, 2009, 5 PM
1. Consider an array of four identical z -polarized short dipoles with input currents Io = 10 A at locations (x, y, z ) = (d, 0, 0) and (0, d, 0) and Io = 1180 A at locations (x, y, z ) = (d, 0, 0) and (0,
ECE 450
Homework 4
Due: Tue, Sept 22, 2009, 5 PM
1. In class notes it is given that the eective length of a z -directed half-wave dipole antenna is ( ) = a) Use lHospitals rule to determine (0). b) Plot ( ) as a function of from 0 to 180 degrees. c) Plot
ECE 450
Homework 3
Due: Tue, Sept 15, 2009, 5 PM
1. Consider a circular wire loop of radius a carrying a time-harmonic current I = Io cos ( t) and radiating in a homogeneous medium of electric permittivity and magnetic permeability . The loop is placed on
ECE 450
Homework 2
Due: Tue, Sept 8, 2009, 5 PM
1. Consider the time-harmonic charge distribution (r, t) = q [ (r hx) (r + hx) + (r hy ) (r + hy )] cos( t) in free space. a) Write down the phasors for the charge density (r, t) and its time derivative b) C
ECE 450
Homework 6
Due: Tue, Oct 6, 2009, 5 PM
1. A linear antenna array of length of 4.65 m is radiating in air. The operating frequency is 1 GHz. Assume that all antenna elements are identical and that their driving currents are of the same magnitude an