Page 568 - Engineering Electromagnetics, 8th Edition

550 ENGINEERING ELECTROMAGNETICS

lobe intensity. Express your result as the sidelobe level in decibels, given by
S s [dB] = 10 log (S r,main /S r,sidelobe ). Again, use Figure 14.8 as a guide.
10
14.16 Fora dipole antenna of overall length, 2 = 1.5λ,(a) evaluate the locations
in θ at which the zeros and maxima in the E-plane pattern occur;
(b) determine the sidelobe level, as per the definition in Problem 14.14;
(c) determine the maximum directivity.
14.17 Consider a lossless half-wave dipole in free space, with radiation resistance,
R rad = 73 ohms, and maximum directivity D max = 1.64. If the antenna
carries a 1-A current amplitude, (a)how much total power (in watts) is
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radiated? (b)How much power is intercepted by a 1-m aperture situated at
distance r = 1kmaway? The aperture is on the equatorial plane and
squarely faces the antenna. Assume uniform power density over the
aperture.
14.18 Repeat Problem 14.17, but with a full-wave antenna (2 = λ). Numerical
integrals may be necessary.
14.19 Design a two-element dipole array that will radiate equal intensities in the
φ = 0,π/2,π, and 3π/2 directions in the H plane. Specify the smallest
relative current phasing, ξ, and the smallest element spacing, d.
14.20 Atwo-element dipole array is configured to provide zero radiation in the
broadside (φ =±90 ) and endfire (φ = 0, 180 ) directions, but with
◦
◦
maxima occurring at angles in between. Consider such a set-up with ψ = π
at φ = 0 and ψ =−3π at φ = π, with both values determined in the
H-plane. a) Verify that these values give zero broadside and endfire
radiation. b) Determine the required relative current phase, ξ.b) Determine
the required element spacing, d.c) Determine the values of φ at which
maxima in the radiation pattern occur.
14.21 In the two-element endfire array of Example 14.4, consider the effect of
varying the operating frequency, f ,away from the original design
frequency, f 0 , while maintaining the original current phasing, ξ =−π/2.
Determine the values of φ at which the maxima occur when the frequency is
changed to (a) f = 1.5 f 0 ;(b) f = 2 f 0 .
14.22 Revisit Problem 14.21, but with the current phase allowed to vary with
frequency (this will automatically occur if the phase difference is
established by a simple time delay between the feed currents). Now, the
current phase difference will be ξ = ξ f/f 0 , where f 0 is the original

(design) frequency. Under this condition, radiation will maximize in the
φ = 0 direction regardless of frequency (show this). Backward radiation
(along φ = π) will develop, however, as the frequency is tuned away from
f 0 . Derive an expression for the front-to-back ratio, defined as the ratio of
the radiation intensities at φ = 0 and φ = π,expressed in decibels. Express
this result as a function of the frequency ratio f/f 0 .Evaluate the
front-to-back ratio for (a) f = 1.5 f 0 ;(b) f = 2 f 0 and; (c) f = 0.75 f 0 .