Page 569 - Engineering Electromagnetics, 8th Edition

CHAPTER 14 ELECTROMAGNETIC RADIATION AND ANTENNAS 551

14.23 A turnstile antenna consists of two crossed dipole antennas, positioned in
this case in the xy plane. The dipoles are identical, lie along the x and y
axes, and are both fed at the origin. Assume that equal currents are supplied
to each antenna and that a zero phase reference is applied to the x-directed
antenna. Determine the relative phase, ξ,ofthe y-directed antenna so that
the net radiated electric field as measured on the positive z axis is (a) left
circularly polarized; (b) linearly polarized along the 45 axis between x
◦
and y.
14.24 Consider a linear endfire array, designed for maximum radiation intensity at
φ = 0, using ξ and d values as suggested in Example 14.5. Determine an
expression for the front-to-back ratio (defined in Problem 14.22) as a
function of the number of elements, n,if n is an odd number.
14.25 A six-element linear dipole array has element spacing d = λ/2. (a) Select
the appropriate current phasing, ξ,to achieve maximum radiation along
φ =±60 .(b)With the phase set as in part (a), evaluate the intensities
◦
(relative to the maximum) in the broadside and endfire directions.
14.26 In a linear endfire array of n elements, a choice of current phasing that
improves the directivity is given by the Hansen–Woodyard condition:

2πd π

ξ =± +
λ n
where the plus or minus sign choices give maximum radiation along
φ = 180 and 0 , respectively. Applying this phasing may not necessarily
◦
◦
lead to unidirectional endfire operation (zero backward radiation), but it will
do so with the proper choice of element spacing, d.(a) Determine this
required spacing as a function of n and λ.(b) Show that the spacing as
found in part (a) approaches λ/4 for a large number of elements. (c) Show
that an even number of elements is required.
14.27 Consider an n-element broadside linear array. Increasing the number of
elements has the effect of narrowing the main beam. Demonstrate this by
evaluating the separation in φ between the zeros on either side of the
principal maximum at φ = 90 . Show that for large n this separation is
◦
.
.
approximated by φ = 2λ/L, where L = nd is the overall length of the
array.
14.28 A large ground-based transmitter radiates 10 kW and communicates with a
mobile receiving station that dissipates 1mW on the matched load of its
antenna. The receiver (not having moved) now transmits back to the ground
station. If the mobile unit radiates 100 W, what power is received (at a
matched load) by the ground station?
14.29 Signals are transmitted at a 1-m carrier wavelength between two identical
half-wave dipole antennas spaced by 1 km. The antennas are oriented such
that they are exactly parallel to each other. (a)If the transmitting antenna