Practical_Antenna_Handbook_0071639586

C h a p t e r 1 4 : r e c e i v i n g A n t e n n a s f o r H i g h F r e q u e n c y 345
amplitudes and notch depth. Receiving loops have also been used as high as VHF and
are commonly used in the 10-m ham band for hidden transmitter hunts.
Let’s examine the basic theory of small loop antennas and then take a look at some
practical construction methods.
Grover’s Equation
Grover’s equation (Grover, 1946) seems closer to the actual inductance measured in
empirical tests than certain other equations that are in use. This equation is
⎧⎪
⎡ K aN ⎤ ⎡
2 2
K4
( N + 1)
b⎤⎫⎪
L = ( K1N a)
× ⎨ln⎢
⎥+ K3
+ ⎢ ⎥⎬
⎩⎪ ⎣( N + 1)
b⎦
⎣ aN ⎦⎭⎪
(14.2)
where L = inductance, in microhenrys (mH)
a = length of a loop side, in centimeters (cm)
b = loop width, in centimeters (cm)
n = number of turns in loop
K 1 through K 4 are shape constants and are given in Table 14.1. ln is the natural logarithm
of this portion of the equation; it is typically obtained from a table or scientific calculator.
(See App. A for information on natural logarithms.)
Shape K 1 K 2 K 3 K 4
Triangle 0.006 1.155 0.655 0.135
Square 0.008 1.414 0.379 0.33
Hexagon 0.012 2.00 0.655 0.135
Octagon 0.016 2.613 0.7514 0.0715
Table 14.1 Shape Constants
Air Core Frame (“Box”) Loops
A wire loop antenna is made by winding a large coil of wire, consisting of one or more
turns, on some sort of frame. The shape of the loop can be circular, square, triangular,
hexagonal, or octagonal, but for practical construction reasons the square loop is most
popular. With one exception, the loops considered in this section will be square, so you
can easily duplicate them.
The basic form of the simplest loop, as shown in Fig. 14.7, is square, with sides of
length A. The width of the loop (B) is the distance from the first turn to the last turn in
the loop or, alternatively, the diameter of the wire if only one turn is used. The turns of
the loop in Fig. 14.7 are depth-wound—meaning that each turn of the loop is spaced in a
slightly different parallel plane—and spaced evenly across distance B. Alternatively, the
loop can be wound such that the turns are in the same plane (known as planar winding).
In either case, the sides of the loop (A) should be not less than five times the width (B).
There seems to be little difference in performance between depth- and planar-wound
loops: the far-field patterns of the different shape loops are nearly the same if the re-