Large loop antennas are those with overall wire lengths of 0.5 λ to more than 2λ. Small loop antennas, on the other hand, have an overall wire length that is much less than one wavelength (1λ). According to a Second World War US Navy training manual such antennas are those with an overall length of ≤0.22λ. Jasik’s classic 1961 text on radio antennas uses the figure ≤0.17λ, while John Kraus (1950) used the figure ≤0.10λ. An amateur radio source, The ARRL Antenna Book, recommends ≤0.085λ for small loop antennas. For the purposes of our discussion we will use Kraus’s figure of ≤0.10λ.
A defining characteristic of small loops versus large loops is seen in the current distribution. In the small loop antenna the current flowing in the loop is uniform in all portions of the loop. In the large loop, however, the current varies along the length of the conductor, i.e. there are current nodes and antinodes.
The small loop antenna also differs from the large loop in the manner of its response to the radio signal. A radio signal is a transverse electromagnetic (TEM) wave, in which magnetic and electrical fields alternate with each other along the direction of travel. The large loop, like most large wire antennas, respond primarily to the electrical field component of the TEM, while small loops respond mostly to the magnetic field component. The importance of this fact is that it means the small loop antenna is less sensitive to local electromagnetic interference sources such as power lines and appliances. Local EMI consists largely of electrical fields, while radio signals have both magnetic and electrical fields. With proper shielding, the electrical response can be reduced even further.
Small loop antennas can be built in any of several different shapes (Figure 4.18). Popular shapes include hexagonal (Figure 4.18A), octagonal (Figure 4.18B), triangular (Figure 4.18C), circular (Figure 4.18D) and square (Figure 4.18E).
(A) (B) (C)The far-field performance of small loop antennas is approximately equal provided that A2 ≤ λ/100, where A is the loop area and λ is the wavelength of the desired frequency.
The ‘standard’ loop used in this discussion is the square loop depicted in Figure 4.19. There are two forms of winding used: depth wound and spiral wound. The difference is that the depth wound has its turns in different parallel planes, while in the spiral wound version all of the turns are in the same plane. The spiral wound loop theoretically has a deeper null than depth wound, but in practical terms there is usually little difference.
The length of each side of the loop is designated A, while the depth or width is designated B. These dimensions will be used in equations shortly. The constraint on the dimensions is that A should be ≤0.10λ/4and B ≤ A/5.
The loop may be either tuned or untuned. The differences between tuned and untuned will be discussed shortly.C1 Figure 4.19 Square loop
Small loop antennas have patterns opposite those of large loops. The minima, or ‘nulls’, are perpendicular to the plane of the loop, while the maxima are off the ends. Figure 4.20 shows the directions of maximum and minimum response. The loop antenna is viewed from above. The nulls are orthogonal to the loop axis, while the maxima are along the loop axis.
The fact that the small loop pattern has nulls perpendicular to the loop axis, i.e. perpendicular to the plane of the loop, is counterintuitive to many people. The advancing radio wave produces alternating regions of high and low amplitude. A potential difference exists between any two points. When the loop is aligned such that its axis is parallel to the isopotential lines low signal levels are induced into the loop. If the turns of the loop cut several isopotential lines, a larger signal is induced from this direction.
Figure 4.20 Small loop azimuth
as well as the strength of the arriving signal and the design of the loop. The angle α is formed between the loop axis and the advancing isopotential lines of the radio signal.
The output voltage of an untuned loop is:V
o
=
2 π ANEf cosα λ
V
o
=
2 π ANQEf cosα λ
where
Vo is the output voltage of an untuned loop in volts (V) A is the length of one side of the loop
N is the number of turns in the loop
Ef is the strength of the incoming signal in volts per metre (V/m)
Q is the loaded Q (figure of merit) of the tuned circuit formed by C1 and the loop inductance (typically 10 to 100)
Loop antennas are sometimes described in terms of the effective height (Heff) of the antenna. This number is a theoretical construct that compares the output voltage of a small loop with a vertical piece of the same kind of wire that has a height of:
Heff
=
2 π NA λ where Heff is the effective height in metres, and all other terms are as defined above.
A loop antenna essentially forms a coil of wire (or other conductor), so will have inductance. There are several methods for calculating loop inductance, but the most common are the Grover equation and the Patterson equation.
Grover equation:L
µ
=
K
1
N
2ALn K2AN+K3+ K4(N + 1)B (N + 1)B AN
where all terms are as previously defined, except K1–K4, which are defined in Table 4.3.
Table 4.3 K factors for calculating loop inductance Shape K1K2K3K4
Triangle 0.006 1.1547 0.65533 0.1348
Square 0.008 1.4142 0.37942 0.3333
Hexagon 0.012 2.00 0.65533 0.1348
Octagon 0.016 2.613 0.75143 0.07153
LµH = (0.00508A)× 2.303 log4A −φd
where
d is the conductor diameter φ is a factor found in Table 4.4
Circle 2.451 Octagon 2.561 Hexagon 2.66 Pentagon 2.712 Square 2.853 Triangle 3.197
Of these equations, most people will find that the Grover equation most accurately calculates the actual inductance realized when a practical loop is built.