222 Radio Engineering for Wireless Communication and Sensor Applications

produced by the driven and parasitic elements add in phase in the forward direction and cancel in the reverse direction.

The driven element of a Yagi antenna is in a resonance, that is, the input impedance is resistive, when the length of the element is 0.45 to 0.48 wavelength. The driven element is often a folded dipole. The reflector is 0.15 to 0.30 wavelength behind the driven element and it is about 5% longer than the driven element. The directors are about 5% shorter than the driven element and their spacings are 0.15 to 0.30 wavelength. Often the directors have equal lengths and equal spacings, although the optimization of dimensions would give a slightly higher directivity. A larger number of director elements means a higher directivity. Usually there are three to twelve directors. The directivity of a seven-element Yagi is typically 12 dB. The narrow bandwidth is a drawback of the Yagi antenna. In a cold climate snow and ice covering the elements may easily spoil the directional pattern.

A log-periodic antenna is a broadband antenna whose properties repeat at frequencies having a constant ratio of t. The structure is periodic so that if all the dimensions are multiplied or divided by t, the original structure, excluding the outermost elements, is obtained. Figure 9.14 shows a logperiodic dipole antenna. The antenna is fed from the high-frequency end, and the feed line goes through all elements, so that the phase is reversed from an element to the next one. Only the element being in resonance radiates effectively. The element behind it acts as a reflector and the element in front of it acts as a director. Thus, the active part of the antenna depends on the frequency. The directivity is typically 8 dB.

9.5 Other Wire Antennas

A loop antenna is a circular or rectangular wire, which may consist of several turns. If the loop is small compared to a wavelength, the current is nearly

Figure 9.14 Log-periodic dipole antenna.

constant along the loop. The maximum of the directional pattern is in the plane of the loop and the nulls are perpendicular to that plane as in Figure 9.15(a). The pattern is like the pattern of a small dipole having the electric and magnetic fields interchanged. Therefore, a small loop can be considered to be a magnetic dipole. The radiation resistance is

where A is the area of the loop and N is the number of turns.

The current of a larger loop is not constant. Then the directional pattern differs from that of a small loop. If the length of the circumference is one wavelength, the maximum of the directional pattern is perpendicular to the plane of the loop and the null is in the plane of the loop. Figure 9.15(b) shows a quad antenna, which is made of such loops. Like the Yagi antenna, the quad antenna has a driven element, a reflector, and one or more directors. Quad antennas operating at different frequency ranges can be placed inside each other because the coupling of such loops is small.

A helix antenna, shown in Figure 9.16, is a helical wire having either the left-handed or right-handed sense. If the length of the circumference L is less than l/2, the helix antenna radiates in the normal mode; that is, the maximum of the directional pattern is perpendicular to the axis of the helix. This kind of a helix antenna operates as a shortened monopole, except the field is elliptically polarized. If L is from 0.75l to 1.25l, the helix antenna operates in the axial mode; that is, the main beam is along the axis of the helix and the field is circularly polarized.

Long-wire and rhombic antennas are traveling-wave antennas, which are used at HF range. The current has constant amplitude but the phase changes linearly along the wire (in a dipole antenna, the amplitude of the current changes but the phase is constant).

Figure 9.15 (a) Small loop antenna and its directional pattern; and (b) quad antenna.

224 Radio Engineering for Wireless Communication and Sensor Applications

Figure 9.16 Helix antenna fed from a coaxial cable through a conducting plane.

The long-wire antenna is usually a horizontal wire, which is terminated with a matched load, as shown in Figure 9.17. The conical directional pattern is

where a is the angle from the direction of the wire and L is the length of the wire. The longer the wire, the smaller the angle am is between the directions of the main lobe and the wire. For an antenna having a length of several wavelengths, the main lobe direction is am ≈ √l/L . A V-antenna is made of two long-wire antennas placed in an angle of 2a m to each other. It has a better directional pattern than a single long-wire antenna because the main lobes of the two wires reinforce each other.

A rhombic antenna is made of four horizontal long-wire antennas (or two V-antennas), as shown in Figure 9.18. It is fed from a parallel-wire line and is terminated with a matched load. The fields produced by the long-

Figure 9.17 Long-wire antenna.

Figure 9.18 Rhombic antenna and its directional pattern.

wire antennas are all in phase in the forward direction. In practice, the main lobe tilts slightly upward, due to the ground.

9.6 Radiation from Apertures

Figure 9.19 shows a surface element d S at the origin in the xy -plane. The electric field Ex and magnetic field Hy = Ex /h are constant over the element. These aperture fields can be replaced with surface currents Ms = −Ex uy and Js = −Ex /h ux . The vector potentials at a point P (r , u, f ) are

Figure 9.19 Radiating surface element.