# Slot antennas

Pieter-Tjerk de Boer, PA3FWM pa3fwm@amsat.org

(This is an adapted version of part of an article I wrote for the Dutch amateur radio magazine Electron, February 2022.)

Most antennas consist of one or more conductores (metal wires or rods) surrounded by an insulating medium (air). But it's also possible to do the reverse: make an antenna consisting of a piece of insulating material (air) in a conductive medium, namely a metal plate. Such an antenna is called a "slot antenna".

This type of antenna is realised often at UHF and higher frequencies by placing a wave guide vertically, and making a series of vertical slots in it. Each slot acts as a little dipole, and together they form an antenna that concentrates most of its radiation in a horizontal plane, while being omnidirectional within the horizontal plane.

In 1941, Henry Booker proved a nice relationship between antennas consisting of wires, and antennas consisting of holes in a conductor. Because of the war, its publication had to wait until 1946 [3]. The relationship is as follows. An antenna consisting of holes in a metal plate has exactly the same radiation diagram as an antenna consisting of metal at the places of those holes, and vice versa, the so-called complementary antenna. However, the following points need to be observed:
(i) The electric and the magnetic field must be interchanged; practically speaking, this rotates the polarization by 90 degrees.
(ii) The feedpoint must be rotated 90 degrees; this makes sense, because after replacing metal by air and vice versa, the feedline would otherwise end in air, not connected to anything.
(iii) The impedance is inverted: if you started with an antenna with low impedance, then the complementary antenna has a high impedance, and the other way around. Just like the first point this is related to the roles of voltage and current having been interchanged.

The figure shows at left a normal half-wave dipole antenna, consisting of a metal strip, interrupted half-way to connect the transmitter. At right, the complementary antenna is shown: a rectangular hole in an infinitely large metal plate, with the transmitter connected half-way across the width of the slot. Point (ii) is immediately clear: the transmitter connection has indeed been rotated by 90 degrees.

Point (i) means that while the dipole is polarized horizontally, the slot works with vertical polarization. That's not so strange: the transmitter voltage is now applied vertically. The interchange of the roles of the electric and magnetic fields can also be seen in another way. In the dipole, electric charges moves back and forth: at some moment the left half is negative and the right half is charged positively, and half a period later it's the other way around. In the slot antenna the electric currents flow in the metal, as indicated by arrows: counterclockwise around the left end of the slot, clockwise around the right end of the slot (and the other way around, half a period later). Thus, we'll have a magnetic north pole pointing toward us at the left, and a magnetic south pole at right: the counterparts of the positive and negative charges on the dipole.

Finally, point (iii) means that while the half-wave dipole has a low impedance, e.g. 67 Ω if the strip's width is λ/200, the slot antenna has a rather high impedance, namely 530 Ω for the same size. The product of these numbers is 35476 Ω2 (apart from rounding). According to Booker's calculation this always holds for the product of the impedances of an antenna and its complement, regardless of the shape and size of the antenna. In order to get a slot antenna with a low impedance, it must be about an entire wavelength long: 0.925 λ long and 0.066 λ wide results in exactly 50 Ω (numbers from [4]).

## References

[3] H.G. Booker: Slot aerials and their relation to complementary wire aerials (Babinet's principle). Journal of the IEE, part IIIA, 1946.

[4] J.D. Kraus: Antennas. 1950