by skywave » 11 Jul 2006, 23:06
The characteristics of slot antennas in large conducting sheets are perfectly complementary to ordinary linear-dipole antennas made from wire or metal tubing. The shapes of their radiation patterns are identical, except the polarizations of the E and H fields in the radiated energy are interchanged and the E component normal to the plane of the conducting sheet is discontinuous.
Frequency response characteristics are also complementary in that slots (the absence of conducting material) that are extremely narrow compared to a wavelength have narrow frequency bandwidths, just as linear-dipoles made from wire (conducting material) that is extremely thin compared to a wavelength have narrow bandwidths; and conversely, in that wide slots have wide bandwidths, just as linear-dipoles made from thick conductors have wide bandwidths.
If a slot dipole in a conducting sheet of infinite size is fed directly across its center points, the input impedance is related to the input impedance of a complementary linear-dipole in free-space with both antennas at resonance as follows:
Z(s)Z(d) = Z(0)Z(0) / 4 = 35,476 ohms
Where:
Z(s) is the input impedance of the slot antenna
Z(d) is the input impedance of the linear-dipole antenna, and
Z(0) is the intrinsic impedance of free space = 120pi ohms = 377 ohms
Therefore, if the input impedance of a complementary linear-dipole antenna (one that has the same conductor thickness and length as the width and length of a slot antenna) made of wire or tubing is known, the relationship above can be used to calculate the center-slot input impedance of the slot antenna at resonance.
That is a precise mathematical way to determine the exact input impedance of a center-fed slot antenna at resonance for the special case of a conducting sheet with infinite size and a linear dipole in free-space. Even though neither conducting-sheets of infinite size nor perfect free-space conditions ever exist with practical antennas, the relationship above is still useful to estimate the approximate input impedances of center-fed slot antennas in reasonably large sheets.
Precise mathematical methods also exist to calculate input impedances of ordinary linear-dipoles made from wire or tubing, but few amateurs use those methods to calculate the impedances of antennas they plan to install. Instead, most everyone knows that the center feed-impedance of a wire dipole antenna in free-space is approximately 72 ohms. If a wire dipole antenna is to be installed high above ground and away from other objects it is generally assumed without mathematical calculation that its center feed-impedance will be about 72 ohms. If the antenna is to be installed closer to ground most amateurs simply assume without calculation that its feed-impedance will be lower.
Similar practical "rules-of-thumb" can be used to estimate the feed-impedance of slot antennas. Slots in large conducting sheets that are open on both sides generally have center feed-impedances near 500 ohms. However, if a slot antenna was cut into one side of a perfectly-conduction metal box, so that zero susceptance was shunted across the input terminals, the input impedance of the slot would double. Note that this is opposite to what happens when a tuned reflector is placed behind a linear-dipole. In that case the linear-dipole feed impedance drops, instead of rises, because the two antennas are complementary.
Just as a linear-dipole antenna can be off-center-fed to raise its feed impedance, a complementary slot antenna can be off-center-fed to lower its feed impedance. At resonance the feed impedance of a slot in a large sheet varies from approximately 500 ohms across its center to near zero across either end, so the feed connecting point can moved along the length of a slot as necessary to match impedances between those approximate limits.
It should already be clear from what I have written above, but in case it isn't, the length of a slot antenna for resonance is precisely the same as the length of wire antenna for resonance at the same frequency if the sheet the slot is cut in is large compared to a wavelength, if the sheet is a near-perfect conductor, if the wire is in near free-space conditions, if the diameter of the wire equals the width of the slot, and if the wire is supported by near-perfect insulators.