NOTES on PARASITIC ARRAYS

 Notes on Parasitic Antennas

There are some basic principles about parasitic antennas that I quickly wrote up thinking it may help a few people understand parasitic antennas a bit better. No one resource seems to have it all. Sometimes it’s hard to understand. I hope to simplify it as much as I can. I will concentrate on only two element arrays here. I hope I do not have any significant errors but if I find any I will make necessary corrections. The date of this paper is December 4, 2024. 

First there is a driven element approximately 1/2 wavelength long as well as at least one parasitic element that receives its energy from the driven element. 

Assuming the driven element is resonate on some frequency, it will have an impedance that is resistive as the reactance will be zero. The resistance will be near 75 ohms. The exact value will vary with the height above ground so it could be anywhere up to 95 ohms. We will just use 75 ohms here as a nominal value. 

When a parasitic element is brought into close proximity to the driven element, it affects the driven element several ways. There is what we call mutual impedance or mutual coupling between the two elements. A good spacing is around 0.15 wavelengths. It can be more or less. 

To see how the two element parasitic array works we can start with the special case of the parasitic element having the same resonant frequency as the driven element. We will see the input impedance of the driven element drop approximately in half. The resonant frequency of the two elements together, which we now call the parasitic array, will not change from what it was. However the impedance match to the feed line will change and and now the 50 ohm coax needs to be matched to about 36 ohms instead of 75 ohms. No big deal. The array will have gain in two directions although not equal gain. The parasitic element will act as more a director but there will be some gain in the reverse direction. If we change the operating frequency by increasing it above resonance we find that the parasitic element is now tuned to a frequency lower than the operating frequency. ( we could also keep the operating frequency the same and lengthen the parasitic element and get the same result). In either case the parasitic element would become less of a director as we increase the frequency above its resonant point until we had reached a point of equal gain in both directions. That gain is approximately 3 dB ( in both directions) over a single dipole element. The resonant frequency of the array obviously remains the same if we simply changed the operating frequency higher. In the case of lengthening the parasitic element, the resonant frequency follows the resonant frequency of the parasitic element and is lowered. In both cases the input impedance to the driven element will change and the match may need to be adjusted if the SWR goes to high. As we continue to increase the operating frequency ( or decrease the resonant frequency of the parasitic element ( by making it longer) we will find the array develops more gain in the direction away from the parasitic element. At some point the gain will reach a peak near 5 dB over a single dipole element, afterwards the gain decreases. That point of maximum gain is approximately 10% above the resonant frequency of the parasitic element.  With the parasitic element operating as a reflector the maximum obtainable gain is 5 dB. 

We could also lower the operating frequency below the resonant frequency of the parasitic element ( or shorten the element) and in that case the element would dominate as a director and reach a peak gain at a frequency only 5% lower than the parasitic resonant frequency. With operation as a director, slightly more gain is possible. 

In addition to the resonant frequency of the parasitic element causing these gain and directivity changes, we also will find the spacing between the elements is significant also. For any given difference between the operating frequency and the parasitic resonant frequency, we find that spacing can be varied slightly to optimize either the gain or front to back ratio. Peak gain and maximum front to back will not be obtained at the same frequency. Usually some gain is sacrificed for an acceptable front to back ratio. That’s a design choice we have to make. Some people go for maximum transmitting gain and accept a poor front to back ratio. 

Parasitic antennas are very forgiving of design errors. It’s hard to build one that does not work reasonably well if you stay in the ballpark with established designs. However it is somewhat difficult to obtain absolute maximum gain and more difficult to obtain maximum front to back ratios. 

SWR band width is another design compromise. Wider SWR bandwidth comes only with some sacrifice in gain. There are many variables. I find it best to study the curves. For example, using a director permits the closest spacing and with a director you can have slightly higher gain. A spacing of only 0.1 wavelengths is necessary.

Using a reflector requires a wider spacing of 0.2 wavelengths but the maximum gain curve is essentially flat from 0.15 to 0.25 wavelength spacings. There seems to be more leeway for boom length errors when using a reflector. 

With wider spacings the feed point resistance will be higher than with closer spacings. 

With a reflector the front to back ratio increases as you move above the design frequency while with a director it increases as you move below the design frequency. 

Gain will peak near the array resonant frequency. Slightly below for a reflector and slightly above for a director. By slightly I mean 1%. In all likelihood it can’t be measured. 

Front to back ratio is usually greater if using a reflector but not by much. There are many plots showing how the various parameters, gain, front to back and feed point R and X vary with spacing and frequency in the book “ Yagi Antenna Design” by Dr. James Lawson, W2PV published by the ARRL. It is an excellent resource. The “Beam Antenna Handbook” by William Orr, W6SAI, although somewhat dated, is another excellent resource. 

Just about all of the above information about Yagi antennas can be directly applied to parasitic vertical arrays. The feed point impedances will of course be different since the impedance of a 1/4 wave vertical is only half that of a 1/2 wave dipole. However the general theory and trends are essentially the same.