Every type of antenna has its own charm and practical advantages for specific purposes. A rhombic has only one feedpoint, it is relatively wide-band, and it needs only a few fixed supports. However, there are a number of straightforward reasons why claims of excessive gain are unrealistic.
Orthogonal radiation versus skew
The main reason that pins rhombics down to a gain limit is the fact that the maximum radiation (the main lobe) is skew with respect to the radiator (the wire of the rhombic). There is a simple method to get much more gain out of the same length of wire, but then it is no rhombic any more (and it would require a huge number of feedpoints).
Today's simulation software gives us a tool to get more exact estimates of rhombic gain, but we can get some approximate feel for the case just by looking at the angle of the wire and the mutual impedance (which should never be forgotten).
Getting a feel for the limit
For an analysis the rhombic can be chopped up into a string of half wave dipoles of alternating phase. Let us refer gain to a dipole, so a single dipole has a gain of 0 dBd when looking at the field orthogonal to the dipole axis. At a 45 degree angle the field is down to -4dBd. However, we know that for the higher gains the main lobe will be found at less than 20 degrees with respect to the wire, which means that a dipole field will be down at least to -12 dBd. This means that we need at least 16 dipoles with identical power as the reference dipole to get back to 0dBd, with the strict requirement that all the far-fields are perfectly aligned. Since a good rhombic has more gain it means that there are much more than 16 dipole equivalents in a real solution.
The hypothetic "16-unit" rhombic would have 4 legs of each 2 waves long, which calls for a 35 degree angle for the wire. The single dipole pattern is down to -6dBd. Which means that we could end up with a rhombic gain of 6 dBd (when neglecting mutual impedance, and assuming equal current distribution, no loss, and perfect phase addition of individual fields). Nature dictates that the mutual impedance of adjacent dipoles (with opposite phase) forces the current to increase in the rhombic wire, and this is the only factor that slightly increases the absolute gain (maximally by 2 dB or so). The radiation loss, phase dispersion, and current decay, will bring the gain down by many more dB's for the longer rhombics. Thus a 6-8 dBd free space gain figure is an acceptable quote for this case.
The bigger rhombic (with 6 wavelength legs)
Now let's take a quick guess for a non-resonant rhombic with 6 wave legs. Such a rhombic would have the main lobe at 20 degrees to the wires (which means -11 dB in a dipole field). The rhombic would consist of 48 dipole units. If these would all have the same current as the single one, then perfect field addition would give about +33 dB but there is no way to run the current unattenuated through all the subsequent sections of radiating rhombic wire. Therefore, it would be a rightout falsification of reality ot claim about +22 dBd of gain for this one.
In this case the mutual impedance works indeed in a way to raise the radiation impedance (referred to the current maxima along the wire), which means a lower field in relation to applied power (for the longer rhombics). The equivalent radiation resistance increases to result in a field decay of up to 5dB in relation to a single independent dipole).
With the current decay along the wire and the growing phase incoherence I would be happy to see more than 13 dBd of gain for a real rhombic with 6 wave legs. Adding of close-in parallel wires will not help much (at least over real ground), as the apertures of the wires will be overlapping. In free space this could sometimes still function as a simulation of a ground reference.
Purposely I have not done any simulations (yet) on the rhombic, but I would like to challenge the rhombic gain to exceed 24 dBd for ANY size of rhombic INCLUDING flat ground reflection gain. I'm not talking about rhombic stacks, but multi-wire is acceptable for this challenge with less than ONE wave spacing permitted between wires.
My view is, that just as with huge yagi-arrays at SHF it is there better to switch to a single feedpoint and a parabolic to keep the phasing together. For rhombics at lower frequencies it is just opposite: switching to multiple feedpoints and orthogonal radiators to keep the pattern together, and to avoid all the sidelobes. This means abandoning the rhombic structure. It also means that there is an asymptotic value for absolute rhombic gain.
Open challenge (valid to July 1st 1997).
I'm willing to award anyone who can prove me wrong, using a couple of independent software simulations, but we still have to agree what the prize would be (how about a donated K6STI antenna software product?).
Definition of the problem: Seek ANY size of 144 MHz rhombic, multi-wire permitted, resonant or non-resonant. Has to exceed +24dBd (including ground gain). No requirements for sidelobe suppression or levels.
Have fun with rhomb's,
73, Zaba OH1ZAA / NNoY
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