A possible method of dealing with the thick vs. thin situation is to model with real wires with a network of smaller model wires that are connected to each other. This was mentioned on the page dealing with explaining the limitations of the thin wire model, and on the page dealing with the dipole near a "thick wire."
Just as in the case of the dipole, the case of a yagi near a boom (or thick wire) can be simulated by a network of much smaller wires. To simulate the horizontal boom, it will be made into the "ladder" structure.
The figure below shows conceptually the yagi and the boom after they have been segmented for analysis. The yagi, represented in the color red, is modeled as three separate single thin-wire structure: one for each of the yagi elements. The boom, represented in blue, is modeled in the "ladder" structure of cross-connected parallel wire segments.
The above picture is conceptual and not to scale. Also many more segments are used than indicated in the drawing.
In a real model, it is necessary to keep all of the wire segments nearly the same size. The limit in segment size variation (found in the User's Manual and the quick reference) is [longest segment]/[shortest segment] < 100
Also, just as in the dipole case considered on the previous page, when wires lay close together, the wire diameter set into the model must be much, much smaller than the closest spacing. For best results, the length of the wire segments making up the "ladder" boom section shouldn't be any longer than the smallest spacing between the wires in parallel. To meet all of these requirements requires a large number of segments even for a small problem.
In the Yagi problem being considered on this page, each of the Yagi elements is described with 51 points joined to make 50 segments. The driven element dipole is fed at the center point. The driven element is 0.5 meters long; therefore each segment is 1 cm long. The reflector element is made 105% the length of the driven element and spaced 0.15 meter behind the driven element. The director element is made 95% the length of the driven element and spaced 0.15 meter in front of the driven element.
Just as in the dipole case, the boom is composed of two parallel wires each 0.5 meters long and are also divided into 1 cm segments. These wires are at right angles to the Yagi wire elements and spaced 4 cm away. The two wires making up the boom are 2 cm apart and are joined together like a ladder by cross connections running between the description points.
All of the wires making up the model are 0.001 meter i.e. 1 mm in radius.
A case without the boom in place and with the boom in place were run for comparison.
The full input file can bee obtained here: YBOOM.DAT (13K)
The Yagi by itself and the Yagi with the ladder boom simulation were run for multiple frequency points to gauge the effect on feedpoint impedance and gain.
The plots below show the input resistance vs. frequency and the reactance vs. frequency on separate plots. The no-boom case and the with-boom case are on the same plot for easy comparison.
Since the difference is fairly close, here are the plots again with the scale zoomed in.
Unlike the half-wave dipole case, the frequency shift is not as great. The shift for the dipole case was about 400 kHz. The shift in resonance (i.e. the zero crossing of the reactance curve) in this case is about 250 kHz. This smaller shift for the Yagi case is probably because the driven element is already being loaded by the reflector and director elements. Nevertheless, the shift is still there. It is also still a shift to a higher frequency.
The gain vs. frequency curves for the Yagi are also affected as shown in the figures below. As before there is both a far-out and a zoom view.
Once again, there is a shift seen in the gain vs. frequency curves. In this case the shift is approximately 250 kHz. The maximum gain is also slightly less for the boom case indicating that the Yagi elements would have to be tweaked in spacing or length. The drop in gain is not much however, amounting to less than a tenth of a dB.
Note: Caution, the data was taken only every 1 MHz. The curves shown above were created with an interpolation/smoothing plot function to give the appearance of more points than were actually taken. Given the form of the data this is reasonable. However, specific conclusions above may be wrong. More data points would be needed to fill in any areas of interest. This is left as an exercise for the student.
If someone really had a lot of energy, it would be necessary to do some experimental work to relate the effect of real booms to what would be acceptable for the ASAP model. For example, is the ladder boom really good enough. I doubt it. I suggest that for the most part, this simple kind of modeling is only going to give some sort of idea about how things may change. Exact answers for real problems are always hard to come by.
Just to give some example of why answers for real problems are hard to come by, it should also be noted that most real Yagi antennas do not have the elements insulated from the boom! To model that situation would require more care in modeling involving at least a rectangular boom model so that the elements can be mounted either to the side or "through" the boom. With elements mounted through the boom it is possible that the effective length of the element length would be increased due to the currents having to travel around the circumference of the boom. {In some technical journal or another I saw something to that effect based on experimental data - don't remember where it was now - maybe QEX magazine}
It would also be necessary to include the effects of any feed structures such as gamma-match and the effects of any feed cables. However, that will be a problem for another day. It can be easy seen how these kind of problems can result in models with ever increasing number of wire segments resulting in greater memory and calculation times.
There are already a number of specialized programs out there just to handle Yagi antenna that would probably be better than doing it the hard way with ASAP. However, feel free to knock yourself out on this problem. If you get any interesting results with ASAP let me know.
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Last modified on: 3 Nov 2007