Optimizing Yagi Design Parameters

There are so many different Yagi designs published in books, magazines, and on the web. But what's the difference between them? For a basic three-element Yagi, design parameters include the spacing, length, and diameter of the elements. Performance parameters include standing wave ratio (SWR) characteristics, gain, and front-to-back ratios. When I see a design, I wonder what the designer's goals were, and if I change one parameter, how will other parameters be affected? 

I started out with the impressive National Bureau of Standards Technical Note 688, titled Yagi Antenna Design. The author built antennas and measured their performance as parameters were varied. I wanted to do something similar using NEC2 simulation software in an effort to understand the relationship between design and performance parameters. I used the PyNEC library so I could programmatically try many different combinations. Using a Python script is much more efficient than using any of the NEC2 applications, because I can simulate and compare hundreds of configurations in a matter of minutes. 

Starting with one of the basic three-element Yagi designs in the technical note, I noticed that the spacing between the elements was the same, and that the spacing was one quarter of the antenna's design wavelength. What would happen if the spacing between elements remained equal, but was increased or decreased. I updated the script yagi_3_element.py to measure the forward antenna gain and plot it. And wouldn't you know it? The script predicted maximum gain at one-quarter wavelength which matched what was measured in the technical note.

The radiation pattern shows a forward gain of almost 9.

And the SWR across the VHF ham band is only slightly more than two, which is easily handled by most radios. 

Then the next question was: could gain be increased with unequal spacing? I wrote yagi_optimize_spacing.py to independently vary the two spacing parameters, creating a surface and plotting it. 

The answer was yes. Gain was increased slightly: half a dB. This could be done by increasing the director spacing to 0.325 λ and reducing the reflector spacing to 0.055 λ, but that seemed really strange. I've never seen an antenna like that, there had to be a catch. Plotting the SWR revealed the problem. 

The SWR was super-high. The complex matching network required for an antenna such as this would more than cancel any of the gain improvement. 

So what I learned was that quarter-wavelength spacing is best for a three-element Yagi. 

The next questions are: what happens if the element lengths are varied? How do Yagis with arbitrary numbers of elements behave? And, if I build one of these on my workbench, how closely will its performance match these designs?