Further Optimization of Yagi Antenna Parameters

In the previous post, I documented my experiments with the spacing between elements in a three element Yagi antenna. What about the length of the antenna elements? 

In a Yagi, the reflector is longer than the driven element, and the director is shorter than the driven element. In the reference design I've been using, the difference in element length was four percent in both cases. Is this optimum? In fact it appears to be. I wrote this script to explore the question: 

https://github.com/umeda/nezumi/blob/master/Projects/antenna_sim/yagi_optimize_length.py

I assumed the difference in lengths to be the same in both cases, then simulated antennas with zero to ten percent difference in their lengths. 

As you can see in the above plot, gain gets better as the difference in element lengths get lesser, but  SWR gets better (lower) as the element lengths get greater. Since most radios prefer an SWR of less than two, we can move a little bit to the left of four percent element length difference before getting into trouble with our final drive transistors. Gain is a little over 8X, which is quite satisfactory. However, if we are at an SWR of two at our design frequency, what are we going to look like over the entire band?

 

And the answer is: we're going to have to give up some more gain if we want an SWR of less than two (indicated by the green area) over the entire band, at least for the two meter ham band. It looks like an element difference between four and five percent would do nicely. Of course if I wanted to design an antenna for a single frequency I could get more gain.

The first time I generated this plot, the green area representing the area of acceptable SWR was skewed way down to the lower band edge. Looking at some reference designs, I realized that the driven element was usually somewhat shorter than a half wave length. So I tweaked the scale factor to bring the best SWR to the middle of the band.

The other thing I realized, is that I should probably go back to my element spacing script and see what the acceptable frequency range was for various element spacings. However, I'm currently more interested in moving forward, so we'll revisit that later.

The next question to be investigated is: what if we let the reflector and director elements vary independently?