A Little Background on Yagi Antennas

I just realized that I've been going on and on about different parts of the Yagi antenna without providing much background. A document describing the Yagi antenna, or more properly a Yagi-Uda antenna, was first published in 1926. Many people are most familiar with this antenna in the form of over-the-air TV antennas that were mounted on the rooftop of nearly every house decades ago. Here's a link to a Google Doodle celebrating Yagi Hidetsugu's birthday that illustrates what I'm talking about.

https://www.google.com/doodles/hidetsugu-yagis-130th-birthday

Each of the metal cross-pieces on the antenna is called an element. There may be as few as three elements, but there can be as many as ten or even more elements. There are three types of elements. The longest element is called the reflector and it's located at the "back" of the antenna, and it redirects signals arriving from the other elements towards the "front" of the antenna. The element next to the reflector, and in the middle of the three element array, is called the driven element. It's slightly shorter than the reflector, and is split into two segments. The two segments are connected to a radio transmitter or receiver. Finally there are one or more directors that focus the radio waves into a narrow beam. The directors are shorter than the driven element, and sometimes get even shorter as more are added.

In the above sketch of a Yagi antenna, the "back" is to the left and the "front" is to the right. If the antenna's connected to a radio transmitter, the direction of greatest signal strength is to the right, or in the direction of the director. If the antenna's connected to a radio receiver, the direction of greatest sensitivity is from the right, or from the direction of the director.

Characteristics of the antenna vary with, among other things, the spacing between the elements and the relative lengths of the elements. In my reference design, the elements are about a quarter wavelength apart. The driven element somewhat less than a half wavelength long. A wavelength is roughly equal to the speed of light divided by frequency of the signal of interest. The reflector is four percent longer than the driven element and the director is four percent shorter than the driven element.

One desirable characteristic of the Yagi is gain - that is the increase in signal strength. This increase is not the same in all directions. In fact, signal strength to the sides and back decrease as forward signal strength increases. You don't get something for nothing! 

This trade-off in signal strength results in other desirable characteristics; for example, directionality. Because the Yagi antenna is most sensitive in one direction it's useful in applications such as wildlife tracking.

The optimizations I'm making in these blog posts are no great new discovery. I'm just starting with a reference design and exploring what happens when I vary certain design parameters in a simulation. The purpose is to give me an opportunity to play with the simulation software, and to get a more intuitive understanding of an antenna design that's always fascinated me.

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?

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?