[TowerTalk] Hairpin Match Calculator

[Brian Beezley]

Accurately calculating rod length and antenna reactance for a hairpin 
match turned out to be more complicated than I expected. I realized 
pretty quickly that my boom model was dubious. I abandoned it. When a 
hairpin shorting strap effectively passes through the boom in the style 
of Hy-Gain HF Yagis, the boom reduces its inductance, which increases 
the required rod length. Even simple contact with a boom will have some 
effect. I may address this problem at some point with a finite-element 
magnetics model. For now I provide some guidance in the documentation. 
In addition to predictability, there is another reason to insulate the 
shorting strap: Any antenna imbalance may cause stray current to flow 
onto the boom. This can degrade the antenna pattern and bypass a 
carefully designed current choke at the feedpoint.

I decided to take advantage of the telegrapher's equations to calculate 
loss. The program models several aluminum alloys as well as copper. It 
displays hairpin inductance and Q. You can use the figures to design a 
coil inductor to replace the hairpin. In the cases I tried, hairpin Q 
was almost always substantially greater than that of a practical coil. A 
hairpin match is very efficient.

Since it was easy to do, I decided to calculate the mutual inductance 
between the leads and hairpin rods. The level of interaction surprised 
me. I knew that lead self-inductance could affect a hairpin match, but I 
didn't realize that magnetic interaction with the rods could be so 
substantial.

Much of the complexity I encountered came from trying to model hairpins 
with the feedpoint offset from the rods. I've seen photos of such 
designs, which effectively put part of the driven element in the hairpin 
circuit. I wanted to allow for them. This geometry spawns several 
additional self- and mutual inductance calculations. The program handles 
most of them, but I found mutual inductance between the leads and rods 
too complicated to calculate for this geometry. It can be done, but I 
ran out of steam. Keeping the leads and rods coincident provides the 
most predictable design.

A hairpin match is easy to adjust. The purpose of my program is to make 
adjustment unnecessary.

http://ham-radio.com/k6sti/hairpin.htm

Brian