SO, you finally broke down and built your first ½ wave dipole antenna, but the darn thing isn't working where you need it to. How do you know where to add or subtract to the length of the wire without trial and error?

### Enter the math!

Just like everything else that has to do with ham radio, eventually you are going to have to break out the calculator and do some equations. Just like you did to find the initial length of the antenna for the band you wanted to work on. But don't worry because this math only causes a few gray hairs. Get the aspirin ready and dig out that old calculator, because here we go!

In an earlier article we discussed how to measure the approximate length of a dipole antenna using the formula:
468/Freq = Total length of antenna /2 (for each half)
468 / 7.050 = 66.4ft (Total length) /2 = 33.2ft
(Don't forget to add at least an extra foot for tie-offs)

Remember to measure twice and cut once, so you don't make any mistakes.

As stated earlier, this equation WILL get you in the ball park, but it is by no means a simple solution for every ham. Factors such as ground, antenna height and configuration also factor in. You can have the antenna strung up flat between two trees, an inverted V that has a single apex in the center with both legs drooping down at 45' angles, or even as a sloper that angles down with one end up high and the other 10 to 15ft off the ground. Each configuration will change the characteristics of the dipole antenna.

OK, so how do we know how much to cut off from the antenna to give us a low SWR and make it work properly.

According to the “Practical antenna design” handbook 2nd edition. by Joseph J Carr.

1. Calculate the length required for the upper end of the band.
2. Calculate the length required for the bottom end of the band.
3. Calculate the difference in lengths for the upper and lower ends of the band.
4. Calculate the width of the band in Kilohertz by taking the difference between the upper frequency and the lower frequency.
5. Divide the length difference by the frequency difference; The result is is in Kilohertz per unit length.

HUH?

But wait, don't run off screaming trying to wrap your head around that concept just yet. It is really a lot easier than it sounds, and just requires a little bit of math. Basically you are just measuring the difference between the top end of the band and bottom end of the band. In this case we could use 80M as the example. Since the top end is 4.0MHZ and the bottom is 3.5MHZ that gives us 500khz to work with. And if you do the equation 468/Freq:
468/4 = 117ft
468/3.5 = 133.7
You have 16.7ft to use. SO far so good right?

This is the really really really hard part, so time to put those thinking caps on. Just take the 500Khz and divide it by the feet, in this case 16.7 which equals 30khz per foot.

500/16.7 = 30

Wasn't that difficult. And their you have it, a quick down and dirty way to figure out how to quickly cut your antenna to resonance using simple math. But how could you use this to make the antenna work at your location ?

This is really fun so far isn't it? If you cut your dipole and find that it's working great in the center of the 80M band but you need it for the lower CW portion and need to lengthen it, this formula will tell you how much to add to the antenna to make it work properly.

Building your own antenna will give you a tremendous sense of accomplishment and get you on the airwaves making new friends from all over the world.