About Units and Accuracy

There are still a few backwards countries in the world that use Imperial units (inches, feet, pounds, etc.) rather than the International Metric system. I happen to live in one such country, but many of the visitors to this site might not be familiar with such archaic systems.

My intent is to provide all measurements in both sets of units. But the acceptable level of accuracy / expected tolerances will be factored into those conversions. What does that mean? Technically, 2 inches = 5.08 cm, but if I write “5.08 cm”, that implies much tighter accuracy than “2 inches” does. If I spaced a pair of wires 2 inches apart, I’ll translate that to 5 cm, because I probably wasn’t precise enough to worry about the last 0.8 mm. Similarly, a 45m loop of wire resonates around 7.05 MHz in some circumstances, which would calculate to 147.6 feet. I will probably round that to 148 feet, but 147 feet would be just as accurate. In practice, the variation due to the wire diameter, insulation thickness, the exact shape of the loop, and height above ground could cause a variation of 5% or more, so rounding to the nearest foot or two is accurate enough.

There are lots of other quirks in writing and using Imperial units as well. Americans often use the single quote mark / apostrophe to indicate feet, and the double quote mark to indicate inches. I’ll try to spell the units out, to avoid any confusion. And then there are those quirky fractions, like 3 7/32 (three and seven thirty-seconds of an inch), along with numbered screw, drill, and wire sizes (wire gauge gets smaller with increasing diameter, but screw sizes get larger). I plan to include a whole list of equivalents and conversions on the Resources page, so you can figure out the local equivalent of a #18 wire, a 6-32 screw, or 3/4 inch plastic pipe (which has different diameters, depending on the type of plastic used).

Either set of dimensions (or any other, for that matter) will work for building antennas with appropriate conversions, and it makes sense to use the ones that work with your tools, available materials, and measuring devices.

Personally, having grown up using Imperial Units, I now use millimeters for modeling and building UHF antennas. I find it much easier and less prone to make measurement errors when tolerances are less then about 1/4 of an inch (6mm), rather than trying to make sense of the usual fractional inches. A yardstick marked in mm (or, of course, a meterstick) is much easier to use when antenna elements are short enough.

Measurement Accuracy

In practice, how accurate do antenna measurements need to be? There are two factors to consider: bandwidth, and repeatability.

Bandwidth means that an antenna cut for one frequency will operate over a range of frequencies with relatively the same performance characteristics. For example, an inverted vee dipole antenna for 40m might cover from 7.0 to 7.3 MHz with an SWR less than 2 : 1, which generally is adequate for many transmitters. That represents about a 0.5% operating bandwidth. If you wanted to operate on a specific frequency, then you would need to cut the antenna wire within 0.5% or so (about 10 cm, or 4 inches), and the antenna should be usable. Some radios may be more fussy: the bandwidth at an SWR of 1.5 : 1 is about half that, which would require cutting the wire to within 0.25%. Note, however, that if your objective was to cover the whole IARU Region 3 40m band from 7.0 to 7.3 MHz with a single antenna, then it would have be trimmed more closely to align the bandwidth with the band edges.

The repeatability, or, more accurately, the lack of repeatability, complicates matters further. The quality of the ground under the antenna, the height of the antenna above ground, the diameter of the wire used, the thickness and type of any insulation on the wire, and even how the insulators are attached to the wire all affect the frequency of minimum SWR. Some of these can be corrected for, and others are more unknown. Cutting your wires to within 0.25% accuracy won’t help much if the frequency shifts 3% due to insulation on the wire.

On the other hand, a 40m rectangular loop designed for vertical polarization and a 50 ohm feedpoint impedance might only have a 2 : 1 SWR bandwidth of 160 kHz, and less than 100 kHz at 1.5 : 1, so would require more accurate cutting.

So I take pragmatic approach: I make the best estimate I can for the required wire length, based on modeling studies and past experience. Then I add some extra length, put up the antenna, and shorten the antenna by cutting off (or folding back) the end of the wires a bit at a time until I get the SWR curve where I want it.

Things are more complex for antennas such as multi-element yagi beams, for example, where there are multiple elements, and it isn’t possible to adjust them all just for SWR. Fortunately, such yagis are often installed high enough above the ground with self-supporting elements, which reduces the range of variation, and modeling results are often accurate enough. With UHF beams for the 70cm band, where element lengths are less than about 40cm, I find that a 1mm (0.25%) measurement accuracy is sufficient.