Is Trimming an Antenna Proportional to it Frequency?

table with ham radio equipment
Ham Radio equipment on a table.

Based on what I’ve read so far on antenna theory, the shorter the wire the bigger the band. Although, is cutting the wire proportionately linear? To test this idea, I’m going to adjust a 40 meter End Fed Half Wave Antenna (EFHW). The wire size to resonates 40 meters (7.2 MHz) is 65 feet; the height of a 5 story building! To calculate the wire size, I used the following formula.

L = 468/ƒ

Where L is the length of the wire in feet, ƒ is the frequency you want the antenna to resonate the best, and 468 is a constant with velocity and conversion factors. This is the same formula to calculate the length of a dipole. By placing 7.2 for the frequency, I calculate the size of the antenna wire to be 65 feet long.

For the wire, I used the antenna wire (DEF 61-12 Pt 6). I approximately measured 65 feet and added approximately 1 foot more. Adding one more foot, gives me assurances that the antenna will resonate at a lower band so I may cut the wire shorter and adjust as needed.

To adjust my antenna, I decided not to do it at home. Too much electronic interference, and I don’t have enough space for a 65 foot wire. So, I drove to Lake Perris, CA where they have large open field to place an antenna. I put the antenna together by using a 49:1 transformer from QRPGuys – a Mini 80m-10m No Tune End Fed Half Wave Antenna and a 7 meter mast that I mount to the ground using Grouondhog Tent Spikes. I used the RigExpert 230 Stick to measure the SWR. To read the results easier, I used my phone which connects to the RigExpert via bluetooth.

Small table with cut wires.
Image 2: 1 inch wires that were cut to adjust antenna.

There are two ways to adjust the antenna properly – fold the antenna end or cut the wire from the transformer side. I decided the latter. It easier to cut the wire and measure the SWR than brining down the mast and folding the wire. In addition, folding the wire on to itself eventually will create havoc in your SWR readings. The first measurement was my initial cut of the wire. I was focused on the lowest peak near 7.2 MHz which represents the lowest SWR. Then I would cut approximately an inch of wire and remeasured. The following are my data.

Wire Length (in)Frequency (MHz) SWR
Table 1: 10 SWR measurements for adjusting approximately a 66 foot long wire to resonate on 7.2 MHz on an EFHW Antenna

I would say by the third inch I cut off, I was certain the lowest SWR was moving towards the 7 MHz band. When I reached 7.154 MHz, I stoped because I noticed that 20 meters’ lowest SWR had passed a bit.

When I got home, I created a linear regression line between the frequency vs the amount of wire I cut. Based on the small data sample, the data suggests a linearity between frequency and the size of the wire. The regression equation came out to be y-hat = 0.0306x + 6.8233

Graph 1: Frequency vs wire length cut for an adjustment on a EFHW 40 meter antenna.

The slope of the linear regression (0.0326) describes how the frequency was increasing as the wire got shorter by one inch. This indicates that by cutting 10 inches, I went from approximately 6.8 to 7.13 MHz, which the table 1 confirms.

Table 2: Final measurements for the 7MHz wire
Image 3: Final SWR chart for the EFHW 40 meter antenna.

Overall it’s amazing how the EFHW transformer works. As I was trimming the wire, the antenna was getting closer to the resonating point I desired (7.2 MHz). Also, the 40, 20 and 10 bands were resonating on target because of the design of the EFHW transformer. In addition, the 160 and 15 meter bands had low SWR readings. Although, the 160 band might not be as efficient when transmitting.