Now and then, some folks from the San Mateo Radio Club get together at the park to work on a ham radio educational experiment. We cover operating HF, experiments with feed lines, building antennas, or any other ham radio project. These meetings aim to demystify and familiarize beginners and seasoned operators with the components involved with HF.
We've decided to tackle an HF 40-meter to 10-meter Delta Loop antenna for our next meetup. We picked this one because it's a multi-band antenna, which adds a bit of a challenge compared to a simple dipole. However, building it during our few-hour park hangout is still easy enough. It will offer a great opportunity to learn how to set up such a large antenna and the compromises we must make when building a multi-band antenna.
Delta loop
The delta loop antenna is triangle-shaped, like the Greek uppercase letter "delta" (Δ), from which it draws its name. The delta loop is a full wavelength, with elements approximately 2 percent longer than the natural wavelength. The actual length will be a function of the proximity and nature of the underlying ground, so some experimentation is necessary. The approximate total length of the wire is1:
We will build the 40-meter antenna for our project because the second and third harmonics should have a reasonable match on the 20, 15, and 10-meter bands.
Modeling
Theoretically, the antenna has an impedance of 200 Ω, but that impedance will depend on the ground's height and conductivity. To understand what impedance to expect on the harmonics, I have modeled the antenna on my favorite antenna modeling software2.
We will set up the antenna in a public park, and installing it at the optimum height will be impossible. I suggest installing the antenna slopping at 45 degrees. I am using the modeling software to help me see how the impedance and the radiation pattern will be affected if we install the antenna slopping in one direction.
The following graph shows a minimal return loss / VSWR impact between the antenna installed at 90 (straight up) or 45 degrees. The most significant effect is on the radiation pattern. Typically, that antenna has a similar radiation pattern to a dipole, but slanting it at 45 degrees gives it a nice gain in one direction on some bands.

The following graphs show the interesting radiation pattern for an antenna installed at 45 degrees and the feed point at 1 meter off the ground. It is interesting to see a slight gain toward the X-axis on the 20, 15, and 10-meter bands.

Matching
On every band, the antenna presents an impedance between 100 and 300Ω. Now, we need to find a way to match that impedance to the impedance of our radio, 50 Ω.

Matching the antenna to the radio can be achieved in 2 ways. We can use a piece of a 3-meter 75 Ω coax or a 4:1 transformer. The graph below shows the difference between the two methods.
The graph below compares a matching network using a coax or a transformer. It shows that by utilizing a coax, we can better match the 40 and 20-meter bands with a VSWR below 1.5:1, but on 20 and 10 meters, the VSWR is just slightly below 3. On the contrary, a transformer will give a great VSWR on 20 and 10 and a decent VSWR (around 2) on 40 and 15.

Conclusion
As the table below shows, this antenna should perform well with an antenna tuner in the shack and no matching network at the feed point. The power loss due to the mismatch can be improved using an impedance-matching network as simple as a few meters of 75 Ω coax.
| Setup | 40 m | 20 m | 15 m | 10 m |
|---|---|---|---|---|
| No matching network with tuner | 85 W | 72 W | 77 W | 65 W |
| 75Ω coax match | 82 W | 68 W | 80 W | 64 W |
| 75Ω coax match and internal tuner | 89 W | 83 W | 83 W | 75 W |
| 4:1 transformer | 74 W | 88 W | 76 W | 84 W |
| 4:1 transformer and internal tuner | 89 W | 89 W | 84 W | 85 W |
Note
The table shows the power transferred to the antenna (cable loss + VSWR loss), with a 100 Watt source and 50 feet of RG8x cable.
Of course, all these data and graphs come from the antenna modeling software. Reality will be different because the environment, such as the antenna's height and surroundings, buildings, trees, and soil, will affect the impedance and resonance. Modeling the antenna will give us a good idea of what impedance and power transfer to expect and allow me to be ready to help the participants achieve that goal.
The following post include pictures of the antenna construction and more graphs showing our results.