Geometric Mean: The Secret to Multiband RDF Balance

When designing multiband RX arrays—especially phased arrays like our EchoTriad (our 3-element trilateral system) or QuadraTus (our FourSquare system)—the challenge is choosing a spacing that works across several bands without sacrificing performance. Most hams instinctively pick a spacing based on one band (usually the lowest), but that tends to result in skewed RDF on higher bands. The solution? Use the geometric mean of the wavelengths involved.

The geometric mean offers a way to balance RDF performance across multiple bands. Unlike the arithmetic mean, which treats frequencies linearly, the geometric mean respects the logarithmic nature of frequency and wavelength scaling. It's the only averaging method that gives equal weight (in dB terms) to both ends of the spectrum.

Why It Works

Imagine you're optimizing an RX array for both 160m and 80m. Pick a spacing that works perfectly at 160m, and RDF on 80m may collapse. Optimize for 80m, and 160m may suffer. But if you calculate the geometric mean wavelength:

λ_mean = sqrt(λ_160 × λ_80)

...and then use a fixed lambda-fraction spacing (like 0.139λ for a 3-pole equilateral array or 0.20λ for a 4-square), you'll often land on a spacing that keeps RDF within a sweet spot across both bands.

Real-World Example

Say we’re designing a 3-element triangular RX array for both 160m (1.83 MHz) and 80m (3.6 MHz):

  • λ_160 = 164m
  • λ_80 = 83.3m
  • λ_mean = sqrt(164 × 83.3) ≈ 117.1m

Then 0.139 × 117.1m ≈ 16.3 meters spacing between elements.
This spacing won’t give you the absolute peak RDF at either 160m or 80m, but will provide solid RDF on both, and avoid destructive nulls or overly broad lobes.

Multiband Extensions

Want to optimize for 160–40m? Just apply the same idea:

λ_mean = √(λ_160 × λ_40) = √(164 × 20.7) ≈ 58.3m
spacing = 0.139 × 58.3 ≈ 8.1 meters

That’s a usable compromise that keeps lobes tight and RDF above 8dB from 40m down to 160m.

Conclusion

Using the geometric mean of wavelengths and then applying your array’s optimal lambda-fraction spacing (e.g., 0.20λ for QuadraTus, 0.139λ for EchoTriad) is the cleanest way to make your multiband RX system sing across the bands. It’s not a compromise—it’s balanced optimization.

 

Interested in more technical content like this? Subscribe to our notification list — we only send updates when new articles or blogs are published: https://listmonk.rf.guru/subscription/form

Questions or experiences to share? Feel free to contact RF.Guru or join our feedback group!

Written by Joeri Van Dooren, ON6URE – RF, electronics and software engineer, complex platform and antenna designer. Founder of RF.Guru. An expert in active and passive antennas, high-power RF transformers, and custom RF solutions, he has also engineered telecom and broadcast hardware, including set-top boxes, transcoders, and E1/T1 switchboards. His expertise spans high-power RF, embedded systems, digital signal processing, and complex software platforms, driving innovation in both amateur and professional communications industries.