Radio Remi guidesA technician must decide whether free-space wavelength is safe before changing classic channel frequency on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.
See the relationship before changing it
The figure reads from left to right. The blue card is classic channel frequency. The middle card applies this page's rule. The green card is free-space wavelength. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only classic channel frequency, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 2480 MHz.
- 2
Name the relationship. wavelength = 300,000 / frequency in MHz
- 3
Substitute with units. 300,000 / 2,480 = 120.97 mm
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change classic channel frequency
Try Predict the direction of wavelength = 300,000 / frequency in MHz. Test another classic channel frequency, then compare free-space wavelength.
Observe The wavelength changes only slightly across the Classic Bluetooth band. Reset classic channel frequency to 2480 and compare free-space wavelength.
Explain The wavelength changes only slightly across the Classic Bluetooth band.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
1. Frequency and wavelength share one speed
Radio waves travel near the speed of light. If their cycles happen more often each second, each wave must be shorter. A quarter-wave is one common starting scale for a resonant PCB or chip antenna.
2. Name every algebra move
Divide speed by frequencyλ=c/f.
Take one quarterℓ=λ/4.
Compare fixed-distance lossΔFSPL=20log10(fhigh/flow).
3. Distance cancels in the edge comparison
Both channels travel the same 10 m in the worked comparison. Their ratio therefore depends only on frequency, while real reflections and interferers remain outside this clean baseline.
4. Try one controlled change
TryMove from the low edge to the high edge while distance stays at 10 m.
ObserveAt 2480 MHz the wavelength is about 120.97 mm, the quarter-wave is 30.24 mm, and the clean loss is only 0.278 dB above 2402 MHz.
ExplainThe hop set is narrow relative to its centre. A well-matched broadband Bluetooth antenna can cover it, but room reflections and interferers can still make individual channels poor.
Free-space wavelength gives a starting scale, not a finished antenna.
- Substrate and ground
- Change electrical length and matching
- Enclosure and body
- Load and detune the antenna
- Channel and orientation
- Change the realised link
Use antenna measurements, efficiency, multipath, and interference evidence for the installed design.
5. Reproduce the chapter values
At 2402 MHz, λ=3.00×10⁸/(2.402×10⁹)=124.9 mm and λ/4=31.2 mm. At 2480 MHz, λ=120.97 mm and λ/4=30.24 mm, a 0.982 mm change. At 10 m, FSPL moves from 60.05 to 60.33 dB, so Δ=20log10(2480/2402)=0.278 dB.
6. Carry the evidence forward
Keep antenna geometry and match, enclosure, device orientation, conducted and radiated tests, per-channel RSSI/PER, interference scan, AFH map, temperature, and representative room checks.
7. Check yourself
Why does wavelength shrink as frequency rises?
Does 0.278 dB make all channels equally reliable?
What does AFH respond to?
The page compares ideal free-space values across the Bluetooth hop band.
- 2,402 MHz
- Lower stated hop centre
- 2,480 MHz
- Upper stated hop centre
- Quarter-wave and FSPL
- Ideal scale and ideal spreading loss
The small ideal differences do not prove antenna or channel performance.