The formula
% remaining = 100 × 10^(−dB ÷ 10) · dB = −10 × log10(% remaining ÷ 100)
Decibels are a ratio on a log scale, so equal steps in dB are equal fractions of the light, not equal amounts. Every 3 dB halves what is left, and every 10 dB cuts it to a tenth.
Worked example
A 1×32 splitter loses about 16.5 dB. 10^(−1.65) = 0.022, so only about 2.2% of the light reaches each output, which is why the splitter dominates every PON loss budget. A good fusion splice at 0.05 dB lets 98.9% through.
dB to percent table
| Loss (dB) | Remaining | Lost |
|---|---|---|
| 0.05 | 98.9% | 1.14% |
| 0.1 | 97.7% | 2.28% |
| 0.3 | 93.3% | 6.67% |
| 0.5 | 89.1% | 10.9% |
| 0.75 | 84.1% | 15.9% |
| 1 | 79.4% | 20.6% |
| 2 | 63.1% | 36.9% |
| 3 | 50.1% | 49.9% |
| 6 | 25.1% | 74.9% |
| 10 | 10.0% | 90.0% |
| 15 | 3.16% | 96.8% |
| 17 | 2.00% | 98.0% |
| 20 | 1.00% | 99.0% |
| 28 | 0.158% | 99.8% |
| 30 | 0.100% | 99.9% |
Where these numbers show up
- 0.05 to 0.3 dB: fusion splices. Each one costs a percent or a few.
- 0.3 to 0.75 dB: mated connector pairs. 0.75 dB, the TIA design maximum, loses about 16% of the light.
- 3 dB: half the light. A 1×2 splitter, at best.
- 20 to 28 dB: a full PON link. At 28 dB, the GPON class B+ maximum, about 0.16% of the light launched reaches the ONT, and it still works.
To convert an absolute power reading instead of a loss, use the dBm to mW converter.