Understanding the RF unit converter — concept and principle
This converter changes radio-frequency signal levels between dBm, dBW, watts, milliwatts, dBµV, dBmV and RMS volts for a given system impedance, usually 50 Ω or 75 Ω. It also shows the peak-to-peak voltage of a sine wave. Radio amateurs, RF engineers, technicians and students use it to read datasheets and test equipment.
How it is calculated
- dBm = 10 × log₁₀(P ÷ 1 mW); dBW = dBm − 30
- P = V² ÷ R, with V the RMS voltage across a resistive load R
- dBµV = 20 × log₁₀(V ÷ 1 µV); dBmV = dBµV − 60
- Peak-to-peak voltage of a sine = 2√2 × V(RMS)
The principle
Decibels express ratios on a logarithmic scale, which keeps huge ranges of signal level manageable and turns gains and losses into additions. Power ratios use 10 × log₁₀; voltage ratios use 20 × log₁₀ because power is proportional to the square of voltage. A level in dBm or dBµV is an absolute level relative to a fixed reference (1 mW or 1 µV). Because P = V²/R, the same power produces a different voltage in a 50 Ω and a 75 Ω system: 0 dBm is 107.0 dBµV at 50 Ω and 108.8 dBµV at 75 Ω.
Worked example
Defaults: 10 dBm at 50 Ω.
- P = 10^((10 − 30) ÷ 10) = 0.01 W = 10 mW; dBW = -20.
- V = √(0.01 × 50) = 0.707107 V RMS.
- dBµV = 20 × log₁₀(0.707107 ÷ 10⁻⁶) = 116.99; dBmV = 56.99.
- Peak-to-peak = 0.707107 × 2√2 = 2 V.
dBm: 10.
| Value | Power (dBm) |
|---|---|
| 2.5 | 2.5 |
| 5 | 5 |
| 7.5 | 7.5 |
| 10 | 10 |
| 12.5 | 12.5 |
| 15 | 15 |
| 20 | 20 |
How to read the result
Every 3 dB doubles the power and every 10 dB multiplies it by ten. A signal 6 dB stronger has twice the voltage. When comparing receiver sensitivity or cable loss, make sure both figures use the same impedance and reference.
Common mistakes
- Using 10 × log₁₀ for voltage ratios.
- Mixing 50 Ω and 75 Ω figures.
- Reading peak-to-peak or peak voltage as RMS.
- Applying the sine-wave peak factor to modulated or noise signals.
Frequently asked questions
How many milliwatts is 0 dBm?
1 mW.
What is the difference between dBm and dBW?
dBW is referenced to 1 W, so dBW = dBm − 30.
Why does impedance matter for dBµV?
Voltage depends on impedance for the same power, since P = V²/R.
Sources: ITU-R Recommendation V.574-4 (2000), "Use of the decibel and the neper in telecommunications"