For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
\mathrm{dBm} = 10\log_{10}\frac{P}{1\ \mathrm{mW}}, \qquad \mathrm{dBW} = \mathrm{dBm} - 30P = \frac{V^2}{Z}, \qquad \mathrm{dB}\mu\mathrm{V} = 20\log_{10}\frac{V}{1\ \mu\mathrm{V}} = \mathrm{dBm} + 90 + 10\log_{10} ZS = \frac{E^2}{\eta_0}, \qquad \eta_0 = 376.730\ \Omega1\ \mathrm{W/m^2} = 0.1\ \mathrm{mW/cm^2}\lambda = \frac{c}{f}, \qquad \lambda_\mathrm{dielectric} = \frac{c}{f\sqrt{\varepsilon_r}}Variables
| Symbol | Meaning | Unit |
|---|---|---|
P | Power | W |
V | RMS voltage across the load | V |
Z | Load impedance | Ω |
E | Electric field strength (rms) | V/m |
S | Power density, far-field plane wave | W/m² |
\eta_0 | Impedance of free space | Ω |
Worked example
| Input | Value |
|---|---|
| Power | 30 dBm |
30 dBm is 1 W, 0 dBW, and 7.07 V rms across 50 Ω (136.99 dBµV). Every +3 dB roughly doubles the power; every +10 dB is ten times.
Load this example in the calculatorValidity
- Voltages are RMS. Peak voltage for a sine wave is √2 times larger.
- The field-strength relation holds in the far field of the antenna, in free space.
- dBµV depends on the impedance; the tool defaults to 50 Ω.
Sources
- ITU-R Recommendation V.574, Use of the decibel and the neper in telecommunications.
- CODATA 2018 recommended values (speed of light, impedance of free space).