dBm, W and dBµV: Sorting Out Units That Get Mixed Up

On an EMC test bench one screen can show dBm, dBµV and dB(µV/m) while the datasheet quotes watts and dBW. The names look alike, and one wrong conversion shifts a result by several dB or even tens of dB. This guide explains what each unit measures, how to convert between them and where people most often slip, with worked examples.

1. What each unit measures

2. The basic formulas

• dBm = 10·log₁₀(P / 1 mW), and P(mW) = 10^(dBm/10). 0 dBm is 1 mW and 30 dBm is 1 W.
• dBW = dBm − 30. The same power written in dBW is a number 30 smaller.
• dBµV = 20·log₁₀(V / 1 µV). Power is proportional to voltage squared, so the factor is 20 rather than 10.
• Voltage and power are linked by P = V² / R. In 50 Ω, dBm = dBµV − 107. In 75 Ω, dBm = dBµV − 108.75.
• Where 107 comes from: 1 µV across 50 Ω is (10⁻⁶)² / 50 = 2×10⁻¹⁴ W = −137 dBW = −107 dBm.

3. Worked example: from signal generator to receiver

A signal generator delivers 0 dBm into a 50 Ω load. The power is 1 mW and the voltage is V = √(P·R) = √(0.001 × 50) = 0.2236 V. In dBµV that is 20·log₁₀(0.2236 / 10⁻⁶) = 106.99 dBµV, which rounds to 107 dBµV. This matches the shortcut dBm + 107.

(Calculators: dBm ↔ W, dBm ↔ dBµV)

Now the other direction. A 5 W transmitter is 5000 mW, so 10·log₁₀(5000) = 36.99 dBm, or 6.99 dBW. In 50 Ω that is 36.99 + 107 = 143.99 dBµV, and the voltage is √(5 × 50) = 15.8 V.

The same conversion is needed in pre-compliance work with a spectrum analyzer. If the analyzer shows −59 dBm in 50 Ω, the level is −59 + 107 = 48 dBµV, and the voltage is 10^(48/20) = 251 µV. Conducted emission limits are written in dBµV, so convert first and compare second.

The voltage conversion does not depend on impedance. Impedance only matters when you convert to power. (Calculator: dBµV ↔ V)

4. Situations where the units get mixed up

• dBm versus dB: dBm is absolute power and dB is a ratio. 20 dBm plus a 3 dB gain is 23 dBm. But two 20 dBm signals do not add up to 40 dBm; if they are unrelated, the sum is 23 dBm. Since 1 W + 1 W = 2 W, 30 dBm + 30 dBm = 33 dBm. (Calculator: dB level summation)
• 10 versus 20: use 10·log for power and 20·log for voltage or field. Doubling the voltage is +6 dB and doubling the power is +3 dB.
• dBm versus dBW: they differ by 30. If you do not check whether a datasheet uses dBW or dBm, the result is 30 dB off.
• Impedance: the 107 offset is valid only for 50 Ω. Using it in a 75 Ω system gives a 1.75 dB error.
• dBµV versus dB(µV/m): the first is a voltage at the receiver input and the second is a field strength at the antenna. Antenna factor (AF) and cable loss connect them: E (dBµV/m) = V (dBµV) + AF (dB/m) + cable loss (dB). Example: 30 dBµV + AF 12 dB(1/m) + 2 dB cable = 44 dB(µV/m). (Calculator: dBµV/m ↔ V/m)
• Detector: for the same signal, the peak, quasi-peak and average readings of an EMI receiver differ. When comparing against a limit, use the detector the limit specifies.

5. Habits that catch conversion errors

• Memorise one anchor point: in 50 Ω, 0 dBm = 107 dBµV. If a result is far off, suspect the unit first.
• Convert back and check that you recover the original value.
• Write the unit and the impedance next to every number in a table. A bare number copied without them cannot be interpreted later.