How it works
A voltage ratio is converted to dB with a factor of 20 times log10, and a power ratio with a factor of 10. dBm is an absolute power unit that sets 1 mW to 0 dBm.
Voltage ratio in dB = 20 × log10(V2 / V1)Power ratio in dB = 10 × log10(P2 / P1)P[W] = 10^((dBm − 30) / 10)dBm = 10 × log10(P[W]) + 30Vrms = √(P × R), Vpp = Vrms × 2√2
Worked example
10 dBm is 10 mW. In a 50 Ω system this power corresponds to 0.707 V rms, and the peak-to-peak value of a sine wave is about 2.00 V. A voltage ratio from 1 V to 10 V is 20 dB, and a power ratio from 1 mW to 100 mW is also 20 dB.
Design tips
- Useful values to remember: 3 dB is twice the power, 6 dB is twice the voltage, 10 dB is ten times the power, and 20 dB is ten times the voltage.
- dBm only has meaning with a reference impedance. RF usually uses 50 Ω, audio 600 Ω, and video 75 Ω. Changing the reference impedance changes the voltage for the same dBm.
- Units such as dBV and dBu on instruments use different reference voltages. Check the reference of your meter first.
- Attenuation is shown as a negative dB value. −3 dB means the power is halved.
Limitations
- A voltage dB and a power dB give the same result only at the same impedance. When comparing two points with different impedances, calculate with power.
- Vpp = Vrms × 2√2 applies only to sine waves. Pulses and modulated signals have different peak values.
- Inputs must be greater than zero for the logarithm to be defined.
Frequently asked questions
What is the difference between dB and dBm?
dB is a relative unit for the ratio of two values. dBm is an absolute power unit referenced to 1 mW. A dB value without a reference is incomplete.
Why are the voltage dB and power dB formulas different?
Voltage relates to power through the square, so voltage uses 20 log and power uses 10 log. At the same impedance, a voltage ratio of 2 (6 dB) and a power ratio of 4 (6 dB) give the same dB value.
Which waveforms does the Vrms to Vpp conversion apply to?
Vpp = Vrms × 2√2 applies only to sine waves. Square and triangle waves have different Vpp relationships for the same RMS value, so check them on an oscilloscope.