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Decibels & dBm

Decibels & dBm: the circuit drawn with the example's values
3.01 dB = × 2 in power

A decibel is a ratio on a log scale: +3 dB doubles the power, +10 dB is ten times.

Opens in the app on 1 December, with Circuit Notebook 1.0 See it worked out

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The example, worked out

Given

Convert
Ratio → dB
The ratio is of
Power (10 log)
Ratio (out / in)
2

Working

  1. power: 10 log

Results

Decibels3.01 dB
Power ratio× 2
Same dB as a voltage ratio× 1.414

The formulas

  1. dB = 10 log10(P2 / P1) = 20 log10(V2 / V1)power 10 log, voltage 20 log
  2. P = 1 mW × 10^(dBm / 10)0 dBm is one milliwatt
  3. Vrms = √(P × Z)the voltage of a power in an impedance

The usual traps

  • 3 dB is twice the power but only 1.41 times the voltage.
  • dBm is an absolute level; dB is a ratio: they add, they do not multiply.

Questions

How do I convert decibels to a power or voltage ratio?

dB = 10 log10(P2 / P1) = 20 log10(V2 / V1): power 10 log, voltage 20 log. P = 1 mW × 10^(dBm / 10): 0 dBm is one milliwatt. Vrms = √(P × Z): the voltage of a power in an impedance.

What does it give for typical values?

3.01 dB = × 2 in power. Decibels: 3.01 dB.

What are the usual mistakes?

3 dB is twice the power but only 1.41 times the voltage. dBm is an absolute level; dB is a ratio: they add, they do not multiply.

In the app

Your circuit, drawn live

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The part you can buy

Results rounded to standard values (E12, E24, E96) and power ratings.

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Opens in the app on 1 December, with Circuit Notebook 1.0

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