dB: definition and intuition
Common units in RF include dB, dBm, and dBW. When readers see dBm and dBW they often wonder why conventional prefixes like milli, kilo, or mega are not used. Signals from a transmitter can be orders of magnitude larger or smaller than signals at a receiver, so logarithms are used to convert multiplication and division into addition and subtraction.
In RF the key points about logarithms are: first, a logarithm expresses the ratio of two values; second, that ratio is expressed in decibels (dB). The definition is 10·log10(output power / input power). For amplifiers using voltage, the definition is 20·log10(output voltage / input voltage).
For example, if an amplifier increases signal power by a factor of 100, the gain in decibels is 20 dB. If an amplifier increases signal voltage by a factor of 100, the gain in decibels is 40 dB. Note that power ratios use the factor 10 while voltage or current ratios use the factor 20.
Common dB conversions for quick work
- +3 dB = 2×
- +10 dB = 10×
- -3 dB = 1/2
- -10 dB = 1/10
- 0 dB = 1 (no change)
Example 1: Convert linear gain to dB
If an amplifier has a linear gain of 4000, what is the gain in dB?
Formula method: use the definition G(dB) = 10·log10(G).
Quick factor method: 4000 = 2 × 2 × 10 × 10 × 10, so gain = 3 dB + 3 dB + 10 dB + 10 dB + 10 dB = 36 dB. The quick method avoids a calculator and gives the same result for simple values.
Example 2: Small linear gain to dB
If the linear gain is 0.000125, what is the gain in dB?
Formula method: use G(dB) = 10·log10(G).
Quick factor method: 0.000125 = 1 ÷ 2 ÷ 2 ÷ 2 ÷ 10 ÷ 10 ÷ 10, so gain = 0 dB - 3 dB - 3 dB - 3 dB - 10 dB - 10 dB - 10 dB = -39 dB.
dBm and dBW: power reference units
dBm and dBW are power units referenced to fixed power levels. By definition, 0 dBm = 1 mW and 0 dBW = 1 W. Using these references avoids very large or very small absolute numbers when comparing RF power levels.
Conversion between watts and dBm:
Conversion between watts and dBW:
Note that +30 dBm = 0 dBW, and -30 dBW = 0 dBm. In RF engineering the most commonly used power unit is dBm.
Example 3: Convert dBm to watts
A device has an output power of 33 dBm. What is the power in watts?
33 dBm = 0 dBm + 10 dB + 10 dB + 10 dB + 3 dB = 1 mW × 10 × 10 × 10 × 2 = 2 W. So the device output power is 2 W.
Example 4: Convert milliwatts to dBm
A device has an output power of 0.00025 mW. What is the power in dBm?
0.00025 mW = 1 mW ÷ 10 ÷ 10 ÷ 10 ÷ 2 ÷ 2 = 0 dBm - 10 - 10 - 10 - 3 - 3 = -36 dBm. So the device output power is -36 dBm.
