dB, dBm & RF Power Units

The decibel (dB) is the most important unit in RF engineering. It turns multiplication into addition, making cascade analysis practical. Once you're fluent in dB arithmetic, working with gain, loss, and power levels becomes fast and intuitive.

Why Logarithmic Scales?

A receiver handles signals ranging from 10⁻¹⁵ W (noise floor) to 10⁻³ W (nearby transmitter) — a range of 10¹². Writing and plotting these on a linear scale is impractical. Logarithms compress that 10¹² ratio to a 120 dB range that fits on a graph. More importantly, a cascade of gain and loss stages multiplies powers together — in dB you just add.

The Decibel (dB)

The decibel expresses a ratio between two power values:

For voltage or current ratios (into the same impedance), the factor is 20 instead of 10 because power is proportional to voltage squared:

Key values to memorise:

Power ratio	Voltage ratio	dB	Memory aid
10×	3.16×	+10 dB	One order of magnitude
2×	1.41×	+3 dB	Double the power
1.26×	1.12×	+1 dB	Smallest audible difference
1×	1×	0 dB	No change
0.5×	0.71×	−3 dB	Half the power
0.1×	0.316×	−10 dB	One tenth
0.001×	0.0316×	−30 dB	One thousandth

Absolute Power: dBm and dBW

dB alone is a ratio — it needs a reference to become an absolute level. dBm uses 1 milliwatt as the reference:

dBW uses 1 watt. The conversion: P(dBm) = P(dBW) + 30.

Power	dBm	dBW	Context
1 kW	+60 dBm	+30 dBW	AM broadcast transmitter
10 W	+40 dBm	+10 dBW	Handheld radio TX
1 W	+30 dBm	0 dBW	Bluetooth TX max
100 mW	+20 dBm	−10 dBW	Wi-Fi typical
1 mW	0 dBm	−30 dBW	Reference level
1 µW	−30 dBm	−60 dBW	Strong receiver input
1 nW	−60 dBm	−90 dBW	Typical receiver input
−100 dBm	−100 dBm	−130 dBW	Near noise floor
10⁻¹⁵ W = 1 fW	−120 dBm	−150 dBW	Thermal noise floor, 1 MHz BW, room temperature

dB Arithmetic in Cascades

This is where dB pays off. A system with a 20 dB LNA, a 7 dB cable loss, a 10 dB mixer loss, and 30 dB of IF gain, driven by a −90 dBm signal:

Compare doing this in linear: 10⁻¹² × 100 × 0.2 × 0.1 × 1000 = 2×10⁻¹² W. Much harder to get right mentally.

Other dB Variants

Unit	Reference	Use
dBm	1 mW	Absolute RF power, transmitters and receivers
dBW	1 W	Satellite EIRP specifications
dBc	Carrier power	Relative: spurious, harmonics, phase noise
dBi	Isotropic antenna	Antenna gain (absolute)
dBd	Half-wave dipole	Antenna gain (relative to dipole). 0 dBd = 2.15 dBi
dBµV	1 µV	EMC and receiver sensitivity specifications in Europe
dBµV/m	1 µV/m	Field strength in EMC measurements
dBFS	Full scale	Digital audio and ADC levels (always ≤ 0 dBFS)

Noise Floor and kTB

Thermal noise power available from a resistor at temperature T in bandwidth B:

In a bandwidth B (Hz): \(P_{noise} = -174 + 10\log_{10}(B)\) dBm. In 1 MHz bandwidth: −174 + 60 = −114 dBm. In 20 MHz (Wi-Fi): −174 + 73 = −101 dBm. Add the receiver noise figure to get the actual noise floor.

Converting Back to Linear

Shortcut: 0 dBm = 1 mW, every +10 dB multiplies by 10, every +3 dB doubles.