dBm, dBW and watts

Three anchors and two rules of thumb cover most of the arithmetic an RF engineer does in a day.

Why decibels at all

A link budget spans an absurd range. A microwave transmitter puts out a few watts. The receiver at the far end is working with something around a hundred femtowatts — 10⁻¹³ watts.

Written in watts, a budget runs across fourteen orders of magnitude, and nobody can scan a column like that and spot an error. Written in decibels it is a list of two-digit numbers that add up.

That is the actual reason for the unit. Not compression for its own sake, but turning multiplication into addition, so that a chain of a dozen components can be checked by reading down a page. Every gain and loss in a system multiplies; in decibels they simply add.

The three anchors

0 dBm = 1 mW. By definition. The m in dBm means the reference is one milliwatt.

30 dBm = 1 W. Because 30 dB is a factor of 1000, and a thousand milliwatts is a watt.

0 dBW = 1 W. dBW references a watt instead of a milliwatt, so dBm and dBW always differ by exactly 30. A figure quoted in dBW is a figure in dBm minus 30, every time, with no exceptions.

The two rules of thumb

10 dB is exactly ten times. Not approximately — exactly, by construction.

3 dB is very nearly double. The exact figure is 3.0103 dB, and treating it as 3 is fine for anything but a precision measurement.

Between those two, most everyday arithmetic goes in your head:

• 40 dBm is 10 W. (30 dBm is 1 W, plus 10 dB is ten times.)
• 43 dBm is 20 W. (40 dBm plus 3 dB doubles it.)
• 37 dBm is 5 W. (40 dBm minus 3 dB halves it.)
• −30 dBm is a microwatt. (0 dBm is a milliwatt, minus 30 dB divides by a thousand.)

A receiver threshold of −80 dBm is 10⁻¹¹ watts — ten picowatts. Which is a good illustration of why nobody works in watts.

dB and dBm are not the same thing

This trips people up constantly, and the distinction is worth being pedantic about.

dB is a ratio. It describes a relationship between two powers — a gain, a loss, a margin. “The feeder loses 3 dB” is a complete statement.

dBm is an absolute level. It describes a power, referenced to a milliwatt. “The output is 30 dBm” is a complete statement.

So you can add a dB figure to a dBm figure and get a dBm figure — that is exactly what a link budget does. You cannot meaningfully add two dBm figures together. Two transmitters each at 30 dBm do not make 60 dBm; they make 33 dBm, because the powers add, not the decibels.

Antenna gain in dBi is a ratio too, referenced to an isotropic radiator. dBd references a half-wave dipole instead, and the two differ by 2.15 dB — a figure quoted in dBd is 2.15 higher than the same antenna in dBi.

Adding powers, when you have to

Occasionally you genuinely need to add two levels — two carriers in the same amplifier, or an interferer on top of a noise floor. Convert to watts, add, convert back. There is no shortcut in the decibel domain.

One useful special case: two equal powers combine to exactly 3 dB above either one. Which is the same rule of thumb, running in the other direction.

Frequency and wavelength

The relationship is λ = c / f, and the number worth carrying is that 300 MHz is almost exactly one metre. From there everything scales: 3 GHz is 10 cm, 30 GHz is 1 cm, 6 GHz is 5 cm.

The catch is that c is the speed in the medium, not in vacuum. Inside coaxial cable the wave travels at typically 66% to 85% of the vacuum figure; in optical fibre about 67%. A quarter-wave stub cut to the free-space figure will be too long, which is what the velocity factor exists to correct.

Frequently asked questions

How many watts is 30 dBm?

Exactly one watt. dBm is referenced to a milliwatt and 30 dB is a factor of 1000, so 30 dBm is 1000 mW.

What is the difference between dBm and dBW?

The reference. dBm is relative to a milliwatt, dBW to a watt, so they always differ by exactly 30. A figure in dBW is the same figure in dBm minus 30.

Is 3 dB exactly double?

Almost. The exact figure is 3.0103 dB. Treating it as 3 is fine for everything except precision measurement, and 10 dB genuinely is exactly ten times.

Can I add two dBm figures together?

No. dBm is an absolute level, and adding two of them is meaningless. Two transmitters at 30 dBm each produce 33 dBm, not 60 — the powers add, not the decibels. Convert to watts, add, convert back.

What is the difference between dBi and dBd?

The reference antenna. dBi is relative to an isotropic radiator, dBd to a half-wave dipole, and they differ by 2.15 dB. The same antenna quoted in dBd shows 2.15 lower than in dBi, so mixing them understates gain.

Why is my quarter-wave stub too long?

Because the wave travels slower in cable than in free space — typically 66% to 85% of the vacuum speed in coax. The physical length must be scaled by that velocity factor.

What frequency is one metre?

Almost exactly 300 MHz — the precise figure is 299.79 MHz. From there everything scales: 3 GHz is 10 cm, 30 GHz is 1 cm.