Decibels and power

Almost every number in radio is a ratio, and ratios in radio are written in decibels. Learning to think in dB saves money, because it tells you which upgrades are worth buying.

The three numbers to memorize

Everything else is built from these. Twenty times is 10 dB + 3 dB = 13 dB. One hundred times is 20 dB. A tenth of the power is −10 dB.

The formula behind the table is dB = 10 × log10(P2 / P1) for power, and dB = 20 × log10(V2 / V1) for voltage — the factor of 20 exists because power goes as the square of voltage.

dB versus dBm, dBd and dBi

A plain "dB" is a comparison with no reference and means nothing on its own. The suffixed forms do:

• dBm — power referred to one milliwatt. 0 dBm = 1 mW, 30 dBm = 1 W, 60 dBm = 1 kW. Receiver

sensitivity is quoted here (a strong signal might be −73 dBm, which is S9).

• dBd — antenna gain compared with a dipole. dBi compares with an isotropic radiator and

reads about 2.15 dB higher for the same antenna. Manufacturers prefer dBi; when comparing two antennas, make sure both are in the same units.

• dBW, dBc, dBV — referred to a watt, a carrier and a volt.

What that means for your station

An S-unit on most receivers is nominally 6 dB, so a full S-unit needs four times the power. Going from 25 W to 100 W moves the other operator's meter by one unit; going from 100 W to 1500 W moves it by about two and a half. Antenna height and pattern usually beat both.

Losses subtract in the same currency:

• 100 feet of RG-58 at 28 MHz costs roughly 2.5 dB — nearly half your power, before the antenna sees

it. The same run of LMR-400 costs well under 1 dB.

• A 1.5:1 SWR costs about 0.2 dB of mismatch loss. This is why chasing a perfect match matters far

less than most people believe; see feedline, SWR and tuners.

• Each connector, switch and choke adds a small amount. On HF it is negligible; at 440 MHz and above

it is not.

ERP and EIRP

Repeater coordination and some rules are written in terms of effective radiated power — power at the antenna plus gain minus loss, referred to a dipole (ERP) or an isotropic radiator (EIRP). A 50 W transmitter, 2 dB of line loss and a 6 dBd antenna gives 48 dBm + 6 − 2 = 52 dBm, about 160 W ERP.

Part 97 also has a handful of power limits expressed as PEP output at the transmitter and, on 630 m and 2200 m, as EIRP — the only bands where you must do the ERP arithmetic to stay legal.

Power ratios worth remembering

• QRP is 5 W. Compared with 100 W that is −13 dB: two S-units. People work the world with it; see

QRP operating.

• FT8 and other weak-signal modes decode about 20–25 dB below what an ear can hear, which is worth

more than any amplifier you can buy.

• Doubling antenna height on HF often gains more than doubling power, because it changes the takeoff

angle rather than the amplitude.