Decibels
| Decibels | |
|---|---|
| Symbol | dB |
| What it is | A logarithmic way of expressing the ratio between two power levels |
| Power formula | dB = 10 × log (P2 / P1) |
| Voltage formula | dB = 20 × log (V2 / V1), at the same impedance |
| Rules of thumb | |
| 3 dB | Twice the power (−3 dB is half) |
| 10 dB | Ten times the power |
| One S-unit | 6 dB, four times the power |
| 0 dBm | 1 milliwatt |
Decibels (dB) are the units hams use to compare power levels: transmitter output, signal strength, antenna gain and the loss in a feed line. A decibel figure is a ratio, not an amount, and it is logarithmic, so each step stands for a multiplication rather than an addition. The unit is one tenth of a bel, named after Alexander Graham Bell.
Logarithms suit radio because the numbers involved span an enormous range. A transmitter may put out 100 watts, while a strong signal reading S9 at the far end delivers about 50 trillionths of a watt to the receiver. That ratio of two trillion to one is simply 123 dB.
The basic formula
The decibel difference between two powers is 10 times the logarithm (base 10) of their ratio:
- dB = 10 × log (P2 / P1)
Raising 100 watts to 1,000 watts is a ratio of 10, and the log of 10 is 1, so the change is 10 dB. Raising 100 watts to 200 watts is 3 dB; dropping it to 50 watts is −3 dB. Because power is proportional to the square of voltage, voltage ratios use 20 instead of 10, so doubling the voltage across the same impedance is 6 dB.
| Decibels | Power ratio | Decibels | Power ratio |
|---|---|---|---|
| 1 dB | 1.26 | −1 dB | 0.79 |
| 3 dB | 2 | −3 dB | 1/2 |
| 6 dB | 4 | −6 dB | 1/4 |
| 10 dB | 10 | −10 dB | 1/10 |
| 20 dB | 100 | −20 dB | 1/100 |
| 30 dB | 1,000 | −30 dB | 1/1,000 |
Adding decibels is the same as multiplying ratios. 13 dB is 10 dB plus 3 dB, so it is 10 × 2 = 20 times the power. 7 dB is 10 dB minus 3 dB, or 10 ÷ 2 = 5 times.
S-units
A receiver's S-meter shows signal strength in S-units. Under the standard recommended by IARU Region 1, part of the International Amateur Radio Union, one S-unit is 6 dB, a fourfold change in power, and S9 below 30 MHz is 50 microvolts at the antenna input. On 144 MHz and higher bands the recommended S9 is 5 microvolts, 20 dB lower. Many S-meters are not accurately calibrated, so treat their readings as rough.
S-units show why modest power changes make little difference on the air. Doubling power adds 3 dB, half an S-unit. Going from 100 watts to a 1,500-watt amplifier, a ratio of 15, adds about 11.8 dB, just under two S-units. A QRP station running 5 watts is 13 dB, a little over two S-units, below a 100-watt station. A change of about 1 dB is often given as the smallest a listener can notice.
dBm and other references
A decibel figure becomes an absolute measurement when it is stated against a fixed reference, shown by letters after "dB".
- dBm is decibels relative to 1 milliwatt. 0 dBm is 1 milliwatt, 30 dBm is 1 watt, 40 dBm is 10 watts, 50 dBm is 100 watts and 60 dBm is 1,000 watts. S9 is about −73 dBm below 30 MHz and about −93 dBm on 144 MHz and higher bands.
- dBW is decibels relative to 1 watt, so 100 watts is 20 dBW.
- dBi and dBd express antenna gain relative to an isotropic radiator and to a half-wave dipole; dBd = dBi − 2.15.
- dBc is decibels relative to the carrier, used in transmitter specifications. Harmonics at −50 dBc are 100,000 times weaker than the main signal.
Why hams care
In decibels, a whole station can be worked out with simple addition. A transmitter producing 100 watts is putting out 50 dBm. If its coax loses 2 dB and its beam has 5 dBd of gain, the effective radiated power is 50 − 2 + 5 = 53 dBm, about 200 watts relative to a dipole.
Decibels also make different improvements easy to compare. Three decibels of antenna gain is worth exactly as much on transmit as doubling the transmitter's power, and unlike an amplifier it helps on receive as well. Feed line loss works the other way: 100 feet of RG-58 coax on the 2-meter band loses about 6 dB, three quarters of the power, before the signal reaches the antenna, and better cable recovers that loss in both directions.