1. Useful Physical Constants
2. Unit Conversions
3. Radio Systems Equations

Decibels

Decibels are measures of relative power. When a power is expressed in dB, that means that the log of the value has been taken and multiplied by ten.

Once values are expressed in dB, the logarithm theory we were all taught at school becomes practically useful as multiplication and division become a simple matter of addition and subtraction or "Gain" and "Loss". Some useful conversions are:

10log10(1.0) = 0 dB
10log10(2.0) = 3 dB	10log10(0.5) = -3 dB
10log10(4.0) = 6 dB	10log10(0.25) = -6dB
10log10(5.0) = 7 dB	10log10(0.2) = -7 dB
10log10(10) = 10 dB	10log10(0.1) = -10 dB
10log10(100) = 20 dB	10log10(0.01) = -20 dB
10log10(1000) = 30 dB	10log10(0.01) = -30 dB

To go from dB back to a power, riase 10 to the power of the value in dB divided by 10.

e.g. 13 dB == 10^13/10 = 10^1.3 = 20

Decibels are ratios of power, so doubling a power is equal to a 3 dB increase, whatever the power actually is. An amplifier with 20 dB of gain raises the power by a factor of 100. A cable, with 6 dB of loss only transmits 1/4 of the power.

Where the units are in a ratio to some known value, for example power in Watts, frequency in Hz, temperature in Kelvin, the unit is appended after the dB as in dBW, dBHz, dBK respectively.

So power in expressed in Decibels relative to 1 watt (dBW), i.e. Power in dBW = 10log₁₀(Power in Watts)

0 dBW = 1 Watt

20 dBW = 100 Watts

-10 dBW = 0.1 Watts

To convert from dBm to dBW, simply subtract 30. This is because dBm are relative to one milliwatt and as 1mW is 1/1000th of one Watt to convert between the units we need to add 10log₁₀(1/1000) = - 30.

0 dBm = -30 dBW

-10 dBW = 20 dBm

dB Voltages

Decibels are always related to power, but it it common to see decibels relatve to volts - what it going on?

As dB always relative to power, we need to remember that the ower is proportional to the voltage squared, (Power = V²/R). By remembering that for logs that:10LOG(X²) = 20LOG(X), decibels of voltage are defined as 20log₁₀(Voltage) so for example:

0 dBV = 1 Volt and,

20 dBV = 10 Volts

Other useful values in common use are dB relative to one microvolt, dBuV.

0 dBuV = 1uV

20 dBuV = 10uV

120 dbuV = 1 V

dBs of Sound

Decibles are not limited to RF power, audio power or any other sort of power can equally easily be expressed in dB. Generally, the units that are used are dBA.

The dBA is rather loosely defined relative to the threshold of human hearing, so 0 dBA is the quietest sound anyone can hear. It is about a power flux of 10^-12 watts/m². To put this in perspective, normal speach is of the order of 60 dBA.