# Decibels

The main things to take away from this topic are that decibels are by far the easiest way to compare power output levels and gain and that calculating the power output coming out of the antenna can be as simple as adding all the gains and subtracting all the attenuation together.

Just the term dB is short for decibel (tenth of a Bell). It is a relative way of comparing the ratio between two values.

Decibel is not power nor loudness nor frequency nor voltage or anything; it is just a comparison between two values with some quantity.

The Bel (named after Alexander Graham Bell) is expressed in base-10 logarithms. Feel free to do a google search for how to use dB and what Logarithms are all about but please come back here when finished.

If we read that a signal is 3dB more powerful we need to instinctively ask ourselves: “more powerful than what?”

This is where the lower-case letter ‘m’ (in dBm) comes into play. The ‘m’ in dBm in the datasheet stands for ‘deciBels in comparison to one milliwatt’.

When we get to the chapter on antennas we’ll use decibels again, but there we use the dBi (ratio in relation to an ‘isotropic radiator’) and dBd (for a dipole).

This means that 0dBm is equal to 1mW (not zero milliWatts!). Yes, 1 mW may not sound like a lot but it is enormous when compared with the very low power levels that your mobile phone antenna picks up. Power levels less than 1mW can be expressed in a negative number, e.g. -10dBm, just as easy as power levels greater than 1mW can be expressed with a positive number, like +20dBm (it is okay to leave out the ‘+’ sign).

Here is a great video that explains decibels and illustrates the concept on a spectrum analyzer:

# Some Formulas & Math Examples

The formula for calculating the power levels from mW to dBm is as follows:

dBm = 10 x ( log10 (mW) )
(the Log here is the Base-10 Log, not the Natural Log!)

### Example 1

5 mW is how many dBm?
PdBm = 10 x Log(5) = 6.98dBm

### Example 2:

0.5 mW is how many dBm?
10 x Log(0.5) = -3dBm

To calculate the power level from dBm to mW:

PmW = 10 ^(PdBm / 10)
(^ is the “to the power of“operator)

### Example 1:

20dBm is how many milliWatts?
10 to the power of (20/10) = 100mW

### Example 2:

13dBm is how many milliWatts?
10 ^ (13/10) = 19.95mW

For easy reference, here is a basic lookup table with the most common values: After this little excursion into decibels, we come back to the topic of output power and see that the maximum output power of the various Moteino radio modules is:

• RFM69HW and RFM69HCW: 20dBm (100mW)
• RFM69W and RFM69CW: 13dBm (20mW)

This output power is only meaningful to us if we can use it to generate a wireless RF signal so we can bridge some distance. In more concrete terms, the device that can turn (most of) this output power into a radio signal is an antenna.

The signal that comes out of the transmitter is an alternating current (AC) at certain frequency.