## Understanding decibels

The decibel (dB) that we constantly find when talking about an antenna or a radio link are just a very useful tool to simplify the calculations.

The decibel is a logarithmic unit, as opposed to linear units. It is defined as:

Value in dB = 10 x logarithm of the linear value

Thus, power of a received signal in linear units is:

Received Power = Power Emitted x Transmitter Antenna Gain x Receiver Antenna Gain / Transmission Loss

The advantage of working with decibels (logarithmic units) is that the logarithms have an interesting property:

log (A x B) = log (A) + log (B)

That means that if we handle the simplified equation of transmission with decibels it becomes much simpler:

Received Power (dBm) = Power Emitted (dBm) + Transmitter Antenna Gain (dB) + Receiver Antenna Gain (dB) – Transmission Loss (dB)

Or what is the same, decibels convert multiplications into additions, subtractions and divisions, which makes calculations much easier and intuitive.

As a rule of thumb is practical to remember some values:

+3dB is equivalent to multiplying the power by 2

-3dB is equivalent to dividing the power by 2

+6dB is equivalent to multiplying the power by 4

-6dB is equivalent to dividing the power by 4

+10dB is equivalent to multiplying the power by 10

-10dB is equivalent to dividing the power by 10

Thus, if we remember that to double the distance of the link we need 4 times more power, this implies that we need to “find” 6dB more in our link. This can be achieved by multiplying by 4 the transmitted power (eg, from 100mW to 400mW, which is to pass on a logarithmic scale from 20dBm to 26dBm), or using an antenna with additional 6dB gain (for example, using a 14dB patch rather than an 8dB one).

For example, if we have a link with an omnidirectional antenna at the receiver of 2dB, and with a specific transmitter and receiver we get 2Km link, replacing the 2dB omnidirectional antenna by a 14dB patch antenna, we are improving the link in 12dB. If we remember that 6dB involve doubling the maximum distance of the link, and considering that:

12dB = 6dB + 6dB

With the 14dB patch antenna we can “double up twice,” or multiply by 4 the range, so we can reach up to 8 km instead of the 2 km we could get with the omni.