# Foundation License - Decibels

## Decibels

The information below is beyond the scope of the Foundation License, but candidates are advised to try to understand the table and examples below in order to b able to estimate effective radiated power (ERP)..

The decibel is a comparative unit, that means it is not a thing in itself but instead it must relate to something. The decibel is written dB followed by the unit to which it is related, so in the case of power dBW means decibels over 1 Watt, dBV is decibels over 1 Volt. In the case of antenna gain, the gain is written in two ways;

1. dBi - decibels over an isotropic antenna. This is a theoretical antenna which does not exist in the real world, but is a handy reference for antenna designers.
2. dBd - decibels over a half-wave dipole. This is a much more meaningful measure for radio amateurs in that it allows us to calculate ERP.

Gain (dB) | Gain (times)
3 | 2
6 | 4
9 | 8
10 | 10

Every time we add 3dB, the gain multiplies by 2. Thus for 6dB gain we multiply by 2 and then multiply by two again, giving us a gain of "times 4".

Example 1.

Q. An antenna has a gain of 13dB. What is the ERP for a power input of 1W

A. Gain = 10dB (x10) + 3dB (x2) = 10 x 2 = 20

ERP = Input Power x Gain = 1W x 20 = 20W

Example 2

Q. An antenna has a gain of 15dB. What is the ERP for a power input of 10W

A. Gain = 15dB = 6dB (x4) + 9dB (x8) = 4 x 8 = 32

ERP = Input Power x Gain = 10W x 32 = 320W

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