Decibels can be one of those little things that you can get a mental block about. It is not that there is anything difficult about the maths, but rather the concept of handling voltage and power ratios in this way. However, it is worth learning to use decibels, because they make life so much easier for the radar engineer.

The idea behind decibels is that the numbers used in radar calculations are often very large (e.g. R ⁴) or very small (e.g. P _r), and they must usually be multiplied and divided. This makes life difficult and can easily lead to mistakes. Converting these numbers to logarithms means that, first, they become a sensible size and, secondly, they only have to be added and subtracted. This greatly facilitates repeating calculations, when one of the parameters is varied.

The definition of decibels is that, if P ₁ and P ₂ are two amounts of power then the first is said to be n decibels greater than the second, where

The ratio of two voltages V ₁ and V ₂ can be converted to decibels by

In radar, it is more common to find the 10 log ₁₀ power version used in calculations, rather than voltage ratios, but this is not necessarily so in other subjects. To escape from decibels and return to linear numbers, divide n by 10(or 20 for voltage ratios) and then use the 10 ^x function on your...