Decibel Math

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Decibels Defined

The decibel system (and the properties of logarithms) makes the mathematics involved in some equations much simpler. For instance, recall the Friis Transmission Formula:

power received from Friis equation           (*)

To convert this equation from linear units in Watts to decibels, we take the logarithm of both sides and multiply by 10:

friis transmission equation converted to dB

A nice property of logarithms is that for two numbers A and B (both positive), the following result is always true:

the multiplicative to addition property of logarithms

Equation (*) then becomes:

logarithms used for antenna theory

Using the definition of decibels, the above equation becomes a simple addition equation in dB:

Friis formula in dB

The above representation is easier to work with, which is kind of cool.

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