# Decibel

The **decibel** expresses a ratio of quantities and not a quantity by itself. it does not express an exact quantity. The decibel expresses how many times more or how many times less, a quantity in relation to another quantity is. It is an expression that is not linear but logarithmic. It is a relative measurement unit.

At audio frequencies a change of 1 decibel (dB) is barely noticed. The decibel is represented in abbreviated form by dB. There is also the Bel. 1 Bel = 10 dB.

## Power ratio expressed in dB

If there are two powers P1 and P2, the ratio P1/P2 is NdB. NdB = 10 log10 P2/P1

## Voltage ratio expressed in dB

If you have two voltages V1 and V2, the ratio V1/V2 is NdB. NdB = 20 log10 V2/V1

## Current Ratio expressed in dB.

If there are two currents I1 and I2, I1/I2 ratio is NdB. NdB = 20 log10 I2/I1

If the result in dB is positive, it means that the relation between the two values is greater than 1 and if it is negative means that the relation between the two values is less than 1.

For example: An amplifier with:

- V1 = input voltage = 100mV
- V2 = output voltage = 70.7mV

The amplification is the ratio between de output voltage V2 and the input voltage V1.

NdB = 20 log10 (70.7/100)

NdB = 20 log10 0.707

NdB = 20 x (-0.1506)

NdB = -3.012 dB

That means that there is a negative amplification.

## Why use the decibel system?

It is a very simple reason. If we have a system with gains and losses (negative gains). It is much easier to add or subtract gains (not to multiply them) to obtain the final gain.