# Decibels - Electrical quantities expressed in decibel

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Seeing that the dB measures the perception of sound quantities by the human ear, it makes sense also to expresses in dB a series of electical quantities related to sound. The following are the most commonly used quantities:

dB_{m} (power)

Originally used to measure the power levels of telephone lines. Generally speaking the circuits used for this scope had an impedance
[Impedance
]
of 600Ω. The reference value for the power was 1mW, from which:

**Equation 3.8. dB**_{m}

Out of this formula we can extract an equivalent one in which we have voltage rather than power.

Substituting power with voltage as expressed in the following formula:

and putting:

we obtain the following:

As we can see, in this formula in order to find the dB value from the voltage value, the multiplying factor of the logarithm is now 20. Therefore with powers we have a multiplying factor of 10, whereas with voltages this factor equals 20.

dB_{u} (Voltage)

This value was introduced out of necessity, as a result of the need to take into account circuits with impedances values other than 600Ω. The 'u' in dB_{u} states that the quantity is 'unloaded', in other words free from impedance. To calculate dB_{u}, the load is encompassed within its reference voltage which can be obtained from the following calculation:

from which:

This voltage therefore encompasses a reference power of 1mW and a reference resistance of 600Ω.

The final formula for the calculation of dB_{u} is the following:

**Equation 3.9. dB**_{u}

dBV (Voltage)

In this case the reference voltage equals 1 Volt and therefore the following formula is used:

**Equation 3.10. dBV **

dB_{fs} (Full scale)

The digital dB scale is slightly different. First of all the measuring unit is dB_{fs} and its highest value is always 0 dB_{fs}. Beyond this level digital distortion takes place. The sound of digital distortion is very different to analogue distortion and, furthermore, analogue distortion progressively increases as we go beyond the headroom zone whereas a digital signal switches swiftly from a correct reproduction (below 0 dB_{fs}) to distortion (beyond 0 dB_{fs}). The following are some comparisons between the dB_{fs} scale and the dB_{u} scale. We can see how, in this example, 0V_{u}, in other words 4dB_{u}, equals -15 dB_{fs}:

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Related topics on Wikipedia

Typical dB

_{fs}values