Seeing that dB's produce perception of sound quantities by the human ear, the dB unit also expresses a series of electical quantities on a practical level. The following are the most commonly used ones.
Originally used to measure the power levels of telephone lines. Generally speaking the circuits used for this scope had an impedance [Impedance ] of 600Ω. As a reference value 1mW was used, from which:
Equation 3.8. dBm
From this formula we can extract an equivalent one in which we have tensions rather than power. By substituting the formula:
and putting:
we obtain the following [4 ] :
This value was introduced by necessity, as a result of the need to take into account circuits with impedances that differ by 600Ω. The 'u' in dBu indicates that the value is 'unloaded', in other words, free from impedance. To calculate dBu, the charge is enclosed within its reference tension which can be obtained from the following calculation:
from which:
This tension therefore encompasses a reference power of 1mW and a reference resistance of 600Ω.
The final formula for the calculation of dBu is the following:
In this case the reference voltage is equal to 1 Volt and therefore the following formula is used:
Equation 3.10. dBV
The digital dB scale is slightly different. First of all the measuring unit is dBfs and the highest value is always 0 dBfs. Beyond this level we have digital distorsion. The sound of digital distorsion is very different to analogical distorsion and furthermore, analogical distorsion increases progressively as we go beyond the headroom zone, whereas a digital signal switches swiftly from corrected reproduction (below 0 dBfs) to distorsion (beyond 0 dBfs). The following are some comparisons between the dBfs scale and the dBu scale. We can see how 0Vu, in other words- 4dBu, equals –15 dBfs:
[4 ] As we can see, in this formula in order to find the dB value from the tension-value, the multiplying factor of the logarithm is now 20. Therefore with powers we have a factor of 10, whereas with tensions the factor equals 20.
Related topics on Wikipedia
Typical dBfs values