A: How are dB and dBu, dBV etc. related?

The pseudo unit dB (decibel) on its own represents a ratio of two numbers, but does not say anything about the exact size of a value. This is where so-called “reference values” come into play.

If we return to our example of “human hearing” (as described in section "Decibel & Level calculation" ) or sound pressure, the quiet hearing threshold, i.e. p₀ = 20 µPa is defined as a reference value for the sound pressure level and is included in the denominator of formula [2] (see section "Decibel & Level calculation"). In order to make it clear that the reference value is “sound pressure” in this case the quiet hearing threshold, the pseudo unit is given the addition "SPL" = Sound Pressure Level as shown in formula [3].

 

L_{p}=20*log(\frac{p}{p_{0}})\enspace\enspace[dB_{SPL}]

            [3]

As soon as the pseudo unit dB has an additional letter (designation), it is an absolute level related to a physical quantity, here “Pascal”. By changing formula [3] into formula [4], sound pressure level can be converted back into the physical quantity at any time. E.g.:

p = p_{0}*10^\frac{level in dB_{SPL}}{20}\enspace[Pa]

         [4]

If the reference value is also placed in the numerator of the logarithm equation, the result is 0. Consequently, the level of the reference value is always 0 dB“x” or, in our example, 0 dB_SPL. And that regardless of the reference value. To check this, we simply set p = p₀.

L_{p_{0}}=20*log(\frac{p_{0}= 20\,µPa}{p_{0}= 20\,µPa})= 0\,dB_{SPL}

In addition to sound pressure, there are other physical quantities that are simplified in terms of handling and calculation using the pseudo unit dB. Let us look at the most common reference values in audio and acoustics with their respective units:

When it comes to electrical voltage levels, two units are used, dBu and dBV. They only differ in the respective reference level:

L_{u}=20*log(\frac{u}{u_{0}= 0,775\,V})\enspace\enspace[dB_{u}]

           [5]

L_{u}=20*log(\frac{u}{u_{0}= 1\,V})\enspace\enspace[dB_{V}]

                   [6]

When it comes to power signals with the unit “Watt” it should be noted that the prefactor in front of the logarithm is not 20, but 10.

L_{p}=10*log(\frac{p}{p_{0}= 1\,mW})\enspace\enspace[dB_{m}]

              [7]

If you want to know why this is the case, you should use the popular formula or relationship P = U²/R or P₀ = U₀²/R for P and P₀ and you will see that you can get the corresponding level formula for voltages by simply transforming it and vice versa. For more information see links below „dB or not dB“, section 5. 

For simplicity, we can remember the following: If we want to convert power signals into the dB world, we use the prefactor 10 in our logarithmic formula. For all other conversions into the dB world, the prefactor 20 is used.