An unloaded decibel (dBu) is a unit of measurement of the ratio of an amount of voltage V to V0 = 0.7746 volts given by the formula 20 log10(V/ V0) = 20 log10(V/ 0.7746), where voltage is measured using quadratic mean (also called root mean square, RMS).
For example, the professional audio and studio recording level of +4 dBu means
4 = 20 log10(V/ 0.7746)
and so V = 0.7746 (10^(4/20)) = 1.2277 volts. Thus, the voltage used in professional audio is 1.2277 V. Similarly, if some voltage is equal to 0.7746 then its dBu measure is 20 log10(0.7746 / 0.7746) = 0 dBu.
The formula for this unloaded decibel measure is exactly the same as the regular measure of decibels (dB), except that dBu is specific to measuring electrical potential difference (voltage) and is fixed to the reference 0.7746 VRMS. Thus, this is simply a measure of voltage. The reference point of 0.7746 VRMS was chosen historically as it represented the voltage that produces 1mW of power in a 600W resistor ((0.001 * 600)^(1/2) = 0.7746).
Since the voltage decibel (dBV) is also a measurement of voltage, there is a direct relationship between dBu and dBV. The dBV measure of a voltage V is 20 log10(V) and the dBu measure of voltage is 20 log10(V / 0.7746). We can use these two formulae to express the amount of voltage as 0.7746 (10^(dBu measure / 20)) and the dBV measure as 20 log10 (0.7746 (10^(dBu measure / 20))) = dBu measure + 20 log10 (0.7746) = dBu measure - 2.21845. In short
dBV measure = dBu measure – 2.22845
For example, +4 dBu = +4 - 2.21845 = 1.78155 dBV.
Comments
Error correction
The maths is incorrect. 4dBu does not equal 1.2283! It does equal 1.227658...
4=20 log V1/Vo - Vo = 0.7746
therefore V1 = 10^(4/20) * 0.7746 = 10^0.2 x 0.7746 = 1.584893... * 0.7746 which does not equal 1.2283
True
The difference between 1.227658 (precise) and 1.2283 (not precise) is the use of 0.775 instead of 0.7746. I'll change the numbers above
really
dBV does not equal dBu!
dBv does equal dBu
dBV is something else
Please check you facts before publishing errors. People read this stuff and believe it. YOu have e responsibility, as a publisher to ensure that it is correct.
Correct
Well, yes. dBv and dBu are not exactly the same, because of the strict 600 ohm load requirements for dBv. I'll remove the "offending" sentence in the middle I guess, but I don't know if this distinction is useful today.
Incorrect
The "u" in dBu DOES NOT mean "unloaded". It means "unit". The dBu unit of measurement, unlike dBV (voltage relative to 1 volt regardless of load), considers the load of 600 ohms. This is where the 0.7746Vrms reference comes from. It is the voltage that would result in 1mW dissipated by a 600 ohm load, which results in 0.77459666924148337703585307995648Vrms. We conveniently round this off to 0.7746Vrms.
P = (V^2) / R
0.7746^2 / 600 Ohms = 1mW
With 0dBu on a 600 Ohm load, power dissipated by said 600 Ohm load is equal to 0dBm.
ok
OK. I'll suspend this topic for a bit until it is rewritten...
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