Use of dBu on limiter threshold settings.

I was looking at some plate amplifiers with the DSP option. Looking at their DSP software, the threshold setting for their Noise Gate, Compressor and Limiter were all in dBu and I went berserk. In my research and study for these type applications over the past 10 years, I do not remember any of these Threshold settings being in dBu. I had lengthy argument over this with this vendor and was about to tell him where he could stick it. So I backed up to rethink the situation.

First of all, we are working with the voltage relationship to the speaker and the amplifier. This is calculated by square root function of the wattage divided by the impedance. SQRT(watts*ohms)

Speaker Program Power of 800 watts at 8 Ohm load = 80 volts
Amplifier of 1000 watts at 8 Ohms load = 89 volts

With dB calculations you are using the 20 * Log function with the ratio between the speaker voltage and the amplifier voltage output to define your speaker protection. 20*Log(Speaker Voltage/Amplifier Voltage). The result of this would be -0.97 dB. Your setting on your limiter would be -1 dB for the thermal protection of the speaker.

Now, dBu using a reference of .775 for the denominator for the equation 20*Log(Voltage/.775) and I could not relate to that at first. Then I finally found something to answer that question.

Now we will still use the voltage for this calculation but we will use 20*Log(Voltage/.775) where this voltage will be the speaker or amplifier voltage as we did before and find the result for each device.

Speaker Program Voltage 80V would be 20*Log(80/.775) = 40.3 dBu
Amplifier Voltage 89V would be 20*Log(89/.775) = 41.2 dBu
In this case the amplifier sensitivity is .775

Now using the difference between these two dBu values (Speaker dBu minus Amplifier dBu) will provide you with the Threshold setting in dBu. Now looking at this, the dB calculation and the dBu calculation will be the same because the reference for the dBu calculation is .775 and the amplifier sensitivity is also .775.

Now there is a snag. What if the sensitivity is 1.4 or 1.7 that I found in some of these amplifiers? Instead of the .775 in the amplifier voltage calculation, you would use the sensitivity of the amplifier.

Amplifier Voltage would be 20*Log(Voltage/1.4) = 36.1 dBu for a 4.17 dBu
Amplifier Voltage would be 20*Log(Voltage/1.7) = 32.4 dBu for a 5.86 dBu

FYI – Reference Selecting the limiter threshold for a loudspeaker power limiter.