Decibels are decibels. There is no such thing as "root-power decibels".
By definition a decibel (dB) is a ratio of two powers. The formula is 10 * log10(P1/P2) where P1 and P2 are the power of two signals, respectively.
In electronics, however, we usually manipulate and measure voltage levels. It's convenient to represent the ratio of two voltage levels in dB. To do this you would need to square the voltage to get the power (since P = V^2 / R). We also assume R = 1 for convenience. With a little math you get dB = 20 * log10(V1/V2).
Therefore if we reduce the voltage level of a signal by a factor of 0.1 then the signal is now -20 dB relative to before.
dB is simply an easy-to-read logarithmic-to-linear mapping. Music, human perception, and many other things in nature typically have a logarithmic response. The decay of, for example, a cymbal is logarithmic. If you plot this on a linear axis it's hard to display because of the dynamic range. But if you use a logarithmic axis you "compress" the data into something that's easier to view. Decibels are just a widely accepted mapping. You could use any base for the log; log2, ln, etc but since we have 10 fingers log10 is nice.
The point is that X dB is X dB. If you reduce a signal by 20 dB you've reduced it's voltage to 10% of what it was previously. You also reduced it's power to 1% of what it was previously. These are the same things: 20 * log10(0.1) = 10 * log10(0.01).
I've been having issues with the output level of my axe-fx 2 xl+ for a while now and I'd really love it if you could answer a few technical questions for me regarding the output and alignment levels FAS chose to go with.
When I place a synth block next to the output bar and set it to 0db (voices 1 and 2 disabled) and use voice 3 for a 1khz test tone the output meter in the UTILITY menu shows -1.1 dB. At this very same moment I'm measuring the output level from OUT 1 R (left is going into my mixer so I can keep an eye on the VU meter there) using a Fluke 87 V (True RMS) multimeter and my results are 0.7841 volts AC (calculated I'm getting a Vp of 1.109. Measured with the Fluke it's showing 1.113 to 1.119 volts peak).
What's up with the UTILITY meter not showing 0db despite the synth block being set to 0db? Is there something I'm not understanding about the meter alignment to the internal signal flow? Perhaps the attack rate of the VU meter is slow? I'm not sure this would matter with a sustained test tone though and more explanation would be really helpful in clearing this up for me.
Might I also ask why the output of the device isn't showing proper +4 dBu voltages (1.228) when the synth is set to 0db 1khz? If my understanding is correct this is giving closer to a 0 dBu signal of 0.775 volts. Most meters are aligned at +4 dBU and current SMPTE alignment level is -20 dBFS = +4 dBu.
Now comes my second issue. When I generate a test tone in adobe audition at -20 dBFS and use the AFX ASIO playback I'm not getting anywhere NEAR the voltages that I should be at -20 dBFS (aligned to +4 dBU). I'm getting around .627 volts. Now I understand that dBFS alignment is not set in stone and runs the gamut from -20 to -14 (more on -14 in a second). So I am curious, is my unit messed up? Are my test tone settings wrong? Or is there something I'm not understanding?
The most perplexing thing is the synth block being at 0db but showing up on the UTILITY vu meters as -1.1 dB. If I adjust the synth block to make it read 0 dB by setting the output level of the synth to 1.1dB I get a measurement of 0.89 v. This internal mismatch is driving me crazy and again, further explanation would be really welcomed (perhaps something is set wrong? The output block is set to 0.0 across the board and on the main slider so I know it's not that.
So I got curious, I set my adobe audition test tone generator to go up fractionally until I reached the "correct" voltage for +4 dBu line output (1.228) and it required an alignment of -14.05 dBFS. This shows up on the UTLILTY meter as 2.8 dB (the synth block had to be set to 3.9 dB to get the same results).
Honestly I am trying to figure all of this out so I can properly gain stage this into my mixer using the unity markings on the dials (yes I know they're not that accurate but I have an accurate DMM and I can adjust accordingly) but the whole thing is so far away from +4 dBu/1.228 volts that I don't know what's up and the internal mismatch with itself (synth at 0db but UTIL meter showing -1.1) is further cloudying my situation.
Basically I wanted to use the synth block set to 0db and get 1.228 volts out of the device and set my gains on my mixer using the synth as a test tone generator. This is very clearly not happening and I am confused as to why. If I'm understanding correctly, you want to set your mixer VU meter to read 0 (no change) at 1.228 volts.
In no way is this written from the point of view that I know what I'm talking about. I hope it didn't come off that way, I'm sincerely just very confused about these levels not matching up. Is it possible the AFX2 was set to align at 0dBu instead of +4? Is it also possible that the -1.1 dB mismatch was an attempt at maintaining some kind of headroom in the device? I honestly am baffled. Thank you for your time and yes I know this is a 5 year post from the dead but this thread seemed the most fitting considering the search results I came across when trying to figure all of this out. Hopefully someone else will find it as well. Of course, If necessary I don't mind this being moved to the AFX2 sub forum.
Thanks for your time and also thank you for making such an amazing device!