Yes RMS math is SQRT of integral of x^2... I have made multiple RMS circuits using transistor Vbe junctions to form the ^2 and ^0.5 math with a simple inverting op amp and feedback cap to compute the integral (plenty of examples in old Analog Semi handbooks).diffuse371 wrote:
I think the maths for RMS detection relies on a linear integrating capacitance?
I even coded up RMS for a microprocessor based meter I did for a friend's console company several years ago but i could not see a difference with complex music, so removed it to keep it simple. I had to roll my own square root function (not standard in RISC processor) that took 1+ clock tics per bit of sqrt product resolution. The processor could easily handle it, but I didn't see any difference or value in the visual meter display vs. using simple average****. Note this comparison was made with very precise matched attack and release time constants for both (which dominated the visuals IMO). Many swear about audible benefits from RMS detection, and dbx pimped their tape NR systems for decades claiming more accuracy dealing with less than perfect tape transfer functions because of the RMS. It's a bit late to re-litigate old marketing arguments, and I try to never argue with people about what "they" hear.
I wouldn't expect RMS to offer much benefit for a static sine wave control loop.
*** In hindsight I didn't have to perform the SQRT calculation in real time for a LED RMS meter displaying discrete ranges. I could just map the integral of x^2 to an output table that had the SQRT embedded in the table values. The X^2 is a one clock tic multiply function so no processing overhead penalty.