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Old 20th Jun 2021, 7:14 am   #2371
Radio Wrangler
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Default Re: The Audiophoolery Thread.

Root of mean square is an operator that only makes sense in terms of values which are dimensionally voltages or currents.

Take voltage samples (or current) and square them and you get a result proportional to power. Take the mean of these power samples and you get the mean power, of course!

Take the root of the mean power and you're back to voltage (or current) again. You now know the fixed DC voltage (or current) that would have the same average heating power as the AC+DC components of the original samples.

If I sampled the voltage coming out of a mains socket here, I'd get sam[les ranging from -339.4V to +339.4V, all being well. If I took them quickly, I could plot out a sinewave. If I took plenty of samples, many cycles of the sinewave, and took the average of them all, I'd get zero volts. This looks like an oddity. Stick a resistor across the mains and it gets warmer. The thermal mass averages the heating over many cycles and some calorimetry will tell me the average power being dissipated. So something with zero average voltage is producing non-zero average power. This ought to strike you as odd. But it's the way things work.

Voltage and current are alright, but it's the power that does the real work. Like the exhortation to people analysing crime to 'follow the money' in electrical, electronics and RF work, keep an eye on the power. You need to know it when you want to see signal to noise ratios.

Noise throws you another googlie.

Mean voltage of pure gaussian noise is zero. Peak voltage is +/- infinity.

So we put the noise through a properly impedance-matched 10dB attenuator. That must reduce the power tenfold, right? so voltages are reduced by root(10), which is a factor of 3.16228 etc. So infinity divided by 3.16228 is, oops! still infinity! If you look at peak voltage, there has been no decrease at all. The mean voltage is still zero, and the peaks are still infinite. The shape of the probability density function has narrowed, that's what.

So statisticians, engineers and the like need a tool to get a grip on the 'power' of a gaussian random signal that tells them something other than zeroes and infinities. So they picked the points on the Gaussian pdf where the probabilities are one-over-root-two of the peak probability of the bell-shaped curve. If these were voltage samples, then these would be the points where their 'power' was halved. The spacing between these points is called the "Standard Deviation" which is the usual way to talk about the amount of variance on some parameter. In electronics terms, the standard deviation is the same as the RMS value of the samples that make up the population, neglecting the DC component (if any). So the recipe for Standard deviation is to remove the mean (DC component) and take RMS of the remainders.

Think of an investment fund manager. He doesn't make money off of the absolute prices of the stocks he deals in, he makes money off of the fluctuations. If stock prices all stayed stationary, he'd starve.

So in terms of power, it makes sense to talk of average power or sustained power.

If you look at this in terms of voltage (or current) then this can be expressed as RMS volts into a defined impedance (or RMS amps, of course)

Talking of RMS of power, when what is actually meant is the mean power, is an indication that someone doesn't understand what they're saying, probably just mindlessly following others.

If I take an RMS voltage and square it, then divide by the resistance of the load, I get the mean power as my result.

If I have some power and I take its mean value, I multiply by the load resistance and then square root it, I get the RMS voltage as my result.

Mean is important in terms of power

RMS is the equivalent in terms of voltage or current.

David
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