what is the difference between rms and peak

[mgarrett]

In the 'classical' (engineering) sense, the RMS value is the DC value that creates the same amount of work (or heat in a resistor) in a load as the AC..

So when said that the RMS is the 'equivelent DC' of the AC signal, its the DC voltage that generates the same thermal energy as the AC signal when placed accross the same load resistor. (the DC (Non Changing) signal that does the same amount of work as the AC signal)

There are RMS converters (linear Technologies) that have two resistors, the signal is applid to one, and an internal circuit servo loops the DC trough the other one, to make them the same temperature. This DC value is the RMS value of the AC...

It happens that If I have a sine wave accross a resistor, is generates the same energy as a DC signal (PKPK/2)*0.707, the 'RMS Value'.

Crest Factor is an expression for the deviation from a sinusoid... If I have a very narrow pulse (low duty cycle, lots of off time) that has a peak to peak of 2 Volts, it will not generate as much heat as a sinusoid, but if we correct it utilizing the 'crest factor' we can get the RMS answer, based on knowledge of the wave shape (crest factor).

The RMS value, can have an averaging time associated with it, which is really the amount of time that we are going to use to determine the signal ENERGY (not power!!) (energy heats), (power applied for some amount of time). So to know the amount of heat that would generated (energy consumed) we would need to apply the signal for some amount of time, in order to determine the DC voltage that would generate the same heat, DC in the sense of the non changing voltage over the averaging time chosen.

50 mSec is usually chosen as the integration (or averging time) because it is one cycle of 20 hZ. One cycle is required to determine the RMS value for 20 hZ..... a 50 mSec averaging time would give incorrect results for a 5 hZ sine wave..

So... The RMS value is indicative of the amount of energy, energy transfered from the radiator into the absorber... Voltage into Current into magnetic field into air movment into ear drum vibration... all energy transfer... the amount of work done.

The RMS value give you a quick way of determining how much work you can get out of a 'waveform' or signal.

[dcollins]

Originally Posted by mgarrett

In the 'classical' (engineering) sense, the RMS value is the DC value that creates the same amount of work (or heat in a resistor) in a load as the AC..

So when said that the RMS is the 'equivalent DC' of the AC signal, its the DC voltage that generates the same thermal energy as the AC signal when placed across the same load resistor. (the DC (Non Changing) signal that does the same amount of work as the AC signal)

There are RMS converters (linear Technologies) that have two resistors, the signal is applid to one, and an internal circuit servo loops the DC trough the other one, to make them the same temperature. This DC value is the RMS value of the AC...

It happens that If I have a sine wave accross a resistor, is generates the same energy as a DC signal (PKPK/2)*0.707, the 'RMS Value'.

Crest Factor is an expression for the deviation from a sinusoid... If I have a very narrow pulse (low duty cycle, lots of off time) that has a peak to peak of 2 Volts, it will not generate as much heat as a sinusoid, but if we correct it utilizing the 'crest factor' we can get the RMS answer, based on knowledge of the wave shape (crest factor).

The RMS value, can have an averaging time associated with it, which is really the amount of time that we are going to use to determine the signal ENERGY (not power!!) (energy heats), (power applied for some amount of time). So to know the amount of heat that would generated (energy consumed) we would need to apply the signal for some amount of time, in order to determine the DC voltage that would generate the same heat, DC in the sense of the non changing voltage over the averaging time chosen.

50 mSec is usually chosen as the integration (or averging time) because it is one cycle of 20 hZ. One cycle is required to determine the RMS value for 20 hZ..... a 50 mSec averaging time would give incorrect results for a 5 hZ sine wave..

So... The RMS value is indicative of the amount of energy, energy transfered from the radiator into the absorber... Voltage into Current into magnetic field into air movment into ear drum vibration... all energy transfer... the amount of work done.

The RMS value give you a quick way of determining how much work you can get out of a 'waveform' or signal.

All true and well-put! We generally see an integration time of more like 300ms for things like VU meters, though, but it's a minor point.

The problem with viewing an audio signal as the total energy, is that full-scale 20Hz and full-scale 20kHz sines measure exactly the same. And you probably can't hear either one!

Without some kind of weighting, RMS has little connection to the apparent level of music.


DC

[mgarrett]

Originally Posted by dcollins

All true and well-put! We generally see an integration time of more like 300ms for things like VU meters, though, but it's a minor point.

The problem with viewing an audio signal as the total energy, is that full-scale 20Hz and full-scale 20kHz sines measure exactly the same. And you probably can't hear either one!

Without some kind of weighting, RMS has little connection to the apparent level of music.


DC

Absolutely!! By work I meant in the classical 'thermal' sense. As Dave points out two signals with the same RMS value can be very different in percieved volume and tone... although in narrow ranges, and in calibrated situations, the RMS level can be an indicator of 'loudness' (Controlled Situlations).

This is taken advantage of in RMS level gain control and compression. In these applications, it is common to see varying time constants that can get shorter than the 'balistic standards' used for VU meters (published in various specifications for VU meters and indicators).

Some DAW meters allow the RMS time constant to be set. The longer the averaging time, the slower the response, but the more accurate for longer term signals.

When looking at the properties of an audio file in total, such as the statistics window in Audition, the RMS value is reported, the averaging interval being the entire song length. Some posts that I have seen, use this statistics number to report the approximate 'volume' or loudness of a song, which is misleading for a whole song.

Making a relative comparison of the full song RMS pre and post compression and limiting, gives some idea of the loudness increase, but is somewhat academic for a whole song, but valuable for sections of songs with the same program material loudness.

One thing to clear up, the RMS voltage or current is NOT a measure of enrgy by itself. The actual thermal energy created, is a function of ((V(RMS)**2)/Resistance)*Time, which is the integral of the power, or power times time.

If our voltmeter says that a voltage source is 110V RMS, we may not be able to source a 110 AMPS RMS, connected to a one ohm resistor, so here, the fact that we have a 110V RMS, the indication of available potential energy is not valid for this particular source load combination.

[mgarrett]

Originally Posted by mgarrett

I

Crest Factor is an expression for the deviation from a sinusoid... If I have a very narrow pulse (low duty cycle, lots of off time) that has a peak to peak of 2 Volts, it will not generate as much heat as a sinusoid, but if we correct it utilizing the 'crest factor' we can get the RMS answer, based on knowledge of the wave shape (crest factor).

Crest factor is an expression for the deviation from the RMS value, an expression that corrects the RMS or peak(whichever one you know) based on waveform characteristics (Provided you know the crest factor...)

CF=|Peak|/RMS, to say it simple, the ratio of peak to rms value... In the world of dB, division is subtraction so dB(CF)=dB(|Peak|)-dB(RMS) as Bob K refered to earlier, the difference between the Peak in dB and the RMSin dB.

To make it confusing, Peak is not the PKPK value, but the Peak (notice the magnitude operator) from 0 to the positive peak... complicated for non symetrical waveforms..

So for a sine wave, with a Peak of 1 Volt (PKPK of 2 volts), the Crest factor is 1.414 or 1 / 0.707...

Applying a 2 Volt PKPK sinewave to a resistor, gets it the same temperature as 0.707 Volts DC...



mcg

[ckett]

Hello all,

This is a great thread going on here. I would like to ask a few questions to broaden this discussion.

If I were mixing music that has a style like a film score or even classical music, at what dynamic range should I shoot for? One of the things I am discovering is that as a mixing engineer I need to have some reference in mind for the lows and the highs. Bob Katz's K system has been of great help in at least establishing a monitoring environment that is consistent.

In relation to RMS levels, a piece of music should have a target in which to bring the mix to. I think by establishing a reference high and low RMS level, based on the music per track, the mix can achieve a more acceptable dynamic range before going to the mastering phase. This way the mix only needs very little compression/limiting in the mastering phase and would only need an overall gain increase in level (not normalization or heavy limiting/compression) to bring it close to 0dbfs.

I have found that a lot of compression/limiting in the mastering phase greatly affects the sound of the mix in terms of the tonal balance. It's almost like it can destroy the mix!

The other question I have for more experienced engineers is that I find that to get a mix louder you have to begin cutting the low end. Will having an established RMS reference for the mix aid in getting the tonal balance correct? This way the engineer will know that the equalization of the tonal balance of the mix is in the right place based on the loudness level of the mix.

Anyways, I hope this encourages some discussion!!

Hope to get John and Bob in on this!!

Thanks all!!

[Babaluma]

what is the difference between rms and peak?

the crest factor - it's like the x factor but sounds better.

[Alécio Costa]

This topic should be a sticky!

Congrats and thanks for all the very good information!