A POINT OF VIEW: Crest Factor and how it applies to headroom in an amplifier

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Paul McGowan writes: I promised yesterday we’d start to learn what Crest Factor is and how it applies to headroom in an amplifier. While understanding this concept isn’t all that important to making your amplifier power decision, getting a basic understanding of how it all works and why is probably useful for most of us who have been under the impression that anything over a few hundred watts is “overkill” when I would suggest anything under 500 watts is “underkill” for any speaker system.

Crest Factor is the ratio between peak power and average power.  Sounds technical – but it’s actually rather simple.  Think of a sine wave in terms of energy distribution – where is the biggest part of the energy in a sine wave?  Right in the middle where it is fatest as viewed from left to right (the time dimension).

And, of course, the least amount of energy viewed in the same plane is the top and bottom of the sine wave called the peak.  Now view the sine wave in the up and down plane (the loudness dimension) and the greatest amount of energy is the highest and lowest point of that wave (although the shortest width).

If we average the amount of energy in a sine wave (add the peak and the middle together and average) and then compare that average to the peak by itself, we get something called the Peak to Average ratio – the Crest Factor – expressed in dB.

For example, a sine wave has a crest factor of 3dB meaning that on average the ratio between the average energy and the peaks is double (3dB is double the power) – where the peak is twice the power of the average.

Why is this important?  For our purposes we want to know this ratio between quick short peaks and longer average power because that’s going to tell us how many watts we need to cover the peaks and the average.

A lot of these figures have meaning only in relationship to the type of music we will be listening to.  As I mentioned earlier on, we don’t listen to sine waves.

We do listen to people speaking and singing and here the ratio between the average and the peak is far higher: 12dB is typical.

So, to put this in perspective, if you listen to a sine wave on your system, aside from people thinking you’re weird, you’d notice a steady sound pressure constantly permeating the room.  But if you listen to someone speak it’s really made up of lots of short “bursts” of sound energy – as opposed to a constant steady tone like that of a sine wave – therefore we can safely say that speech has more and higher peaks than steady tones, hence the higher dB number for our ratio between the two.

So how does this relate to our amplifier power needs?  Remember when we started I explained how we measure efficiency in a loudspeaker: 1 meter, 1 watt gives us the efficiency.

If I place 1 watt of sine wave energy into a loudspeaker and it gives me 90dB of sound, that’s all the power I will need if I am only going to play sine waves at 90dB (which is fairly loud).  But if I want to then play speech from a CD, I need 9 more dB of power to cover the crest factor of speech, which is 12dB (3dB for the sine wave + 9dB more = 12dB).

Each 3dB is double the amp power so 9dB is 8 times more power!  This means I need a a power amplifier to produce 8 watts, instead of 1 watt, if I want to play speech over my speakers at the same loudness level.

OK, enough for today.  As you can probably figure out, music is an even higher crest factor than just ordinary speech.

Paul McGowan

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Hi. I’m Michael Vronsky - the Commercial Manager here. If you’d like details of where to buy PS AUDIO equipment AT SPECIAL PRICES (but only for our members) then please contact me at commercial@hifianswers.com Thanks. Michael.

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