Crest factor.

[Diabolical Artificer]

Not really sure where to put this one....

Why is the crest factor important in audio engineering (as it probably is in lots of applications)? As far as I can make out the crest factor is the level difference between RMS and peak power of a wave form.

In some stuff I read online it gave an example of the difference between a pulse and a sinewave both having an AC current of 5A, the crest factor of a sine being 1.414, the pulse having a higher crest factor. The outcome being that the PSU specs for the pulse needs to be beefier, ok, so far so good.

I've noticed that when testing an amplifier it's normal to test amp power at x RMS V/load using a sinewave as input into a resistive dummy load, which gives the power rating, of say 50w for example, however when the same amp is in use with music as the source or IP, even at full volume it will never reach 50w. some of this difference could be down to the different loads, but I'm thinking this is where the crest factor comes in.

If I have it right the disparity above is down to the different crest factors of source or IP, music is a complex wave most of the time so bog knows how you would compute it's crest factor, suffice it to say it must be lower than 1.414 or 3dB.

Do I have that right? As we don't often play repetitive gunshots or kickdrums (IE pulses) on our hifi's, though some drum and bass or grime sounds like it, where does the crest factor come in as regards amp design?

Andy.

[Radio Wrangler]

Originally Posted by Diabolical Artificer

Not really sure where to put this one....

Why is the crest factor important in audio engineering (as it probably is in lots of applications)?
Andy.

Quite simply because music and speech has so much of it!

In comms engineering, white noise has an almost infinite crest factor. Amazingly high peaks can be reached, but they are amazingly infrequent. In a comms link, it is the noise crests which create the errors in the data flow, so I spent part of my life designing noise-based test equipment for comms systems, and the crest factor of the noise was very very important.

Back to audio, good design practice involves acceptance that no system can reproduce everything. (anathema to audiophiles!) and then getting on with life and choosing where clipping points should be. Clapping is very noise-like and has very high crest factor. It's a useful thing to judge results on.

The crest factor is really the ratio of the level when the soloist coughs, the piano lid collapses, or the group really hit 11, to the longer-term average level. Percussion puts crests throughout music.

Dynamic range is the ratio of the loudest momentary sound to the quietest momentary sound.
Crest factor is the ratio of the loudest momentary sound to the long term average.

David

[G6Tanuki]

Originally Posted by Radio Wrangler

Quite simply because music and speech has so much of it!

David

And it's why us amateur-types put our audio through various degrees of level- and peak-management (AGC and clipping) to control the dynamic-range, allowing us to increase the average speech-level at the expense of the peaks and so achieve greater communications-efficiency without overdriving the output-stage and causing bandwidth-widening 'splatter' (in SSB systems) or overdeviating the carrier (FM) both of which which interfere with adjacent channels.

A typical human voice - minus any sort of audio processing - gives an average level of 15-20% compared to its peak. So your amplifier/transmitter - which needs to be able to handle the peaks - would spend most of its time not really working that hard, but it still needs to be able to do so when a crest comes along. A bit like your typical bus that has 50 seats which are only ever fully occupied for a few journeys a day and spends the rest of its time running round with only a couple of passengers.

Clip off or level-clamp the crests/voice peaks [which don't really contain much 'information'] and you can then increase the average level to something nearer to 50%.

[Diabolical Artificer]

Ok, so we are essentially talking about headroom yes? What sort of figure are we talking for peak above average, I presume design for 1.5 times average.

Andy.

[Dickie]

When I was responsible for the design of a professional true-rms voltmeter we had a crest factor spec. of 7:1 (voltage). This was presumably to cater for all real-life waveforms, including things like SMPS supply line spikes. I'm not sure how that compares to audio stuff, especially the implied crest factor of 49:1 power.

[Radio Wrangler]

Originally Posted by Diabolical Artificer

What sort of figure are we talking for peak above average, I presume design for 1.5 times average.
Andy.

Whether your figure is voltage or power, it is far too low. Speech or music clipped at 1.5 times average rms voltage would sound very objectionable.

Tanuki was talking about amateur radio transmitters getting understandable speech around the world without ant need for quality of reproduction, just comprehension. We compress the living daylights out of audio and employ costly RF or multiband processors to do it.

Broadcast radio has to create the impression of reasonable quality, yet must not be able to over-modulate their transmitters else the authorities close them down. These people need peak management that isn't too obvious. Their marketing people want the mean level high so they sound louder than their competitors. Have a look at the discussions about Orban Optimod processors and you'll get the gist.

Radio 3, well-recorded records and CDs are where you get serious crest factor.

From a microphone, there has been no processing and crest factor is huge.

Look at this problem backwards. Decide on the crest power you want to handle and then look at how cool you amplifier can loaf along most of the time.

David

[mhennessy]

Roughly working out what the RMS and peak values of a piece of music is actually dead easy.

Simply play back the audio in Audacity: https://www.audacityteam.org/

You have to switch the meters to "RMS" rather than the default of "Gradient". Having done this, you get two shades of green on the level meters, representing the RMS and peak levels.

You'll get different numbers for each track you play, but for something that is well-recorded, around 20dB might be seen. For something that is excessively compressed, perhaps 10dB or less...

Next, you need to convert from dB to power ratios:

10dB is 10:1
20dB is 100:1
30dB is 1000:1

So if you play a decent track (PMR of 20dB) through a 100 watt amplifier which is only just clipping the peaks, the mean value delivered to the speakers is only 1 watt.

That surprises a lot of people, but it's true, and very easy to prove. Don't forget that 1 watt is actually quite loud - how sensitive are your speakers?

The amplifier designer will quite legitimately take liberties with power supplies and heat sinks, because it's the average power that determines how hot things get. Speaker designers are quite glad about this too, for exactly the same reason.

Headroom is just the difference between the peaks and the maximum power your amplifier can deliver. That is not the same as the difference between the RMS and peak value - these are 2 distinctly different things, so don't confuse them. For a given piece of music played back with no clipping, the PMR will always be the same, but the headroom will depend on how far you turn the volume control.



(PMR means "peak to mean ratio". In audio, that's preferable to "crest factor", though CF is in common usage, for better or worse)

[Lucien Nunes]

Headroom management in audio is an important matter and the approach varies according to the type of equipment and purpose to which it is put.

The key compromise to be made is between headroom and noise. Any height of peak can be accommodated and reproduced, but possibly at the expense of reducing the average level down amongst the noise. Since much more information is usually present in long quiet passages than in transient events, it's usually important to keep the SNR high for average content and accept that extreme peaks will get clipped, as RW describes. There are similarities and differences between managing crest factor and managing dynamic range, but they both make demands on channel headroom.

What constitutes an extreme peak depends on the kind of content and how it is being listened to. Live orchestral music can exhibit over 100dB of dynamic range, while some highly compressed pop contains only 10-20dB. In the concert hall, we can hear about 80dB of what is on offer to us, but in the car, anything over maybe 20dB will be either uncomfortably loud or inaudible. Thus, what constitutes a clippable event in some content, is part of the music in others.

Historically, recording media and transmission channel performance have dictated what we listened to in our homes. As a rough guide; LP's 60dB, cassette and FM 50dB, AM 30dB. An amplifier capable of reproducing the output of even a good FM tuner might get away with 30dB less than one intended for monitoring in the recording studio. CD, with its 96dB, increased the demand for headroom in reproducing equipment. In practice, much broadcast content is compressed beyond the compression in the recording, to make it more acceptable for people in non-ideal listening environments and to make it seem 'louder'.

'Loud' stations are ones that sound loud for a given signal strength and gain. Broadcasters process the signal to sound subjectively loud and eliminate peaks, to pack the greatest listener impact into a given carrier without overmodding. Typical processes are multi-band compression (which levels out vocals and instruments without them ducking to the drum beat), and phase rotation. This is subtle but it significantly reduces crest factor without much audible degradation. It works by de-correlating the phase of the harmonic components of peaks (as the ear is not very sensitive to relative phase) so that the same amplitude of each harmonic in a sound is present, but at such phase as to minimise crest factor, Thus, listening to a CD may demand tens of dB more headroom than listening to a good quality broadcast of the same CD. Broadcasters vary in their agressiveness: Radio 3 used to allow an extra 10dB of headroom relative to Classic FM, due to their different target audiences and likely listening conditions (Classic FM optimised for car, R3 for living room). Other than classical, crest factor overall has been falling in recent years. It surged with the improvement in recording equipment but started falling again in the loudness wars of the last couple of decades.

Another factor to consider is what exactly happens when the peaks do get clipped. Conventional valve stages are fairly graceful. Solid-state devices can also be graceful but many early designs were poor and led to much of their initial bad reputation. Blocking effects, where a stage goes deaf while it staggers slowly out of overload, are particularly nasty. Ordinary intermodulation can be nearly as bad when a transient comes along that, while of limited impact in itself, creates non-harmonic distortion of the rest of the program. Harmonic distortion due to loss of linearity as the signal reaches its limits, can be the least or the greatest of the problems depending on the type of device.

So, what then is a 'good' figure for domestic audio system headroom? By way of example, a 'line level' signal through a pair of phono sockets typically works at -10dBV, i.e. it is expected that the highest level of program envelope (averaged as defined in the specs for VU meters) will ride at about 10dB below one volt, 316mV. The maximum swing defined in the standard is 5.6V p-p, i.e. 2V RMS, which gives 20 log (2/0.316)=16dB. So that's the headroom you have in the signal interface, when the level is adjusted to what the designers probably intended. Average program might be another few dB below, in which case a crest factor of 10:1 is about what you will get. In pro audio, you would be expecting at least 24dB headroom, which with signals of average dynamic range accommodates a crest factor of 30:1

[Radio Wrangler]

In an attempt to design a good amplifier, you have to bite the bullet and accept that it will get clipped. Maybe from time to time, maybe frequently.

The only defence is to design it so that it clips and does not make things any worse than they need be.

Many early transistor designs were lousy in this area, and a number of later designs, too. They would upset their bias systems while clipped and then take an age to recover. Valve amps through thier simplicity were not as prone.

We've learned to avoid this trouble, but its problems have entered genetic memory and are assumed to still apply.

Crest factor is the usual term in comms and RF engineering.

David

[mhennessy]

The need for headroom is governed by how controlled the signals are.

At the input end of a chain - at the mic pre-amp - then headroom is really important. The signals arriving from the microphone are as uncontrolled as signals get. Imagine a fixed microphone in an unattended "down the line" studio, where a guest is shown to the room by a receptionist, who does nothing more than open the door and turn on the lights. One day, your guest might be someone not used to talking on microphone who is therefore is very nervous and quiet, and perhaps not close enough to the mic. The next day, the guest could be Brian Blessed! Clearly, that mic pre needs to have excellent headroom.

The signal from a mic pre might be manually controlled, or automatically controlled to some extent by a compressor/limiter. Whatever the mechanism, this signal is now regarded as controlled, so headroom is less important. But still desirable, in case of operational error, and usually easy to provide.

With a digital sound desk, the headroom is determined by 2 factors: the ADC and DAC converters, and the internal number-crunching. There is analogue gain ahead of the ADCs, so adjustment of that (by an operator) is crucial, but essentially arbitrary (they will have to make a decision based on how uncontrolled the signal will be, knowing that people play/talk/sing louder when the red light goes on, so it's a judgement call - lining up to a known reference during rehearsal might be asking for trouble if it only leaves 10dB of headroom!).

The internal processing might be floating point or fixed-length - that's up to the manufacturer to decide - but one desk I know about at work has an internal headroom of 300-and-something dB as a result of the floating point processing. No risk of clipping mix buses there!

Finally, the output converters are usually lined up such that -18.06dBFS equals 0dBu. As we peak to PPM 6, which is +8dBu (for a sine wave - another massive can of worms!), then there is 10dB of headroom a the output of a typical broadcast desk, which isn't exactly generous. Some analogue desks might be better than that. But the operator has had plenty of opportunity to control the levels by this point, and of course, the desk config might include an emergency compressor/limiter at the output, before the DAC. As described, headroom is a non-issue while it is inside a well-designed digital system, and it's only at the conversion points (to analogue, or to digital, where AES and similar is not floating point).

By the time you've put a recording onto a CD, there is no need for headroom whatsoever. Headroom is there to provide for unexpected events, but a fully produced CD contains no surprises. It will typically be mastered so that the peaks hit 0dBFS, give or take.

Likewise, for FM broadcast, there is no headroom to speak of because the optimods will have ensured that the signal is within a fraction of a dB of hitting the limiter on the input to the transmitter.

So what about headroom at home?

Given that FM and CD don't need headroom, headroom boils down to a question of how much amplifier power you have, and how loud you like to listen. If you don't mind mild clipping, then you'll be happy with negative headroom!

Obviously, that's an over-simplification because apparently people still listen to vinyl. Scratches, etc, can be a lot louder than the recorded programme, so it's important that the pre-amp doesn't clip these. But it's really not difficult to build a pre-amp using op-amps that run from +/-15V that will have no headroom issues with any source you care to throw at it. So assuming a basic level of competence at the design stage, headroom in a preamp is academic.

If you use digitally controlled volume ICs, then it's a bit more complicated if you select one that doesn't run from +/-15V. Years ago I was battling with the LM1972, which is good for +/-5V only. This meant having to attenuate before the IC, and amplify afterwards - clearly this incurred a small noise penalty. Nothing that would have been a problem in practice, but it still felt wrong. Luckily, the +/-15V PGA2310 arrived, and is still in production today. It is a remarkable IC that I continue to recommend.

Today we assume that the nominal maximum signal level is 2V RMS. Headroom is defined as the difference between programme peaks and the clipping point (nothing to do with the mean levels). A pre-amp running from +/-15V should handle 9V RMS before clipping - probably a bit more in practice - so if you have an op-amp before the volume control, it has at least 13dB of headroom. If headroom is especially important to your Marketing department, you can power NE5532s from +/-22V if you're feeling brave. That's at least 14V RMS, or 17dB of headroom. Pure specsmanship, of course...

What about the op-amp after the volume control? Well, this has infinite headroom. Why? Because the power amplifier will clip long before this op-amp can. Power amp sensitivity will be in the 1V RMS ballpark, so there's no way the op-amp driving it will clip first. Simple.

So as I said earlier, the headroom of your home hi-fi is determined by how far you turn the volume control, relative to how much power you have. The only caveat is the assumption of half-competent design in the pre-amp, so that the clipping only occurs in the power amplifier. That's "audio design 101" - very rare to see people make that mistake in practice.

That leaves only one challenge for the designer: given that power amp clipping is completely and absolutely inevitable, you'd better spend time making sure your amplifier clips "nicely". There's a lot of art and science in that. Or you could cheat and use valves

[Ambientnoise]

When I worked in measurements in underwater acoustics, crest factors of 30dB were the normal baseline. As in general comms, voice signals were compressed, in our case to a crest factor of 10dB before modulation onto an 8kHz carrier.

Ken

[Diabolical Artificer]

Thanks all, some very well written and explained posts there. I'm going to have to read and re-read them to assimalate all the info.

A lot of my recent question's seem to revolve around or concern noise in amplifiers. I'm struggling a little at present with a practical example of this, EG trying to design a voltage amplifier stage with enough gain but not too much gain that the stage amplifies all the nasties, particularly ripple on the power supply. Lots to think about.

"There's a lot of art and science in that. Or you could cheat and use valves " that made me smile.

Andy.