Amplifier power and clipping points: are power ratings supposed to be related to clipping points?

HappyPantherFan

Member
Hello ASR, thank you in advance for answering my silly question. I have a hunch that this has been standardized in the industry, only that I'm not good enough at googling.

As we know, there are two ways wave-forms add: for coherent ones, two equal signals in phase adds into something with 2x amplitude and 4x power; for non-coherent ones (say, two signals with different frequencies, same amplitude), the amplitude doubles as well as the power. Basis for free power of proper bi-amping. But viewed another way, the power is cut in half if an amplitude 'budget' is split equally between two signals.

It's easy to deduct further that for the 32-tone test signal we sometimes see in reviews, the output power is 1/32 of the a 1kHz sine of the same peak voltage... For an amp that is rated for 50W, it can only hope to output 50/32 = 1.5625 W of said 32-tone signal, and be already at the brink of clipping!!! That is, my hypothetical 50W amplifier has trouble pumping out even 2 Watts of real music power into speakers... Can barely reach 85 dB SPL @ 1m using an ordinary 83dB-per-watt speaker, oh boy.

Or is it that, any designer worth his salt would construct amplifiers, such that a 50W-1Vrms sensitivity design can output voltages corresponding to 50*32=1600W pure sine[1], and really won't clip a 5.657 Vrms input[2]? This way, the sustained output may be 50W only, but it outputs 50W real music power (modeled with a 32-tone) as well as pure sines.
[1]: sqrt(1600W * 4 ohm) = 80 Vrms, or 113V peak, 226 Vpp
[2]: =1Vrms * sqrt(32), the level needed for a 32-tone to have the same power as a 1Vrms pure sine

I really hope it's the latter. If so, that'd explain the always-too-low sensitivity figures of power amps - sure, 0dbV sine gets us max power already, but it'd take 32-tone of some +16 dBV amplitude to output that much power into our speakers, so they actually do not clip before that. Totally ready to be plugged to a DAC whose 0 dBFS = 2 Vrms. Or am I wrong, and everyone really needs that 1600W amp to drive his/her 83 dB/W @ 1m speaker to 'fill the house'?

Unfortunately you are not wrong. The ratio of the peak voltage to RMS voltage is called the crest factor, and single tone sine waves have a crest factor of 3 dB (= 1.4X). Typical music has crest factors a lot higher than 3 dB, and therefore with music an amp will clip at a power output level well before its "headline" power rating (which is measured with a single tone sine wave) is reached.

The M-Noise test signal by Meyer Sound (incorporated as AES75) for measuring loudspeaker maximum output, for example, has a crest factor of about 18 dB. The M-Noise was designed to emulate the dynamics of music in live performances.

So, if you want to avoid clipping your amp, the amount of headroom you'll need is (the 3 dB is crest factor of the original sine wave test signal):

Amplifier headroom = Dynamic range + Crest factor - 3 dB​

Example: Assuming your music has a dynamic range of 10 dB and a crest factor of 13 dB, the required amplifier headroom over the averaged power level is 20 dB (= 100X). Therefore, if the average power required at the desired listen level is 1 W, the amplifier will need a maximum output rating of 100 W to avoid clipping (with source materials having the given dynamic range and crest factor).

The saving grace is that occasional well behaved clipping is actually not very audibly offensive (see this post, unlike popular belief). So you may be able to get away with 3 - 6 dB less than the calculated number (i.e. power headroom of 25 - 50X).

Charles Sprinkle of Kali has expressed similar sentiment regarding amplifier power ratings in this post:

t's easy to deduct further that for the 32-tone test signal we sometimes see in reviews, the output power is 1/32 of the a 1kHz sine of the same peak voltage... For an amp that is rated for 50W, it can only hope to output 50/32 = 1.5625 W of said 32-tone signal, and be already at the brink of clipping!!! That is, my hypothetical 50W amplifier has trouble pumping out even 2 Watts of real music power into speakers... Can barely reach 85 dB SPL @ 1m using an ordinary 83dB-per-watt speaker, oh boy.

...If it was that bad, most people would be listening to distorted music most of the time!

It doesn't make that much difference if you have a single tone at 50W or a complex multi-frequency tone at 50W. Except our ears are most sensitive to mid-frequencies and we generally need more power in the bass range. There are also limits to the format, and digital is (generally) limited to 0dBFS. When a CD is made it doesn't matter if it's a single acoustic guitar or a full orchestra or a rock band, the peaks can't exceed 0dBFS. The acoustic guitar will "sound quieter" and will require more headroom for the peaks if turned-up.

The peak-to average ratio is more important because you don't want to clip on the peaks. It depends on how dynamic the music is and that's unrelated to the number of simultaneous frequencies.

Continuous RMS ratings are conservative (if they are honest measurements). Some amplifiers have headroom for short term peaks and they can momentarily put-out more power.

...even 2 Watts of real music power into speakers...
In the old days, "music power" had the opposite meaning... And amplifier might be advertised as having 50W or 100W of "music power" and 10W RMS. It was an exaggerated (perhaps made-up) spec that was supposed to represent the maximum short-term peak power, probably without regard to distortion. Consumer protection laws were passed to stop that, but manufacturers seem to be fudging their specs again.

Thank you for your kind replies. I'm now illuminated.

Also note that real music does not at all look like a 32 multitone. It has a heavily slanted spectrum:

So at 1 kHz it’s already more than 20 dB down in level, which is a factor of 100 in power! So anything above 1kHz contributes for about 1% of the total power needs.

Interesting, so does that mean it's bass (or the peak around 60-100 Hz) that causes clipping?

Interesting, so does that mean it's bass (or the peak around 60-100 Hz) that causes clipping?
In the vast majority of cases: yes!

Also note that real music does not at all look like a 32 multitone. It has a heavily slanted spectrum:

View attachment 303329

So at 1 kHz it’s already more than 20 dB down in level, which is a factor of 100 in power! So anything above 1kHz contributes for about 1% of the total power needs.
Pink noise has a power spectral density proportional to 1/f, a characteristic which is shared by most common music . The total power in each octave is constant when the power spectral density is 1/f, see below:

This characteristic means that power in each octave band is roughly the same, i.e. the power in the frequency octave band 50 - 100 Hz is the about the same as the power in the 1 - 2 kHz band (or 250 - 500 Hz band, or 10 - 20 kHz band, etc.).

Frequency response curves are usually drawn with the frequency (horizontal) axis in the logarithmic scale. However, the frequency bins from an FFT is linearly spaced. Therefore, if you compare the 50-100 Hz octave to the 1-2 kHz octave, the 1-2 kHz octave has 20 times ( = (2000 - 1000)/(100 - 50) ) the number of frequency bins. That's why you see the much lower "grass" heights but higher grass density as frequency increases. (When plotted in dB vs a logarithmic frequency scale, pink noise will show a -6 dB/octave slope.)

Interesting, so does that mean it's bass (or the peak around 60-100 Hz) that causes clipping?
In the waveform, everything rides on top of each other. It is difficult to say where the straw that broken the camel's back comes from.

In the Old Days, amplifiers were usually rated at the onset of clipping, when distortion was still very low. Later, it was realised that rating at 1% distortion, i.e. well into clipping resulted in a satisfyingly bigger number for output power. Later still, these current cheapy (mostly Class D) amplifiers are rated at 10% distortion so even bigger numbers.

Being an old-fashioned sort, I still measure amplifier output and distortion at the onset of clipping, with 1kHz tone, as that results in the most conservative number. The output peak meters on my amplifiers indicate clipping correctly as the point at which clipping starts, using tone, not some notional X% distortion level, or with music signals.

S.

Example: Assuming your music has a dynamic range of 10 dB and a crest factor of 13 dB, the required amplifier headroom over the averaged power level is 20 dB (= 100X). Therefore, if the average power required at the desired listen level is 1 W, the amplifier will need a maximum output rating of 100 W to avoid clipping (with source materials having the given dynamic range and crest factor).
Wow! That was a close call. My heavy Yamaha M-2 beast is good for 2-3 meters ...

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