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Clipping 101

DonH56

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<Reproduced and expanded from the original 11/2/2012 article.>

Amplifier clipping has been cited as the cause of audible distortion, destruction of speakers (especially tweeters), and total annihilation of the known universe. More or less. In fact, clipping does cause distortion that adds significant high-frequency content not in the original signal, and does present higher power to the speaker. But perhaps less that you might expect, at least in some cases…

To address power first, a pure sine wave (undistorted signal) with peak amplitude A has an RMS value of A/sqrt(2) or 0.7071*A. A heavily clipped sine wave approximates a square wave, and thus has RMS value of A, about 30% higher. Assuming voltage is clipped, the square wave has twice the power of the pure sine wave since power is related to voltage squared. That is, a heavily clipped signal puts up to twice the power into the speaker as an unclipped signal of the same (peak) amplitude. Less-clipped signals will not have as large a power increase, naturally.

We already know square waves can be made from a series of sine waves (see related thread), thus clipping must add higher frequency content to create those sharply flattened peaks. An ideal square wave adds odd harmonics in proportion to their harmonic number, e.g. the third harmonic is at 1/3 the voltage of the fundamental, the fifth is at 1/5 the voltage, and so on. Remember power goes as voltage squared, so in terms of power the third harmonic is 1/9 the power of the fundamental, the fifth harmonic is at 1/25, etc. Power dies out pretty rapidly and is one of the common counter arguments to clipping “blowing up” speakers.

The figure below shows a pure 100 Hz sine wave. The signal is sampled at 4 MS/s but is not otherwise quantized (i.e. no explicit DAC; the math program’s resolution is about 38 bits for this example). The signal is 2 Vpp, or about 0.707 Vrms. Note cliplevel = 0 % means no clipping and so the ideal and “clipped” signals are identical in the top plot. The spectral diagram (FFT) shows the resulting frequency content up to 1 MHz, and includes the calculated SINAD (signal to noise and distortion) and SFDR (spurious-free dynamic range, the distance from the signal to the highest distortion spur in dB). The first numbers are for the ideal input, the second for the clipped signal. The ideal and clipped results are again identical for this test since the signal is not clipped. The dynamic range of the math program is ~240 dB and is reflected in the SINAD and SFDR results.

fig1.png


With 1% clipping, the signal flat-topping is barely visible but we see numerous spurs extending to past 10 kHz, and now SINAD is only 51 dB and SFDR around 58 dB. While significant, this is probably inaudible, especially in the presence of more complicated musical (or movie) signals. Notice the clipped sine wave does not look like a square wave, and of course the spectrum does not show the same progression in harmonic levels a square would provide. As far as power, 50 dB is a factor of 100,000 lower in power than the fundamental. If you were putting out 100 W, the total power in the clipped signal is 1 mW (0.001 W). You might hear the clipping as a very quiet harsh buzzing sound if you were to play this as a test tone. However, it is unlikely to cause any sort of speaker damage (IMO).

fig2.png

I performed a couple of other interesting calculations on the clipped waveform. First, the RMS voltage is now 0.713 Vrms, a 1 % increase. Second, I split the audio into three bands to see how much energy is in each band. I used ideal (perfect brick wall) crossovers of 300 Hz and 3 kHz so there is no energy shared among drivers. No, the real world does not work this way, but it was easy to do the math. Adding more realistic filters is possible but a bit painful the way I am doing things (would require a significant amount of programming effort). Note 1 % is -40 dB relative to the maximum signal but the energy in any given band will be less (all the clipping energy combined would yield a -40 dB SINAD). For this test, the low frequency (woofer) SINAD is 58 dB, midrange is 52 dB, and high range (tweeter) is 71 dB. That means the tweeter is actually receiving about 20 dB less of the clipped signal than the woofer or midrange, which are roughly equal. This is expected given the low test frequency.

Next I increased the clipping level to 10 %. The flat top is now clearly visible, and notice the more clearly defined frequency roll-off as we get closer to a square wave. Notice that 10 % clipping reduces SINAD to 27.5 dB and SFDR to 29.7 dB, still fairly small relative to the signal (only 1/1000 the power) but high enough that I suspect many of us can hear it even with the music playing. More complicated signals will produce more complex distortion but the idea is the same; added high-frequency content and higher power than in the original signals. In this case, the signal voltage is now 0.757 Vrms, a 7 % increase over the pure sine wave. The woofer and midrange both have about 30 dB SINAD, and the tweeter about 60 dB. That is, the woofer and midrange are both getting an extra 0.1 W from our (clipped) 100 W output, and the tweeter is getting about 100 uW (0.0001 W). Still seems unlikely to cause damage, at least for this low-frequency signal.

fig3.png


Just for grins I ran a test with 50 % clipping (!) This seems like a lot, but remember if you really are at your amplifier’s clipping point, then an extra 3 dB peak will induce 50 % clipping since it is a request for twice the power. The signal is now pretty close to a square wave; note the third harmonic of a square wave is about -9.54 dB below the fundamental frequency. The woofer range SINAD is 11.2 dB (~8 W of our 100 W) and only the third harmonic lies in that band. The midrange SINAD is up to 23.5 dB (~0.5 W), and the tweeter 48.3 dB (1.5 mW). Notice the frequencies are odd harmonics and more closely follow the expected (square wave’ish) reduction in amplitude.

fig4.png


Now let’s look at some plots using higher-frequency signals for our test. Below is shown a 1 kHz signal with 1 % clipping. Only the spectrum is shown; the waveform looks like the previous waveform except for the time scale. Now there is no energy in the woofer (as expected), the midrange SINAD is about 58.5 dB, and the tweeter’s SINAD is 52.5 dB. Again relative to 100 W, that puts about 142 uW (0.000142 W) into the midrange and 559 uW (0.000559 W) into the tweeter. What is interesting is not the magnitudes, which are still in the mud, but that the tweeter is actually getting more energy from distortion than the midrange driver. However, remember that the midrange’s signal level is still 100 W, far above the distortion levels.

fig5.png


The test is repeated below for 10 % and 50 % distortion. The results are similar to before, with shifts in frequencies. Now woofer power is 0, the signal is 100 W in the midrange driver, and distortion products generate 0.124 W in the midrange and 0.0203 W in the tweeter with 10 % clipping of the 1 kHz sine wave. Clipped 50 %, we see 7.6 W in the midrange and 0.15 W in the tweeter from distortion.

fig6.png

fig7.png


Another set of trials was performed using a 6 kHz input signal. Only the 10 % spectrum is shown – note all distortion products now go to the tweeter, which is again driven with 100 W (pretty unrealistic, but we are looking at relative levels here). With 1 % clipping, there is an additional 0.0008 W tweeter power. There are 0.203 W added at 10 %, and 8.05 W added with 50 % clipping. If tweeter power was 10 W, less than 1 W additional power from 50 % clipping is added.

fig8.png


Applying multiple signals is a bit tricky. If each signal (100 Hz, 1 kHz, 6 kHz) were of equal amplitude, then the higher-frequency signals riding on the low-frequency tone will clip much more and the frequency spectrum of the resultant clipped wave will be weighted to the upper frequencies. This can be seen in the figure below, comprised of three tones (100, 1000, and 6000 Hz) of equal amplitude summed and adjusted so that the peaks are clipped by 10 %. The spectrum has little low-frequency content, then a large “hump” caused by mid- and high-frequency clipping. There are spurs throughout the frequency range, not just above 100 Hz, due to nonlinear mixing products from clipping the three signals. Still, very little power reaches the tweeter.

fig9.png


Increasing the clipping to 50 % yields the spectrum and data below. Now there is a great deal of additional power in the midrange (5.4 W) and even more in the tweeter (31.5 W). This is the sort of signal and clipping that can destroy a tweeter, again assuming a 100 W signal into the speaker system. This sort of distortion will be clearly audible, of course, though in the real world is probably very brief. Barring loud parties and alcohol…

fig10.png


Weighting the 100 Hz, 1 kHz, and 6 kHz signals in the ratio 100:10:1 and clipping the result by 10 % yields the waveform and frequency response below. This is closer to what a “real” signal might look like, with higher-amplitude lows and lower highs. Note clipping products (distortion spurs) are only about 20 dB below the middle tone, and many are at roughly the same amplitude as the high-frequency tone. Still not enough power to damage the tweeter, but enough to make for objectionable listening.

fig11.png


Repeat, this time with 50 % clipping. Now distortion spurs exceed the midrange and tweeter signals as the low signal is grossly clipped. Note that extra power from clipping in the midrange and tweeter bands is still low, however, at 1.03 W and 0.0143 W respectively relative to a 100 W signal. The harmonics and mixing products from clipping fall off quickly so, unless the midrange and tweeter signals are fairly large, not enough power to cause damage is likely to be generated. Some music may have middle and high frequencies higher than this example, however, so caution is in order.

fig12.png


Clearly clipping does add power at higher frequencies, but in practice it would have to be severe clipping to add enough power to cause speaker damage. More likely is that with the volume turned so high the net power into the drivers is simply too large for them to handle, clipped signal or not, since the distortion should be clearly audible. This does not rule out damage from overzealous listening, parties, and so forth.

There are a couple of other things that can cause damage, however:
  1. Amplifiers often clip asymmetrically, that has more on the top or bottom. That will introduce an effective offset that looks like a D.C. signal component that can go through the woofer, potentially causing damage.
  1. As Amir’s testing as reported in other threads has shown, some amplifiers are not stable when they clip. This can cause high-frequency ringing and even oscillation, adding to the clipping distortion and again potentially damaging drivers.
Hopefully this provides some insight into the effects of clipping. Note that clipping can occur anywhere in the chain, from cartridge (or DAC buffer) to speaker. Also remember that many other factors contribute to distortion and potential speaker damage. And that you can always repair or replace your speakers, but you’ve only one set of ears. - Don
 

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DonH56

DonH56

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This was an old thread on another forum copied over here by request. This is actually an expanded version of that thread with more detail and figures. Unfortunately I just copied it into an old dummy thread I created for the purpose long, long ago, so it looks like an old thread when in fact it was created here just tonight (11/5/2020). Thus this nonsense post to explain and bring it to the "new posts" listing.

Enjoy - Don
 

Cbdb2

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Different amps deal with clipping recovery differently ( clipping can saturate transistors ). Some better than others. These differences can be audible. Part of the sound of under powered amps. Tubes come to mind.
 
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DonH56

DonH56

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@amirm has some pictures of misbehaving amplifier outputs and I am sure there are others out there on the 'net.

Back when I was working with a fellow student ca. 1980 on a class D amplifier design we saw an extreme example. I don't recall what the input opamp was, some 709 or 741 variant, and that is when we learned how some opamps invert their output when overdriven. Fortunately it was a low-power amp so no real damage, but it took us a bit to figure out exactly what was happening. If it had been a conventional class A or AB amp it would have been obvious, but it was our first class D and inversion was not real obvious just looking at the raw output. We looked all over and developed a number of brilliant but inapplicable theories before figuring out it was the input opamp making all the fuss.
 
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Head_Unit

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This paper by Montgomery Ross, "An Investigation into How Amplifier Clipping is Said to Burn-Out Loudspeakers, and How Limiters Can Save Them"
https://www.aes.org/e-lib/browse.cfm?elib=5737
says "It is shown that clipping is not what causes the damage, but, rather compression of the audio spectrum" (in other words, the bass power is regularly up near maximum, so turning the gain way up will increase power maybe double for bass peaks. The treble, which is usually much lower in level, can still be amplified way more, and what might normally become a couple watts of treble peaks can be amplified to tens or hundreds of watts. Poof! goes the tweeter.
 

Speedskater

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A few years ago, there was a thread in a pro audio engineering e-mail group on this subject. There was a wide range of view-points on this subject.
 

fpitas

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Different amps deal with clipping recovery differently ( clipping can saturate transistors ). Some better than others. These differences can be audible. Part of the sound of under powered amps. Tubes come to mind.
Yes. And tube amps for guitars are usually designed so the supply sags, especially the screen supply, to give more fuzzy distortion.
 

pma

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@DonH56 , I am afraid there is a problem with your analysis - it does not take into account the effect of speaker crossover, HP filter before the tweeter. I am going to explain it on the simulation of a real-world 3-way speaker.

This is the schematics including crossover, drivers dummy impedances and clipping circuit>

tweeter_clip_cir.png


next image is no-clipping 5kHz sine
tweeter_noclip_time.png


next is 5kHz clipping sine
tweeter_clip_time.png


Now 5kHz clipping sine with spectrum
tweeter_clip_timefreq.png


and 2.5kHz clipping with spectrum
tweeter_clip_timefreq2.png


I guess you would understand my hint.
 

DVDdoug

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:D I think I agree with what think you (DonH56) are saying and I'll add a few comments...

First I'll say, you can blow a speaker with clipping.

Usually the argument is that a higher-power amplifier is safer than clipping a lower power amplifier. I believe this is false.
It's not "safe" to over-power a speaker no matter how you do it. But speaker ratings and speaker power handling are "complicated" and "statistical" so it's never an easy issue.

If you have 6dB more power (4 times the power) that's obviously 4 times the power at all frequencies into all of the drivers. As you say, worst-case clipping can only double the (total) power (assuming continuous sine waves). But in real life you'll never have that much distortion (hopefully!).

The added energy is harmonics but with "regular program material", severe clipping seems to reduce the relative high frequency content. Mostly you're getting harmonics from the dominating lower frequencies and the original high-frequency content is wiped-out. That's what it sounds like audibly and I confirmed that with some quick-and-dirty experiments once...

..In Audacity, I lowered the level of a music recording to get headroom. I don't remember by how much, but by a lot. Then I boosted the volume and saved that file. Then I clipped the boosted file to match the peaks of the lowered-volume file. So now I had 3 files simulating an unclipped low power amplifier, a clipped low-power amplifier, and an unclipped high-power amplifier. When I looked at the spectrums the unclipped high-power version had the most high-frequency energy (more energy at all frequencies) and of course the "original" low-volume unclipped version had the least energy throughout the spectrum.

On the other hand, we aren't normally dealing with continuous sine waves. Music is dynamic so the average power is typically 1/10th of the peak power. It's the short-term average that heats-up and burns-out voice coils. Speakers are rated for peak unclipped power (old JBL paper) so with "bad clipping" you can get a LOT more than "twice the power" into the speaker and fry it. Or, with a 100W continuous test tones you can burn-up a "100W" speaker, and the tweeter can't handle as much power as the woofer so high-power high-frequency test tones easily fry a tweeter, perhaps with a frequency that you can't hear and/or a frequency that the tweeter can't reproduce.

But again. if you're using all of the available unclipped power from an amplifier that's a LOT more powerful you are also putting a LOT more average power into the speaker so you're in the same boat and you can fry the speaker.
 
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DonH56

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@DonH56 , I am afraid there is a problem with your analysis - it does not take into account the effect of speaker crossover, HP filter before the tweeter. I am going to explain it on the simulation of a real-world 3-way speaker.

This is the schematics including crossover, drivers dummy impedances and clipping circuit>

View attachment 257291

next image is no-clipping 5kHz sine
View attachment 257293

next is 5kHz clipping sine
View attachment 257294

Now 5kHz clipping sine with spectrum
View attachment 257295

and 2.5kHz clipping with spectrum
View attachment 257297

I guess you would understand my hint.
I intentionally did not include the crossover because the article focuses on clipping at the amp before the speaker just to illustrate the point and show the amount of energy generated at the amp's output. In the real world, the crossover can help, but does not completely ameliorate the problem. If you clip the amp, then the HF energy above the crossover frequency still gets to the tweeter (note high frequencies riding on lower frequencies in the signal also get clipped as well), though as you say is affected by the tweeter's transfer function. I am not discounting that function, since as you show in your example tweeters are frequently padded (attenuated) to match the sensitivity of the other drivers in the speaker. But that is different for every speaker so, rather than try to account for it, my post just explains the basics without further context. Your post adds real-world context that folk should recognize, but again in general we (the consumer) do not know the tweeter's transfer function so this my numbers lead to a conservative (high) estimate.

Not being a speaker designer, I am not sure how much padding is usually applied to a tweeter. Do you happen to have an idea? It is not something I have researched, and my limited look at various speakers I own show usually around 3 dB or so, a significant but not huge reduction.

This is another of those introductory articles that I know you generally disagree with. Trying to keep things simple for the lay reader necessarily means relevant details (requiring more knowledge and deeper understanding of the whole system) are left out. The line between "ignorance is bad" and "a little knowledge is a dangerous thing" (perhaps worse than no knowledge) is hard to follow.

No worries - Don

Edit: Just realized the original post was from late 2012, ten years ago, so I'd pretty much forgotten about it until it popped up again in another thread.
 
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Cbdb2

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I have seen many NS-10s in studios with fuses added to the tweeters (after the xover) but never on the woofer. You would be surprised how often these got blown with some of the rock engineers. Too loud Macleod comes to mind.
 

pma

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Sending heavily clipped signal is a disaster for the tweeter, for the already explained reason of interaction between the crossover HP filter and tweeter impedance. This cannot be disclosed by using a wave generator + resistor load only.

Below is the situation of heavier clipping. Please forget the even harmonics in the spectrum, they are a product of asymmetry as the DC component after turn-on has not completely disappeared yet. Longer time interval before FFT would fix it. However, it is unimportant. See the high amplitude of tweeter voltage plot v(t) and very high odd harmonics in the spectrum, just correlated.

tweeter_clip_timefreq3.png
 

Rick Sykora

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As am testing the Hypex NCx500 amp under different conditions, with the recommended 1200 watt power supply, the amp clips at about 400 watts. With a higher power supply, the same amp clips about 100 watts higher. The clipping occurs under the rated power of the supply, so am thinking the amp is clipping. If true, why does the higher power supply (also higher rail voltage) allow the amp to produce more output?
 

Sokel

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It may be related,it may be not but in my communication with icePower asking for the recommended 57V hanger version of 1200as2 (so I can hook up 300a2 on it) which was obsolete they told me that the 63V version (which I use for 2 years now under various conditions) would give me higher power before clipping and have no concern (absolute maximum for the 300a2 is 65V according to data sheet,1200as2 hanger aux outputs +/-63.1VDC,measured by me to be sure )

I know you're after technical reason here,so ignore it if it's irrelevant.
 

Rick Sykora

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It may be related,it may be not but in my communication with icePower asking for the recommended 57V hanger version of 1200as2 (so I can hook up 300a2 on it) which was obsolete they told me that the 63V version (which I use for 2 years now under various conditions) would give me higher power before clipping and have no concern (absolute maximum for the 300a2 is 65V according to data sheet)

I know you're after technical reason here,so ignore it if it's irrelevant.

Yes, your scenario is comparable to mine but am looking to understand why it happens. The simple explanation for amplifier clipping is that the power supply can no longer supply sufficient power to the amp. However, I suspect this type is clipping is different than I am observing in my testing.
 

fpitas

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Maybe the amp has pulse-by-pulse current limiting you're bumping into?
 

Rick Sykora

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Maybe the amp has pulse-by-pulse current limiting you're bumping into?
Idk as am not an amp designer and did not find in the Hypex data sheet. I have read something about up clipping versus down clipping. I suspect this may be the reason but am looking for some confirmation from the forum experts.
 
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pma

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As am testing the Hypex NCx500 amp under different conditions, with the recommended 1200 watt power supply, the amp clips at about 400 watts. With a higher power supply, the same amp clips about 100 watts higher. The clipping occurs under the rated power of the supply, so am thinking the amp is clipping. If true, why does the higher power supply (also higher rail voltage) allow the amp to produce more output?
You should be monitoring both power supply output voltage and output current (with a scope) for both power supplies used. You need to investigate if the power supply is not at the current limit or its voltage is not falling. You can use a small resistor like 0R1 to monitor the current. Take care about shorting the rails, use a differential probe e.g.
 

pma

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