Clipping 101

DonH50

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Jun 23, 2010
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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.

To address power, 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. The figure below shows a pure 1 kHz sine wave, and clipped by 1% and 10%. The spectral diagrams (FFTs) show the resulting frequency content up to 50 kHz, and include 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).

clipfig1.JPG

The unclipped signal is a single spike at 1 kHz in the FFT. SINAD and SFDR around 240 dB represent the limits of the math program (resolution of the input signal). With 1% clipping, we see numerous spurs extending to 50 kHz (and well beyond, but I chopped the plot there), 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. However, you can probably hear the clipping as a low but harsh buzzing sound if you were to play this as a test tone.

Notice 10% clipping reduces SINAD to 27.5 dB and SFDR to 29.7 dB, still fairly small relative to the signal but high enough that I suspect most 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.

HTH - Don
 

DonH50

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Couple of other shots showing what happens with more signals. The first picture is with 1 kHz and 10 kHz tones at equal level. Because the 10 kHz tone modulates the 1 kHz tone, fewer peaks are effectively clipped since the signal spends less time in the clipping region. This is reflected in the better distortion numbers. In the second figure, I combined an 80 Hz tone, 1250 Hz tone that is 10 dB lower, and a 7900 Hz tone anther 10 dB below the 1.25 kHz tone (-20 dB relative to the 80 Hz tone). Again you can see the impact of multiple tones "reducing" the impact of clipping. A key caveat is that I am showing fixed clipping levels of 1% and 10%. In the real world, it is just as likely that the additional signals drive the amplifier harder so clipping increases.

Equal amplitude tones at 1 kHz, 10 kHz:
clipfig2.JPG


Tones at ~0 dB/80 Hz, -10 dB/1250 Hz, and -20 dB/7900 Hz
clipfig3.JPG
 

DonH50

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Jun 23, 2010
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Thanks Amir. My math program is supposed to create .wav files from a matrix and I really wanted to add them so people could hear what it sounds like. Unfortunately I could never get the conversion to work. Reading back, I do not want to leave the impression that you cannot hear 1% clipping with a test tone; it is definitely audible, at least to me. It is much harder to pick out of a musical signal, but is one of those things noticeable by its absence when removed.
 

DonH50

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Finally got my .wav function to work! Forgot to scale the data, duh... They are very short test files meant to demonstrate the impact of clipping. They should clearly show why we think clipping is bad!

I have two .zip files with several test cases, all 16-bit, 44.1 kS/s .wav files. They only last about 3 seconds, but it's enough. The actual tone frequencies are chosen using the IEEE ADC Standard for calculating frequencies that are relatively prime so frequency components do not utilize more than one FFT bin and no window function is required (that just means the tones are "clean" without any funny sampling artifacts in the FFTs).

singletone.zip
IDEAL = ideal 1 kHz tone
CLIP1 = 1 kHz tone clipped by 1%
CLIP10 = 1 kHz tone clipped by 10%

threetone.zip
3IDEAL = ideal full-scale 80 Hz, -10 dB 1250 Hz, -20 dB 7900 Hz tones (chosen to avoid harmonic multiples)
3CLIP1 = same three tones, clipped by 1%
3CLIP10 = ditto, clipped by 10%


View attachment singletone.zip
View attachment threetone.zip

(Of course, now I am thinking of all kinds of neat test sound files showing jitter, etc.)
 

DonH50

Member Sponsor & WBF Technical Expert
Jun 23, 2010
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I got curious about the added power clipping causes. There has been a lot of debate about how clipping damages speakers. Looking at the FFTs above, it is clear there is not all that much added power at high frequencies, not all that surprising since going from an ideal sine wave to an ideal square wave (representing extreme clipping) increases the RMS value by 40% (it does not double or triple as some might think). Also note the third harmonic of an ideal square wave is 1/3rd the power of the fundamental, then higher-order terms go down by odd factors (1/5, 1/7, etc.) So there is significantly more power shifted to higher frequencies, but of course it depends upon what frequencies are clipping. Typical music exhibits large low-frequency signals and much smaller high-frequency content, thus little extra power is likely to get to the tweeter even for a heavily-clipped amp.

Using the signal above, comprised of 0 dB @ 80 Hz, -6 dB @ 1250 Hz, and -10 dB @ 7900 Hz, the RMS output voltage ratios are:
unclipped = 1.000
1 % clipped = 1.009
10 % clipped = 1.106​

Setting all signals to equal values such that the peak voltage is the same as above results in three smaller signal tones since the peak values of each signal add in-phase to create higher peaks with equal signal levels than if the higher frequencies are lower. Running the numbers again, the RMS voltage is now:
unclipped = 1.000
1 % clipped = 1.010
10 % clipped = 1.108​

So, the RMS voltage only increases by about 11 % for a signal clipped by 10%. Since power goes as voltage squared, the power increase is about 1.1 * 1.1 = 1.21 or about 20 %. Again, power does not double or triple for this test case. So what does it take? If I set the signal to 10x the limit, that is 10 times the clipping level, then the RMS voltage is about 2.3 times the unclipped signal. So, it takes a (relatively) huge amount of clipping to double or triple the power. Or, putting it another way, a severely under-powered amplifier.

One other concern is that most amps do not clip completely symmetrically. The plus or minus side usually clips at a slightly different level. This will add an offset to the clipped signal, increasing power slightly, but usually only to the woofer since it is the only driver typically DC-coupled (midrange and tweeter drivers usually have a series capacitor in the crossover to roll off low frequencies). This is again usually a small effect for practical levels of clipping.

So, with today's amplifiers and AVRs, clipping is probably not a real concern for most of us. Back when low end systems might output only a few watts, and mid-range systems 25 to 50 W, it was much more a concern. IMO!

Enjoy - Don
 

FrantzM

Member Sponsor & WBF Founding Member
Apr 20, 2010
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Thanks Don!! Great write-up. I thank you for the time taken to make us more knowledgeable..
 

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