Diode clipping

[Fred]

Hi.  Probably a lame question, but having read round links on this and other sites and googling around, I can't seem to find an answer to the following question:
Why does diode clipping result in adding harmonics?  Just a matter of interest, that's all.

Thanks very much.

[petemoore]

v  search for or type in...find 'GM Arts' scroll...

[Fred]

Sorry, I still don't see how limiting the voltage swing of a sine wave using back to back diodes leads to higher order harmonics.  Sorry, am I being daft.  Do higher order harmonics actually get added in the process or are the present harmonics merely emphasised by the frequency response of the circuit?

Thanks

[Jason Stout]

First, let me say that,
IANAMBICS (I am not a mathematician, but I can say that)

Clipping introduces harmonics because a man by the name of Fourier showed that any periodic signal could be represented as a sum of sinusoids.
It's confusing, but the (subtractive) action of clipping a sine wave can be replicated by the summing of sins (adding harmonics.)


http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Freq/Freq4.html

[mgrEIGHT]

The Diode clips the tops off the sine wave which makes it more like a square wave. The  edges of a square wave are caused by high order harmonics. So the output is squared off and therefore has higher harmonics added/ emphasised

[Johan]

its a little hard to describe without using pictures, but every diod has a forward voltage drop, meaning, in the direction that they lead the voltage, you loose a little bit of voltage. if you have a diod with one end connected to ground and the other end connected to a signal source, as soon as that signal source gets biger than the forward voltage drop ( usualy around 0,7Volt ) the diod will start to send all signal straight to ground, but you can still mesure those 0,7volts. it doesnt matter what kind of waveform you send through it. it will all be cut off and leaving a flat top on the waveform and the only remnance of the original wave will be the rise and fall before and after the 0,7v threshold. Basicly, this flatening off the waveform is what couses distortion.


Johan

[spongebob]

Clipping introduces harmonics because a man by the name of Fourier showed that any periodic signal could be represented as a sum of sinusoids.

Exactly, but I think there is no other way to explain this - unfortunately, because the math behind Fourier analysis is ugly!

For example, let's assume you clip a 100 Hz sine wave really hard so it looks like a square wave, then you can reproduce this square wave by adding odd-order harmonics (300, 500, 700, 900, ... Hz) to the original signal!

If your distorted signal contains more even- or odd-order harmonics depends strongly on the kind of distortion, hard/soft-clipping, symmetric/assymetric, etc.

[Jason Stout]

The Diode clips the tops off the sine wave which makes it more like a square wave. The  edges of a square wave are caused by high order harmonics. So the output is squared off and therefore has higher harmonics added/ emphasised

Just a few more lines,

Fourier showed that a square wave could be represented by an infinite sum of sins.
So:
A sin wave is pure, it has only only one frequency. A square wave is the sum of an infinite ammount of sin waves.
And:
This can be coarsely summarized by saying, that any periodic signal that has a flat top or bottom also has a shit load of harmonics, and can be defined as the sum of a shit load of pure sins.

[Chico]

Try googling for Forrier transforms.  Briefly, any periodic signal can be decomposed into pure sine waves having varying amplitude and frequency.

For example, take a look at [/img]http://mathworld.wolfram.com/FourierSeriesSquareWave.html

You do not need to understand the math to get the "big picture" here, so don't sweat it.

Look at the red sine wave and assume that is your original signal.  Now, your back to back diodes clip the signal so that it begins to look more and more like the square wave.  That is, the harder you drive your signal across the clipping diodes, the greater the peaks get clipped.

Now, do you see the yellow, purple, green, blue etc. signals? The more the original wave is "distorted" to look like a square wave, the more of these signals that are generated.  That is, if you sum each of the harmonics to the original signal, the result is the distorted signal.

It turns out that each of these new sine waves (yellow, purple, green, blue etc. signals) are harmonically related to the fundamental frequency of the original signal (in our case, the red sine wave).

Thus, it can be seen that the number of harmonics, their order, and the relative amplitude of each of those harmonics is dependent upon how the original signal is shaped.

Now, in practice, once the signal is clipped, we can play games with the signal by selectively filtering the clipped signal to emphasize, de-emphasize these harmonics.  

Hope that this helps and is clear.

Best regards

Tom

[petemoore]

Take a piece of paper with 10 lines going across it.
 Draw a thick line across the paper centered between the ten lines.
  Now draw a sine wave that goes equal amounts above and below the center line, up and down over lines 1 - 10.
 This is sort of what you'd see if your guitar, playing one note very cleanly was represented visually on an oscilliscope...a wave, having valleys and hills equal distance from 'center line.
 Now...rip the top half of the paper off at line 8...that's the wave [or what's left of it] as it looks after being clipped by diodes on the positive swing.
 Repeat to show the negative half of the wave being clipped [that's the diode facing the other direction you see in DIST + etc] but rip the paper on the bottom half at line 2.
 Now...for even more fun...we'll call the above what a silicon diode does...it's clipping threshold [the voltage at which it begins conducting] is higher than Ge's...
 For a demonstration of what A ge going one way --l<--- and a Silicon going the other way------------------------------------>l---- mgith sort of look like with the Ge clipping the bottom half of the voltage swing...rip off the bottom half of the paper at line 6.
 Notice how the edges of where the clipping occurs gets sharper as you clip harder = closer to center V.
 Now for the real fun...[you'll need a square to do this] measure the distance between 0V [that's where the wave crosses center line] to where the clipping occurs on the top and compare that to the bottom.
 Where the wave goes up your speaker goes out [for purposes of typing...] where it goes down, speaker goes in. these are events that happen at 440 CPS if you're playing the A string.
 But now that you've clipped the signal, you have many more events taking place. 2nd harmonics, 3rd harmonics...all mathmatically related to and sums or differences of the original, simple wave.
 As you move the clipping threshold up [like Si only chopping off line 8] the clip points occur at differnt intervals to the original wave when compared to the lower threshold of ge's as shown at bottom, clipping the wave at line 6.
 Boosting the input, or increasing the average voltage, and voltage swings, does not change the voltage where the diode starts clipping, it makes the wave bigger...producing a similar effect to lowering the threshold.
 If there's not enough voltage to surpass the clipping threshold, look at the picture of the paper before you tore the top and bottom off...no clipping occurs. Up the voltage or lower the clipping threshold enough and you'll be seeing clipping of the wave input.
 Play one note and 'severe' harmonics can be 'cool'....play two or three notes, and the sheer number of harmonics may take the resolution of the original signal and turn it to total mush...your multitude of frequencies coming in [the chord, multiple notes] turns into a squiggle of lines that is hard to sort out looking at it, and hard to discern when listening to it. That's Alot of Clipping.
 A Little clipping or 'ripple' [just a slightly 'wobbled' waveform, produces a more pleasant type of tone...depending on what your ears innately 'like' and what 'you' like...
  [voltage swings from negative to positive in the same time cycle as your strings Vibration ... open A String = 440 cycles per second]

[Fred]

Thank you all so much!  

You have all explained it very clearly and I am now one step closer to stompbox enlightment...

Thanks again, much appreciated.