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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
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In Reply to: What is 'nonlinear distortion?' posted by Al Sekela on June 15, 2006 at 15:24:34:
I think he's just referring in a general way to the input-output relationship of a system. Let me see if I can clarify this. To simplify, we need to neglect bandwidth considerations. In this case, an ideal amplifier might have an input-output relationship given by:Vout(t) = A * Vin(t)
Where A is the voltage gain. But what if the amp has distortion? Then the amp might have the input-output relationship given by:
Vout(t) = f(Vin(t))
Where f() is some function that involves more than just a gain A. It has some kind of a "bend" to it. The trick for calculating distortion begins with expressing f() in terms of a Taylor series expansion as follows:
f(x) = A*x + a2*x^2 + a3*x^3 + a4*x^4 + ...
Where the caret indicates "to the power of". For a distortionless amp, a2=a3=a4=...=0. So the "nonlinear distortion" refers to the input-output relationship f(x).
The second half of the trick is to let x = V * cos(omega*t), where V is the amplitude of the sinusoid. Then there are trig identities that relate powers of cos(omega*t) to harmonics. The squared term gives a second harmonic plus a DC offset error, the cubed term a third harmonic plus some compression of the fundamental, and so on.
This formula results in distortion that varies with signal level. It gets worse and worse as the amplitude gets larger and larger because of the squaring, cubing etc.
For intermods you do a similar thing, except you set x = V * (cos(omega1*t) + cos(omega2*t)). That gets even messier of course.
So you could say that intermods and harmonics are manifestations of the nonlinear distortion, while the "bend" in f(x) (the nonlinearity) is the root cause of them.
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Follow Ups
- Re: What is 'nonlinear distortion?' - andy_c 16:21:52 06/15/06 (2)
- Yes, thanks, but this assumes distortion gets smaller - Al Sekela 12:28:54 06/16/06 (1)
- "crossover" (zero crossing) distortion in particular... - real_jj 13:59:58 06/16/06 (0)
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