bcarso
Well-known member
[quote author="recnsci"][quote author="bcarso"] But typical nonlinearites follow a power law with level, with 2nd growing linearly with level, third rising as the square, etc. [/quote]
Not exactly true. If we are talking about polynomial operators and if input
is sin(wt), x^3 will produce 3w AND w therms, x^4 will produce 4w AND 2w,
x^5 will produce 5w AND 3w AND w etc.
So if you look at second harmonic in THD spectrum, you will have
contributions from all even order therms in polynomial.
Now nice part. Few years ago I developed expression for all harmonic
produced by 7th order polynomial. While that paper is lost amid junk
in my "archive" I do remember that contribution of higher order is
converging (that is x^6 will give highest DC therm, than x^2 than x^4 and
x^6 will be lowest). OTOH all these components are proportional to
coefficient in front of x^n exponent. So they are usually small cus usually
these coefficients for high order exponents are small.
Now even nicer part. Note that all odd parts of polynomial will produce
component at fundamental. Those components ARE DISTORTION.
When you look just
sine wave, this effect resembles compression. With infinite time constants.
I have no idea what is audible effect of this "fake fundamental", cus
I havent figured out how to extract it. Fun
part is, THD wont show these, IM wont show these. BTW even order
exponents will have largest contribution to DC. This is DC when you
use constant amplitude input signal. With real world dynamic signals, even
therms will produce funny "fake transients".
cheerz
urosh[/quote]
I did say typical, not my later example of a cubing operator, which would be an unusual nonlinearity to encounter in an amp.
Try to dig up that ealier work though---it sounds interesting.
Not exactly true. If we are talking about polynomial operators and if input
is sin(wt), x^3 will produce 3w AND w therms, x^4 will produce 4w AND 2w,
x^5 will produce 5w AND 3w AND w etc.
So if you look at second harmonic in THD spectrum, you will have
contributions from all even order therms in polynomial.
Now nice part. Few years ago I developed expression for all harmonic
produced by 7th order polynomial. While that paper is lost amid junk
in my "archive" I do remember that contribution of higher order is
converging (that is x^6 will give highest DC therm, than x^2 than x^4 and
x^6 will be lowest). OTOH all these components are proportional to
coefficient in front of x^n exponent. So they are usually small cus usually
these coefficients for high order exponents are small.
Now even nicer part. Note that all odd parts of polynomial will produce
component at fundamental. Those components ARE DISTORTION.
When you look just
sine wave, this effect resembles compression. With infinite time constants.
I have no idea what is audible effect of this "fake fundamental", cus
I havent figured out how to extract it. Fun
part is, THD wont show these, IM wont show these. BTW even order
exponents will have largest contribution to DC. This is DC when you
use constant amplitude input signal. With real world dynamic signals, even
therms will produce funny "fake transients".
cheerz
urosh[/quote]
I did say typical, not my later example of a cubing operator, which would be an unusual nonlinearity to encounter in an amp.
Try to dig up that ealier work though---it sounds interesting.
