WHERE ARE;AND HOW ARE THE HARMONICS GENERATED?

[el156]

Hi all DIYs!
I have another newbie silly question. I know (i hope)what harmonics are. but the question is how and where are they generated? if we have a tube amp with a input tube ,do this tube generates harmonics? the Caps ,the resistors? Or they are already in the input of the amp (coming from the cd player) and get amplified by the amp?
Thanks

[SY]

Any bit which causes the signal to be distorted "adds harmonics." That's what distortion is, in its essence.

[PMA]

Mostly the transfer characteristics of the active element (or circuit as a whole, depending on circuit design), especially if openloop, is responsible for generation of harmonic frequencies. It can be more complicated by frequency dependence of the transfer characteristics.

[Evenharmonics]

Ideally, all the components should be 100% transparent and preserve what's on the music source (file, grooves ... etc.). In an example of fully differential amplifier, it strips away even harmonics during its summing process. It's good for noise and interference rejection but not good for source preservation.
Some details on differential circuit here.
Links on harmonics here and here.

[Miniwatt]

A non-linear tube will produce distortion and in doing so harmonics.
Non-linear means that the tube will amplifie (a bit) more with the grid between let's say -4V and -2V compared to -4V and -8V.

[Bigun]

I think you'd find a couple of articles by Nelson Pass to be useful reading to add some more context to the topic of distortion. The main one I'd recommend is this "Audio, Distortion and Feedback" and currently you can access it here: Pass Labs: Technical articles

[ChrisA]

Originally Posted by el156

Hi all DIYs!
I have another newbie silly question. I know (i hope)what harmonics are. but the question is how and where are they generated? if we have a tube amp with a input tube ,do this tube generates harmonics? the Caps ,the resistors? Or they are already in the input of the amp (coming from the cd player) and get amplified by the amp?
Thanks

Harmonics are produced any time the gain is non-linear. Linear gain means the graph of input voltage vs. output voltage is a straight line. If the line curves you will get frequencies in the output that were not present in the input. Why? Very hard to explain in a short forum post. But do you remember Trigonometry from high school and all those trig identifies? What happens if the gain function is a polynomial. Look at the simple case where the graph is ax+bx^2. Now if the input to the amp is a simple 1KHz sine wave test signal (written is "sin(x)" what is the output? A hint: From your old text book you look up that
sin^2(x) = (1 - cos(2x) ) / 2

So the output if the graph is ax+bX^2 must be
a * sin(x) + b * (sin(x))^2
which is (using the above identity from your book)
a * sin(x) + b * (1 - cos(2x) ) / 2
Look at the 2x. This explains a second harmonic (double the frequency)
Also as you expect if the "b" is larger the graph is more curved and the 2nd harmonic is larger.

You can explain other things like inter-modulation distortion by looking at the sum and difference trig identities.

The next level of detail has to do with the shape of the gain function and phase The easy case above is for a parabola but likely the shape is more complex than that and simple analysis using high school level math does not work but the simple case does completely explain the origin of harmonic distortion. Well, not really because now you have to ask why the gain is not linear.

[el156]

Originally Posted by Bigun

I think you'd find a couple of articles by Nelson Pass to be useful reading to add some more context to the topic of distortion. The main one I'd recommend is this "Audio, Distortion and Feedback" and currently you can access it here: Pass Labs: Technical articles

Very interesting articles ! Thank you!

[TheGimp]

Another source of distortion (at lower levels) is capacitors.

As charges build up on oposing plates they will exert eletrostatic forces against the plates causing mechanical space changes. Since capacitance is related to plate spacing, the capacitance value shifts with applied voltage. This results in a shift in transfer function and is a non-linearity.

Dielectric absorption is another parameter that may influence signal integrety and thus may impact distortion.

[SY]

Originally Posted by TheGimp

As charges build up on oposing plates they will exert eletrostatic forces against the plates causing mechanical space changes. Since capacitance is related to plate spacing, the capacitance value shifts with applied voltage. This results in a shift in transfer function and is a non-linearity.

With any reasonably decent quality cap (i.e., those made by major manufacturers like Wima or Panasonic on high speed equipment), this effect is as close to zero as is possible to be. It can become an issue with small production volume so-called "audiophile" caps, where one pays much more money to get much worse performance.

At low signal levels, the already negligible effect gets even more ridiculously small. Compared to the nonlinearity of active devices (tubes, transistors), this is well beyond caring.