Where are and how 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]

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]

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]

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.

 

[el156]

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.

Thanks, very nicely explained, but i would like to know(if possible)in the case of a TUBE,what could cause the harmonics. Maybe the electrons at high speed,when they hit the plate,and some of them jump from the plate and go to the grid or cathode? Or can it be another phenomenum?
Thanks

 

[Wavebourn]

Thanks, very nicely explained, but i would like to know(if possible)in the case of a TUBE,what could cause the harmonics. Maybe the electrons at high speed,when they hit the plate,and some of them jump from the plate and go to the grid or cathode? Or can it be another phenomenum?

Actually, harmonics were produced in the math lab of Fourier. It is completely mathematical model, to represent any periodical function by sum of elementary periodical functions.

Distortion measurement equipment uses this mathematical model to observe harmonic content of distorted sinewave signal. Why? Because it is easier than to measure deviation from straight line of triangle signals.

So, percent of harmonics is used instead of max deviation angle. Is it better, or not? I don't know. Otherwise somebody would start the tpic, "WHERE ARE;AND HOW ARE THE ANGLES GENERATED?"

 

[Bigun]

triangle signals are no good as a reference - contain only odd harmonics.

 

[Wavebourn]

triangle signals are no good as a reference - contain only odd harmonics.

I don't mean measurement of harmonics; I mean direct measurement of shape, to get all distortions directly.

 

[DualTriode]

Thanks, very nicely explained, but i would like to know(if possible)in the case of a TUBE,what could cause the harmonics. Maybe the electrons at high speed,when they hit the plate,and some of them jump from the plate and go to the grid or cathode? Or can it be another phenomenum?
Thanks

Hello,
Electrons bouncing around to other electrodes is more about noise than distortion.
The way I understand the nonlinear character of a triode or a JFET for that matter is that the mu is proportional to the current through the device. For a triode the lower the grid voltage the lower the mu. Or to put it another way the lower the grid voltage the grid’s ability to decrease the flow of electrons increases. This results in a curved transfer function or unequal AC voltage swings at the output. The math is a complex set of tools to describe and possibility predict.
DT
All just for fun!

 

[Melon Head]

Just want to add here that music is harmonics and from that stand point I don't think THD is the be all and end all to music reproduction (Actually it probably is but I don't have a lot of confidence in the standard thd measurements using static sine waves into resistive loads).
For me I am more interested in looking at the harmonic profile.

 

[TheGimp]

Harmonic profile is certainly more enlightening than just a number for THD, however THD was popularized as a measure of amplifier quality by marketing hype. It had to be a simple number to keep consumers from becoming confused.

Confidence comes with understanding. Try using a spectrem analizer along with the THD measurement. It can become very enlightening.

 

[Melon Head]

The main thing that I am not comfortable with about THD measurements, is that they don't represent the nature of music and the load is not representative of a speaker load.

I could quite easily imagine a scenario where two different amps perform exactly the same with a resistive load but behave very differently with a reactive load.

 

[Wavebourn]

Even with resistive loads, comparing 2 different topologies using THD numbers is like comparing mental to surgery clinics by average temperatures of their patients.

 

[albin]

hello

springs