# Nonlinear harmonic distortion vs. linear harmonics

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#### capslock

I have seen the statement (among others, by Mr. Timmermanns) that there is no discernible correlation between the sound of a speaker/driver and its distortion figures, at least as long as midrange distortion is below 1%.

You can also find the statement that 2nd can be tolerated, 3rd less so whereas higher orders sound really nasty.

Typical publications will give "harmonic distortion" figures, probably without much thought.

The whole concept of harmonic distortion assumes that there is a nonlinear transfer function. E.g. a transistor amp will deliver an output voltage that is not strictly proportional to the input voltage. Or a spring in a loudspeaker will no longer exert a force that is proportional to the displacement for sufficiently large amplitudes.

A nonlinear transfer function, as can be shown from Fourier analysis, will result in added harmonics at multiples of the original signal frequency. These harmonics increase overproportionally as the signal grows!

However, there can also be linear harmonics. A mechanical resonator such as the air in a pipe, a string in a musical instrument or the membrane of a loudspeaker will oscillate at a multiple of the fundamental, also known as harmonics. As long as the forces (compressibility of the air or stiffness of string or membrane) are linear, these harmonics will remain at a fixed percentage of the fundamental amplitude.

I suspect that linear harmonics will just change the tonal balance but will sound much less nasty than harmonic distortion products, the percentage of which changes with the amplitude.

The standard speaker test will just analyse the harmonic content and report this as "distortion".

Testing the harmonics at different volumes and separating linear and nonlinear portions would be a more meaningful test. Maybe a correlation between the subjective sound and the percentage of true nonlinear distortion can then be found...

I would be particularly interested in how the high distortion of the Newtronics Mega speaker that uses the Manger MSW is composed. A plot can be found in phase_accurate's introduction thread. I have asked Dave to move that to a separate thread.

Eric

#### Grasso789

Hello and Guten Abend,

I have seen the statement (among others, by Mr. Timmermanns) that there is no discernible correlation between the sound of a speaker/driver and its distortion figures, at least as long as midrange distortion is below 1%.
This can become disproved easily with a sine signal. Midrange in the narrow sense is one to two Kilohertz. Running a 1.6 KHz sine thru an exponential function such as an amplifier made of a single bipolar transistor, which produces a monotonously falling harmonic series, and listening to that at around 8 Bel SPL, one can make out less than 0.1% non-linear harmonic distortion. This is, because our hearing is most sensitive in presence range, which is around k2, the first harmonic, of a fundamental of 1.6 KHz, and because our simultaneous dynamic range, say contrast, is 7 Bel for these sines at this SPL. Still few musical instruments have fundamentals above 1KHz; pure tones of these frequencies rarely occur. Yet we detect them in all their purity.
You can also find the statement that 2nd can be tolerated, 3rd less so whereas higher orders sound really nasty.
Non-linear harmonic distortion is less obnoxious (thanks, X!) at lower fundamentals, unless it contains large harmonics as hi as to fall into the presence range. This is because of masking, which is a firmly wired filter between ears and consciousness, at lo levels, and because of non-linear harmonic distortion within our ears, at hi levels. For fundamentals above 1.6 KHz, higher harmonics become less obnoxious, because our hearing deteriorates within narrow-sense treble range, which starts at 5 KHz.
However, there can also be linear harmonics. A mechanical resonator such as the air in a pipe, a string in a musical instrument or the membrane of a loudspeaker will oscillate at a multiple of the fundamental, also known as harmonics. As long as the forces (compressibility of the air or stiffness of string or membrane) are linear, these harmonics will remain at a fixed percentage of the fundamental amplitude.
We detect non-linear harmonic distortion by testing with linear signals, say sines. We detect linear signals and linear harmonic distortion by testing with non-linear signals, say noise, generated by air blowing over an edge of a pipe. Devices emit a mostly exponential, even or odd harmonic series. So we can say, this pipe sounds mello, that pipe hard, another one hollow, yet another one whistling. Looking at fullrange drivers one can often make out the first cone break-up at x Hertz, the second one at ruffly twice or thrice of that, the third one at fourth or fifth, and so on, forming a harmonic series. Testing with a sine might reveal, that at x the driver were prone to non-linear distortion, generating the harmonics.

Uli

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#### peufeu

IThe whole concept of harmonic distortion assumes that there is a nonlinear transfer function.

Yes.

A nonlinear transfer function, as can be shown from Fourier analysis, will result in added harmonics at multiples of the original signal frequency. These harmonics increase overproportionally as the signal grows!

Not "proportionally" ; the amplitude of harmonics versus signal depends on the distortion mechanism.

However, there can also be linear harmonics. A mechanical resonator such as the air in a pipe, a string in a musical instrument or the membrane of a loudspeaker will oscillate at a multiple of the fundamental, also known as harmonics. As long as the forces (compressibility of the air or stiffness of string or membrane) are linear, these harmonics will remain at a fixed percentage of the fundamental amplitude.

I think this is misleading. If you measure distortion using a pure sine, and there are no non-linearities in the transfer function, then the harmonics you are talking about will not be excited, and will therefore not appear in the output.

For example, if you have a pipe which resonates at n*100 Hz, and you play some 130 Hz through it, only your original 130 Hz will come out.

When a speaker reproduces a sine (ie, for a distortion test) the only way to have harmonics is to have a non-linearity. Of course, any linear distortion (ie, resonances or whatever which modifies the frequency response) will modify the amplitudes of harmonics generated by nonlinearities.

#### MarcelvdG

However, there can also be linear harmonics. A mechanical resonator such as the air in a pipe, a string in a musical instrument or the membrane of a loudspeaker will oscillate at a multiple of the fundamental, also known as harmonics. As long as the forces (compressibility of the air or stiffness of string or membrane) are linear, these harmonics will remain at a fixed percentage of the fundamental amplitude.

I suspect that linear harmonics will just change the tonal balance but will sound much less nasty than harmonic distortion products, the percentage of which changes with the amplitude.

The standard speaker test will just analyse the harmonic content and report this as "distortion".

Testing the harmonics at different volumes and separating linear and nonlinear portions would be a more meaningful test. Maybe a correlation between the subjective sound and the percentage of true nonlinear distortion can then be found...

Eric

The output signal of a linear time-invariant system can only contain frequency components that are present in its input signal(s), so you would have to excite the system with a test signal that contains all the frequency components of interest (Grasso789's noise, for example). Basically you then test in what ratio these components come out of the system, that is, you just devised a complicated way to characterise the frequency response.

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