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[Art Welter]

I recall some recent posts that mentioned how to figure out the percentage of distortion as to the harmonic compared to the fundamental dB down.

I could not find that post, and would like to know if the figures below are correct. The source for this list is a little suspect.

-60dB = 0.1%
-55dB = 0.2%
-50dB = 0.3%
-45dB = 0.5%
-40dB = 1%
-35dB = 2%
-30dB = 3%
         =4%
-25dB = 5%
-24dB =     %
-23dB =     %
-22dB =     %
-21dB =     %
-20dB = 10%
-19dB =     %
-18dB =     %
-17dB =    %
-16dB =    %
-15dB = 15%
-14dB =    %
-13dB =    %
-12dB =    %
-11dB =    %
-10dB = 30%
-9dB   =     %
-8dB   =     %
-7dB   =     %
-6dB   =     %
-5dB   = 55%
-4dB   =     %
-3dB   =     %
-2dB   =     %
-1dB   =     %
 0dB   =100%

Appreciate corrections and your help in “filling in the blanks”.

Art Welter

[Andy Peters]

Total Harmonic Distortion takes into account the levels of all harmonics present, so your table isn't really helpful.

You can calculate THD as follows:

THD(%) = 100 * SQRT[(V2^2 + V3^2 + V4^2 + ... + Vn^2)] / Vt

where V2 is the rms voltage of the 2nd harmonic, V3 is the rms voltage of the 3rd harmonic, and so forth to the n harmonic, and Vt is the total rms voltage (which includes the fundamental).

-a

[Art Welter]

Andy,

The scale I posted was for speaker testing, pulled from an old Wayne P. post during the subwoofer shootouts.

I do find it helpful, even though it is not a THD measurement. It was a real revelation looking at the harmonics in subs, not uncommon for them to be louder than the fundamental as you approach the low end cutoff frequency. “Free” spl.

I have been running 8” cones in my monitors and mains, and was surprised to see when driven with a sine wave at near their rated power (a driver with a FS of 73 HZ and 125 watts RMS) that the second and third harmonic went from “only” 4% distortion at 120 HZ to 100% at 90 HZ.

The cone has about 6% distortion at 105 HZ, and doubles that at 100 HZ.

Do you happen to know the formula would to convert dB SPL to  RMS voltage?

Art

[Steve Devino]

Testing for Harmonic distortion requires a carefully crafted test signal to be sure that the distortion is coming from the device under test and not the test system. Andy Peters has the correct formula.

In general though most people use THD+Noise instead of just THD. To measure THD+Noise you simply remove the fundamental and sum the rest of the energy in the spectrum.


Steve

[John Roberts {JR}]

Art Welter wrote on Sat, 08 November 2008 20:56

Do you happen to know the formula would to convert dB SPL to  RMS voltage? Art

Apples and oranges...

There will be a transducer involved in the conversion between sound waves in air and electricity in a circuit. You need to apply the conversion efficiency or sensitivity of transducer at frequency of interest.  

JR

[John Roberts {JR}]

Steve Devino wrote on Sun, 09 November 2008 08:11

Testing for Harmonic distortion requires a carefully crafted test signal to be sure that the distortion is coming from the device under test and not the test system. Andy Peters has the correct formula. In general though most people use THD+Noise instead of just THD. To measure THD+Noise you simply remove the fundamental and sum the rest of the energy in the spectrum. Steve

The test signal is just a simple (clean) sine wave.  For loudspeakers it may be more useful to just think of the distortion as what (which harmonic) and how much, since the amounts present at LF are surely audible in many designs.

There are more constraints on the test set receiver wrt bandwidth and of course linearity, but for loudspeakers it all about the in band components.

JR

[Iain_Macdonald]

Dn (%) = 100 (An/A1) - percentage of n-th harmonic distortion
Dn (dB) = 20log(An/A1) - distortion level of n-th harmonic component (Assuming a calibrated measuring system)

THD (%) = 100 sqrt((A2

[Art Welter]

Iain,

Looks like you gave me what I asked for, but I’m unsure what the terms are.

I’m lame at math, would you mind baby stepping me through the equation with the following example:

Fundamental tone =100 dB SPL
Second Harmonic  =80 dB SPL (-20 dB)
Third Harmonic  =70 dB SPL (-30 dB)
Fouth Harmonic  =60 dB SPL (-40 dB)
THD=?

Art

[Andy Peters]

Art Welter wrote on Sun, 09 November 2008 14:19

Iain, Looks like you gave me what I asked for, but I’m unsure what the terms are. I’m lame at math, would you mind baby stepping me through the equation with the following example: Fundamental tone =100 dB SPL Second Harmonic  =80 dB SPL (-20 dB) Third Harmonic  =70 dB SPL (-30 dB) Fouth Harmonic  =60 dB SPL (-40 dB) THD=?

First, arbitrarily declare that the fundamental level at 100 dB SPL is referenced to 1V. So the 2nd harmonic is down 20 dB from 1V, or 100mV. The 3rd harmonic is 30 dB down from 1V, or 31.6 mV. The 4th harmonic is 40 dB down from 1V, or 10mV.

So by the formula, square each harmonic voltage value, then take the square root of the sum of the squares. You get 105.3 mV. Divide by the square of the total voltage, which includes the fundamental. That total voltage is 1.14V; squared is 1.302V, and THD % is therefore 8%.

Does this help?

-a

[Nick Hickman]

Hi Andy,

Andy Peters wrote on Mon, 10 November 2008 00:18

Divide by the square of the total voltage, which includes the fundamental. That total voltage is 1.14V; squared is 1.302V, and THD % is therefore 8%.

If you're calculating (sum excluding fundamental) / (sum including fundamental), you'd surely divide by the square root of the sum of squares of voltages?  

Another definition of THD is what Iain wrote, i.e. (sum excluding fundamental) / (fundamental).

I calculate the THD in the example (with either definition) to be approximately 10.5%.

Nick

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