# How to interpret distortion plots



## npdang (Jul 29, 2005)

Non-linear distortion is when your audio equipment (speakers, amps, headunit) plays signals that are not a part of the original recording. It is one of the defining benchmarks or specifications in audio because it generally can't be corrected or removed. It also has a direct and noticeable affect on sound quality, where equipment (especially speakers) with high distortion often sound muddy, colored, or harsh.

Let's start with a simple distortion graph. This is a plot of a high quality, TC Sounds tc2+ 12" subwoofer.










The red line is the original frequency response. Look to the bar on the left and find the column THD. That stands for "total harmonic distortion". A harmonic is a multiple of the original frequency. For example, the second harmonic of an 80hz tone is 160hz. The third harmonic is 240hz, and so on.

Now look at the green line underneath the red one. That is the second harmonic distortion. It's distortion because it's not a part of the original signal. Look to the column on the left under THD, and that will tell you how loud that second order distortion is as a percentage of the original signal. As you can see, second harmonic distortion is fairly low for this sub at less than 7%. If you want to be more detailed about it, look at the green line at 50hz. It's exactly at 7% thd. That means that while playing a 50hz tone, the sub will also generate "second harmonic" distortion in the form of a 100hz tone, that's 7% as "strong" as the original 50hz signal.

Now lets take a look at the blue line. That's third harmonic distortion. It's much lower than the second harmonic distortion. That's generally a sign of a well built driver. Take a look at 50hz again. It's roughly at 6.5% thd. That means that while playing a 50hz tone, the sub is generating third harmonic distortion at 150hz that's 6.5% as strong as the original signal.

Next, let's look at a different kind of distortion plot. This plot is a comparison of the TC Sounds tc2+ 8" and an Adire Audio Koda 8" taken at 40hz.










Ok, now you're probably thinking what the heck is this? Well, look at 40hz. That is your original test signal. This is just a simple frequency response plot. For a driver with zero distortion, and playing a 40hz tone all you would expect to see is 40hz right? But you can see there's 2 large spikes at 80hz, 120hz, and a smaller one at 160hz. These correspond directly to the second, third, and fourth harmonic. Those spikes are harmonic distortion. .. basically tones that are being generated by the speaker that weren't in the original signal. 

Comparing the two drivers, you can see that the second order harmonic distortion at 80hz is roughly similar. But, notice at the third (120hz), fourth(160hz), and higher harmonics the tc2+ clearly outclasses the Koda. By how much? That's a little trickier. Look at the vertical scale on the left. The original signal is at 80db. The second harmonic at 80hz is roughly 65db. That's a difference of -15 db. Use the following table to convert db to percent distortion.

-50db = 0.3%
-40db = 1%
-30db = 3%
-20db = 10%
-10db = 30%

Or, you can use this handy calculator:

http://www.sengpielaudio.com/calculator-thd.htm

So now you're probably wondering, well that's great but how do I know what distortion level is good or bad?

Well, that's a pretty complicated subject but I'll just shoot off some very simple guidelines.

- Even order (2,4,6, etc.) distortion is more pleasing to the ear than odd (3,5,7, etc.) order harmonic distortion

- Lower order harmonic distortion is less noticeable than higher order (second and third) versus (fourth and fifth).

- The audibility of distortion depends on the frequency. At lower frequencies, we can tolerate alot more distortion because the harmonics are so much closer to the fundamental (original) frequency that our brain has a harder time distinguishing them. For example, at 20hz the second harmonic is 40hz, only 20hz away. At 2khz, the second harmonic is 4khz, which is 2000hz away. We can pick up distortion that is 2000hz away from the original signal as being more distinct than we can something that is only 20hz away.

-Distortion past 10khz is difficult to hear because the second harmonic at 10khz is 20khz... a frequency most humans can barely hear.

-Intermodulation distortion is when 2 or more tones are being played, and the distortion occurs not only at the harmonics but at other frequencies as well. For example a 100hz and 1khz tone are played simultaneously. We could expect to find intermodulation distortion at all linear combinations of those frequencies, such as 900hz (1khz - 100hz), 1100hz (1khz + 100hz), etc.

This type of distortion is far more subjectively "nasty" than simple harmonic distortion. When evaluating speakers, I always recommend testing for intermodulation distortion as well as simple harmonic distortion.


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## pervo (Aug 1, 2005)

THANKS!


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## Kpg2713 (Feb 10, 2008)

Wrong thread...


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## donkeypunch22 (Nov 5, 2008)

Thank you!


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## kryptonitewhite (May 9, 2008)

I am liking all of these "How to interpret the data *READ ME FIRST* " thrads, but I have to say in my humble opinion, it is not easier to tell 2kHz from 4kHz any easier than it is to tell 20Hz from 40Hz, though I agree...the higher order the distortion, the easier it is to notice..But I feel because 20Hz takes 4X the displacement to hear at the same level, and that our hearing has a roll off as well. It's easier to hear the higher frequencies, not the difference between them?


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## amungal (Mar 29, 2010)

npdang That has to be the simplest and best tutorial I have read thus far on interpreting distortion plots. Your explanation of intermodulation distortion in particular was easy to grasp. Thanks.


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## chipss (Nov 13, 2009)

Why do even order distortions sound pleasing? Music theory come in handy to explain this. 

Because it’s a octave above the fundamental tone, so even order distortion is “playing” the same note, 12 Simi tones above the fundamental tone.

Basically even order distortion is “playing” (If you will) in key….and sounds like a thickening of the tone, 
Guitar players thicken tracks by doing the same thing… 

Odd order distortion is out of key… not pleasing at all, 

Intermodulation distortion is something that made sense to me when using distortion boxes on the guitar, 
If you play single notes, it sounds great, play a cord….it sounds like crap…

Stevie ray von’s tone was a guitar tone I have spent years trying obtain in building amps and distortion boxes, the thing about his tone is that although distorted and bluesy sounding, played cords with great definition… 

Then again I could be full of crap….


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## kryptonitewhite (May 9, 2008)

chipss said:


> Why do even order distortions sound pleasing? Music theory come in handy to explain this.
> 
> Because it’s a octave above the fundamental tone, so even order distortion is “playing” the same note, 12 Simi tones above the fundamental tone.
> 
> ...


makes sense to me, but Im no engineer


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## super10s (Feb 17, 2012)

Thanks bikinpunk. You've nicely shown us how harmonic distortion graphs can tell us the composition (orders) of the harmonics that show up at each measured frequency and what that can mean to a listener. I know its been a while since you posted this but since you have Wolfgang's amazing equipment maybe you can answer this futher question about the software which may be of real value to the designers of loudspeaker motors. Maybe also for those of us that just have inquiring minds. 

Is there an option in the Klippel software that clearly associates (sums) all measured harmonic distortion (up to a predetermined number of harmonics, like 9th) that originate from any given fundamental as a percentage of total distortion?

The resulting graph would look similar to a regular HD plot except that the level shown at each frequency would represent the percentage of THD that is contributed by harmonic distortion arising from that fundamental frequency. This would clearly show the frequencies where the driver has stored energy and is undesirably re-distributing as a harmonic noise spectrum. I guess what I'm getting at here is that all the measured harmonic distortion is a clue but the frequency of the fundamental associated with that HD is what we need to know to diagnose driver problems. 

After knowing what the offending fundamental frequency nodes are, you could then get out a laser microphone and play it across the moving elements of the driver and find the physical culprit, whether it is the glob of dust cap glue, the junction of the spider on the VC former, etc. The good thing is that the data needed to derive this has already been gathered and simply needs to be re-arranged to show this output as a new (or hopefully existing) function of the miracle Klippelware. Any thoughts? Or is this too far out there and I should really ask WK himself and leave you alone? Thanks.


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## rdlhifi (Sep 8, 2013)

nice explanation to understand THD!
TY npdang!


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