Software design challenge for Klippel method testing

[augerpro]

Hi all. I've been looking at trying Klippel's performance based testing method here http://www.klippel.de/pubs/papers.asp

I can do all of it, but need two things: a way to measure excursion and a QUICK way to calculate the distortions from a spectrum plot. I found Linkwitz made a pretty clever little excursion measuring device so I'm covered there.

I'll be using a spectrum analyzer in Soundeasy. You can see it in the driver tests in my sig. Similar to MarkK's plots. I think what I'll have to do is take a screen capture. Then I need some software to read the harmonics if possible, and then calculate the distortions per Klippel's formula. I suppose I may have to enter the values in myself, so I may be able to get by with just the calculator software. Anyone interested in designing such software/spreadsheet?

Basically I would like to get a more realistic idea of just how much xmax any given driver has. Klippel's method would also indicate what the limiting factor was, suspension, BL, etc. You could also get a better idea of performance when comparing an underhung versus overhung design how they behave at their limits.

[Dennis H]

Brandon, try the spectrum analyzer in REW. That program just keeps getting better!

When the Calculate distortion check box is selected the analyser calculates distortion figures for the input, including THD and THD+N and the relative levels of the 2nd to 9th harmonics. The highest peak is used to determine the fundamental frequency of the input, this is displayed with the level of the fundamental. The THD figure is based on the number of harmonics whose levels are displayed and is calculated from the sum of those harmonic powers relative to the power of the fundamental. The THD+N figure is calculated from the ratio of the input power minus the fundamental power to the total input power (note that it is possible for THD+N to be lower than THD using these definitions).

[augerpro]

Thanks Dennis, I'll check that this week when I have some time. Do you know if it can do two tone testing and still calculate the THD and IMD? It would need to do this to use Klippel's method, which typically inputs power at the driver Fs (to cause teh required excursion) and 8.5x Fs (to generate the HD/IMD components to be used for calculation).

[Dennis H]

Nope, I don't think it will do that.

Edit: maybe you could make it work if you put a highpass filter between the mic preamp and the sound card. Then the THD+noise calc mentioned above should give you the ratio of the HF fundamental to everything else. It wouldn't be exactly a Klippel but it should give you results you could compare if you did it the same way every time. Tones at Fs and 8.5Fs with the filter set at 4Fs might work. Something like one of the Behringer analog XOs would let you dial in the filter frequency.

[augerpro]

I gotcha...very clever. I'll have to look over the paper again to make sure it's only HD and IMD around the 8.5fs tone that are calculated (I believe so, makes sense), and see how low the HP would have to be to not cut out any of the lowest IMD components.

[augerpro]

Now I just need a speadsheet to input the distortion values in to calculate the THD. It would also be nice to have a graph where one could input a given Fs and 8.5Fs and see a "typical" or idealized spectrum with the all the HD and IMD frequencies listed. Would help me quickly match up what I see on my spectrum plot and input the correct value for all that IMD "fuzz".

[ThomasW]

Here's the spreadsheet Ilkka and Ed Mullen developed

[Saurav]

Do you need help with the Excel part of it, or the actual equations themselves? I have limited Excel formula skills and I could try to help with that, but I have no idea what the formula is for calculating THD or IMD or whatever from a given set of numbers. And I certainly don't have the Windows GUI programming chops to read anything from an image

[brianpowers27]

The ARTA users manual goes into detail regarding the formulas used to calculate the various IMD/HD metrics.

If I were going to build a program like you described, I would try and work with the Speaker WOrkshop code since it is all open source.

P.S. Is it really possible to calculate HD when using a two tone IMD signal? I figure the beat waves would completely destroy any coherance...

[Saurav]

I took a peek at the ARTA manual. Looks like ARTA has the ability to do a 2-tone measurement and report IMD. There are a handful of different standard equations used to calculate IMD. One of them spec'd that the 2 tones should be 8.5x apart, so maybe that's the equation Brandon wants.

[NEO Dan]

Brandon,
if SoundEasy has two tone distortion capability why not use that facility for the "test" while injecting a signal to drive the DUT to x-max. You would still need to filter out the drive siginal on the Mic as mentioned above, but the distortion portion of the test would remain under SE control.

I'd really love to hear how you intend to accurately determine x-max.

[augerpro]

Tom> looks they are halfway there, it just calculates HD, not IMD

Saurav>awesome find. I'll have to check into ARTA. If they had a two tone with one being 8.5 times the fundamental it sounds like it should work. Some one there had to be intending it to work with Klippel's method, you don't just pick 8.5 out of thin air. Actually it was from an AES standard, but Klippel may have had some part in that standard. If you are bored though you could take a look at the files I included, the formula are inside.

Brian> SW had me pulling my hair out the one time I used it.

EDIT> Saurav I'll have to email you the file, send me your address. Tom the board owners really need to increase the file size, before I bash my head into the screen. 100k is so 1998.

[augerpro]

Dan> doing two tone isn't the problem, it's quickly and accurately calculating THD from the HD and IMD components. Even the cleanest drivers have a considerable amount of IMD. I can't imagine trying to read all the values of the "fuzz" and even if I could I'd probably assign one to the wrong IMD or HD component when the spectrum fuzz is dense. Hope that made sense. If you've stared at enough spectrum plots you'll know what I mean.

PM me your email address and I'll send you some papers from Klippel. All I'd like to do is use his performance based method of determining xmax. If I get that far.

BTW new testing baffles and jigs being drawn up now. I'll be buidling them this weekend. Interesting drivers, should be very informative.

[augerpro]

Dan it just occured to me you didn't mean xmax, but the actual excursion? If so Linkwitz made a clever little device to measure cone excursion reasonably accurate.

[Saurav]

According to the ARTA manual (and I didn't read it in much detail), you can set the thing to manual, enter the two frequencies, and ARTA looks at the frequencies and figures out which formula to use. However, it didn't look like it used the equation from the AES standard that said the frequencies should be at 8.5x (though I could be wrong about this). Having said that, I suspect some of the other equations will give similar results, so if you're looking for consistency rather than an absolute metric, that might work.

[brianpowers27]

If you ask me you don't want any form of even multiple for the two tones in the IMD test. For example a 8.5x multiple will create a beat wave every 17 cycles of the lower tone. I would shoot for an uglier number that will not fall upon any of harmonics generated by the lower tone. It would be important to iterate through the harmonic series for each harmonic that way one has the ability to distinguish different orders of harmonics created by other harmonics.

I think that DDF has done a fair bit of research into this exact thing. He let me read some of his catalogged resources once upon a time. Someone has done a much more advanced IMD study than to allow for a simple 8.5x ratio.

[Saurav]

According to the ARTA manual:

IEC 60268 method
For loudspeaker measurements, the standard IEC 60268 – 5 defines two factors:

2nd order Modulation distortion factor (can't show equation)
3rd order Modulation distortion factor (can't show equation)

These factors show dominant intermodulation distortions when f2 >> f1., i.e. for loudspeaker testing we use f2 = 8.5 f1.

The other techniques go up much higher, for example, the "power method" goes up to the 8th harmonic on both tones.

Also:

Calculation and report of intermodulation distortions in ARTA
ARTA uses all described method to calculate the intermodulation distortion. The choice of used method is determined automatically from the ratio of frequencies f2 and f1, in the following way:
• If f2 / f1 < 2 ARTA uses CCIF method and reports difference frequency distortion DFD2 and DFD3 plus IMD (defined with power method).
• If f2 / f1 > 7 ARTA uses DIN (SMPTE) method and reports modulation distortion: IMDDIN, MD2 and MD3.
• If 2 < f2 / f1 < 7 ARTA uses Power method and reports IMD
The ratio of amplitudes, if differs from recommendations in standards, should be additionally reported by the user.

So I was wrong. If you pick f2 = 8.5x f1, ARTA will give you the IMD calculated by the DIN method (a SMPTE standard), as well as MD2 and MD3, which are the two IMD components spec'd in the IEC standard.

I haven't seen the Klippel paper that Brandon is working from. If it just needs the 2nd and 3rd order IMD components, then ARTA may provide all the data he needs.

Edited for typos.

[Dennis H]

Now I just need a speadsheet to input the distortion values in to calculate the THD.

I was trying to avoid the whole spreadsheet thing. REW does it for you with the THD+N calc if you can figure out what you want to include in the calc and filter out what you don't want. It will include harmonics of the higher frequency and also consider all the IM stuff and other peaks to be noise and include them too. If you want to include all the Fs harmonic distortion products but not the Fs, you need a notch filter at Fs. If you don't want those Fs harmonics, you need a steep highpass below 8.5x Fs. You could do it all easily with a Behringer DEQ or DCX -- notch filters and up to 8th order highpass filters.

[Dennis H]

If you really want to do the spreadsheet thing (what a pain!), measure how far each peak you want to include is below the fundamental (example -20dB and -30dB: -20dB is 10% distortion and -30dB is 3% distortion). Uncorrelated sounds add as power rather than pressure so convert each of the peaks' dB to power, 10^(dB/10) -- (example .01 and .001). Add the power of all the peaks together (example .011). Take the squareroot of the summed power to convert to pressure and multiply by 100 to convert to percent, 100*sqrt(summed power) -- (example 10.5%). So we end up with 10.5% total instead of the 13% we'd get if we just added them together because the sounds aren't correlated.

[ergo]

Audiotester is a sw piece from Germany which has some interesting options for THD measurements that migh be interesting.

http://www.audiotester.de/

I have used the option to only select 2nd or only select 3rd harmonic etc. Takes time but is sometimes still faster than hand or table calculation.

Ergo

[brianpowers27]

It is seriously worth considering...

Most distortion plots don't account for voltage changes. It is important to test for the threshold of distortion vs spl using something like a Fletcher munson curve. One would need to test for distortion changes as the driver changes in relation to its output range.

The reality of most of this involves us looking at plots that we can barely detect. The true leaders of the pack emerge at higher volumes.

I am not sure if an appropriate weighting system really exists for measuring the various distortion products. THD is completely meaningless. In my mind it would be great if a system could account differently for f6 distortion vs f2 distortion. To further this line of thinking, the system would need to account for the volume level at which the test was run.

example

f2 weight = .0002 * (spl/freq lookup value (Fletcher Munson for the Fc of the distortion, not the fundamental))
f3 weight = .0012 * (spl/freq lookup value (Fletcher Munson for the Fc of the distortion, not the fundamental))
f4 weight = .002 * (spl/freq lookup value (Fletcher Munson for the Fc of the distortion, not the fundamental))
etc...

Total weight = f2weight + f3weight + f4weight ...etc.

The same concept should be applied for the various orders of IMD distortions.

[augerpro]

Brian I completely agree on using a more accurate standard than THD. I like Geddes formula best of the ones I've seen. Using it would require that we build a spreadsheet though. Which I would love, but I can't do it alone. So I'm going to investigate the other proposals for now because of time constraints. I'd like to start testing the weekend after next.

The rest of the method wouldn't change though, so I'd like to see whether I can pull it off using the current standard of 10% THD defining xmax and later look at using a more complete distortion metric. Maybe I can lobby Bohdan to incorporate the THD (or Geddes formula, or both) calculation into the spectrum analyzer in Soundeasy.He's usually pretty receptive to suggestions, especially cutting edge type stuff.

[brianpowers27]

One last thing. Using ARTA steps there is a power vs distortion tester. THis will continually step up the voltage and plot the corresponding distortion(THD). It operates on one frequency at a time. THis might work perfectly for what you are asking.

[Saurav]

Uncorrelated sounds add as power rather than pressure so convert each of the peaks' dB to power, 10^(dB/10) -- (example .01 and .001). Add the power of all the peaks together (example .011). Take the squareroot of the summed power to convert to pressure and multiply by 100 to convert to percent, 100*sqrt(summed power) -- (example 10.5%). So we end up with 10.5% total instead of the 13% we'd get if we just added them together because the sounds aren't correlated.

Did you look at the spreadsheet that Tom posted? I think that's doing the same thing, but in a slightly different way - it divides the dB value by 20 to get the pressure in Pascals, but then it squares those values when calculating the THD. So I think it's doing the same thing?

Brandon, are you still interested in a spreadsheet that might help reading distortion plots? I was thinking about something along the lines of:

* Enter the Fs frequency (f1)
* Either enter the 2nd frequency, or the spreadsheet assumes it's 8.5x Fs (f2)

From there, the first few IMD frequencies should be:

f2 + f1
f2 - f1
f2 + 2f1
f2 - 2f1

Those are the 4 used in the Klippel formula.

And then maybe try to plot that on a 20-20k log scale so there's a visual reference for where the spectral lines would be.

[augerpro]

What timing. Soundeasy v16 was released today and some sort of new THD calculation was added to the spectrum analyzer. It already had one, so I'm not sure how this is different, waiting for a reply from Bohdan. Silly thing is I forgot the analyzer had teh THD in the upper corner. The solution might have been under my nose already...

[augerpro]

Saurav> unless I missed it the sheet Tom posted only did the HD of a single tone? Your last post is pretty right on though. How many orders of HD and IMD was Klippel using? I'm at work and can't pull it up right now.

[Saurav]

I only looked at the "Determining Xmax_performance based.pdf". In that doc, he says:

The voice-coil peak displacement Xmax at which either the total harmonic distortion dt or the nth-order modulation distortion (where n=2 or 3) exceeds 10%

So... for the HD, I don't know how many components he's using. The formula he lists for HD is a summation to the K'th term, and I didn't see where he said what K should be.

For the IMD, it's the 2nd and 3rd order, which are defined as:

IMD2 = ( P(f2 - f1) + P(f2 + f1) ) / P(f2) * 100%
IMD3 = ( P(f2 - 2f1) + P(f2 + 2f1) ) / P(f2) * 100%

So basically, the 4 IMD frequencies I listed above.

unless I missed it the sheet Tom posted only did the HD of a single tone?

It does. And if I'm interpreting this paper right, you want the HD on the lower tone, and you want those 4 IMD components, all measured from the same test run.

I'm guessing the reason f2 is 8.5x f1 is to keep those distortion products far away. The 2nd and 3rd order IMD products would lie around f2, and you could probably go up to the 4th or 5th order for the HD before the HD and IMD frequencies start overlapping. I think. f2 - 2f1 is the lowest IMD frequency, so that's 8.5f1 - 2f1 = 6.5f1, so the 6th HD component would fall below that.

Hopefully that made some sense

[brianpowers27]

I'm guessing the reason f2 is 8.5x f1 is to keep those distortion products far away. The 2nd and 3rd order IMD products would lie around f2, and you could probably go up to the 4th or 5th order for the HD before the HD and IMD frequencies start overlapping. I think. f2 - 2f1 is the lowest IMD frequency, so that's 8.5f1 - 2f1 = 6.5f1, so the 6th HD component would fall below that.

Hopefully that made some sense

You are on the right track. To put it simply, the HD products need to be way seperate from the upper frequency. Such that no HD product from F1 interferes directly with f2. At a 8.5 x F ratio and 4:1 volume ratio this works fairly well. (IEC std.)

Here is an example
F=100hz
Fd3=300hz
d2Fd3 = 600hz

[augerpro]

And if I'm interpreting this paper right, you want the HD on the lower tone, and you want those 4 IMD components, all measured from the same test run.

Is he using the lower tone (Fs)? I thought it would just be the higher one.

I would like to see a couple more orders added, but THD is so dominated by the first and second harmonics that it probably wouldn't matter much. I assume IMD is the same. I suppose you could raise F2 to 10Fs or something, but Doppler and/or AM distortion may become a factor.

[brianpowers27]

Is he using the lower tone (Fs)? I thought it would just be the higher one.

http://www.klippel.de/download/bin/AN4%20-%20Xmax%20performance.pdf

Performance based definition of Xmax
Current
Definition
The current standard defines the voice-coil peak displacement at which the "linearity"
of the motor deviates by 10%. Linearity may be measured by percent distortion of the
input current or by percent deviation of displacement versus input current.
The measurement shall be made in free air at
fS."

Klippel;'s suggested amendment still states that the free air resonance frequency will be the basis of F1

I don't think that it is possible to take both a THD and IMD measurement from a two tone signal. A two tone signal is really required for the IMD test.

[Saurav]

Thanks for the link, Brian. That's the current definition of Xmax. The paper goes on to say:

The voice-coil peak displacement Xmax at which either the total harmonic distortion dt or the nth-order modulation distortion (where n=2 or 3) exceeds 10% in the sound pressure radiated by the driver in free air excited by the linear superposition of a first tone at the resonance frequency f1=fs and a second tone f2=8.5 fs with an amplitude ratio of 4:1.

The total harmonic distortion dt assesses the harmonics of f1 and the modulation distortion are measured by the modulation components f2± nf1 according to IEC 60268.

(emphasis added, to answer Brandon's question)

Edit: Your edit rendered my post redundant

And I agree, I'm not sure how a standard THD measurement software app will handle this. On a 2-tone test, I'm guessing the distortion chart will contain the HD and IMD spikes, but I don't know how ARTA/SE/etc. will interpret that.

Maybe you can do it in 2 steps, measure the HD with only f1 playing, then measure IMD with f1 and f2? Otherwise you're back to eyeballing distortion charts and inputting numbers by hand.

[brianpowers27]

Here is a great link to a new proposed IMD test. This also does a great job of explaining the reasoning for Frequency selection in a multi-toned IMD test.

http://www.geocities.com/jonrisch/PhiSpectral1.htm

[brianpowers27]

Maybe you can do it in 2 steps, measure the HD with only f1 playing, then measure IMD with f1 and f2? Otherwise you're back to eyeballing distortion charts and inputting numbers by hand.

After re-reading the Klippel test, it appears that their test is done in 4 measurements... resonance, thd, imd2, imd3.

Step 1. Go into Arta steps and use the power vs distortion with a F centered on the fS. Record voltage at 10%

Step 2. Play a two tone generated wave in the traditional ARTA , set both tones appropriately and ramp the volume while monitoring IMD2, IMD3. Record the volume when the threshold is acheived.

[Dennis H]

The total harmonic distortion dt assesses the harmonics of f1 and the modulation distortion are measured by the modulation components f2± nf1 according to IEC 60268.

Okay, that defines it. Put a notch filter (EQ box) between the mic preamp and the sound card. Notch out F2 looking at the REW spectrum to make sure you got it. Read the REW THD+noise. All the IMD products will be considered noise and be included in the calc. Doesn't get much easier than that.

[Saurav]

The voice-coil peak displacement Xmax at which either the total harmonic distortion dt or the nth-order modulation distortion (where n=2 or 3) exceeds 10%

Does REW report THD and N as separate numbers? If not, then I think your technique would define Xmax as the point where the THD + IMD exceeds 10%. Which may be fine, as long as Brandon understands that deviation from Klippel's definition.

Or maybe I have it all backwards

[Dennis H]

Well, it does THD and THD+N but he mentions that it's possible for THD+N to be lower than THD with the way the math works. I guess, if you wanted a strict Klippel test you'd need to separate THD and IMD but I sorta think a measurement that includes all distortion products from whatever source has more value. You could always throw a lowpass between the mic preamp and sound card if you wanted to keep out the really HF stuff.

BTW, I second Brian on using the demo version of ARTA as the signal generator if SE won't do it easily.

[Dennis H]

Hmmm, the more I think about it, I guess it would have to be two tests. THD is relative to the level of F1 and IMD is relative to the level of F2. Mine would make them both relative to the F1 level. Guess I better read the paper.....

[Saurav]

LOL, you're right, I totally missed that as well. I'm sure every manufacturer would be very happy with the IMD numbers the test would have generated

Also, it's really a series of "2 tests". He has to iterate this across multiple signal levels, and the Xmax corresponds to the lowest signal level where any of the distortion components (HD, IMD2, IMD3) exceeds 10%. I think that's why Brandon's been stressing on the 'quick' part of the process.

[brianpowers27]

In reality, it wouldn't take very long to run these two tests. The whole process would take longer to document than it would to take the tests.

I have measured the various IMD products in Arta. It would be quite fast to find the 10% mark with a nicer mixer-type volume slider. I bet you could get darn close in 5 seconds or less.

[Dennis H]

Yeah, I was just looking at ARTA. Looks like it will do the whole works even in demo mode as long as you don't need to save any files. The only thing is you have to use a single sine signal to get THD and then switch to the 2-sine to get IMD2 and IMD3 -- just a click to switch. If you have it calibrated and set it up right, it will give you RMS voltage at the bottom of the chart, along with the distortion percentages, as you turn up the amp's volume control.

[augerpro]

I'll dig into all the comments more tonight when I get home from work, but I just wanted to thank you guys for all the help so far! Finding a more meaningful xmax figure and the ability to determine the limiting factor for the diy'er is pretty invaluable. Not all limiting factors are the same, so two drivers with identical xmax could be quite different if say, one was suspension limited versus inductance linearlty limited. I'd pick the one that was suspension limited (primarily second harmonic dsitortion) over teh inductance limited which causes considerable IMD.

Thanks again guys!

[augerpro]

Right at the beginning it's pretty much all spelled out: http://www.klippel.de/download/bin/A...erformance.pdf

So...we are measuring THD of F1 and IM2 and IM3 of F2. He doesn't seem to do two tests, but because of ARTA's limitation here we would do F1 first then two tone F1 and F2? Sounds about right? Just want to be clear on what's being measured and how.

Also F2 is specified as 4x amplitude. This is what? 6dB?

So something like this:
1) Apply a tone (F1) at the driver Fs
2) When THD equals 10%, note the excursion
3) Apply a second tone (F2) at 8.5Fs at 6dB? higher SPL
4) Raise input until either IM2 or IM3 (or is it IM2+IM3?) equal 10%, note excursion

Looking into SE a bit more there are a couple analyzers that I had forgotten about. I usually use the same one as John Krutke and the spectrum analyzer. There are two others. I had actually talked to John about this last year. At the time he was hoping to do write up on one of them as it was pretty similar to Klippel's parameter based method.

Well I'm pretty excited to do this!! It would be even more interesting if we could use Wigan's or Geddes' formula for distortion audibility, but we'd for sure be back at square one with having to write an easy to use spreadsheet. I agree with Brian there is a better measure that could be used.

[Saurav]

Also F2 is specified as 4x amplitude. This is what? 6dB?

I got confused by this too. From the article:

Operate driver under free-field condition and excite driver with a two-tone signal f1=fs and f2=8.5 fs and amplitude ratio U1=4*U2

The way I read that, I think the lower tone should have the higher amplitude.

4) Raise input until either IM2 or IM3 (or is it IM2+IM3?) equal 10%

Until either one reaches 10%. Again, that's how I read this:

The voice-coil peak displacement Xmax at which either the total harmonic distortion dt or the nth-order modulation distortion (where n=2 or 3) exceeds 10%

Do you have a link to a writeup on Geddes' distortion metric?

[Dennis H]

So something like this:
1) Apply a tone (F1) at the driver Fs
2) When THD equals 10%, note the excursion
3) Apply a second tone (F2) at 8.5Fs at 6dB? higher SPL
4) Raise input until either IM2 or IM3 (or is it IM2+IM3?) equal 10%, note excursion

What Saurav said, the Fs tone is 4x louder than the 8.5*Fs tone. So do a single Fs tone and crank it up until you get 10% THD. Then switch to the 2-tone and see if either IMD2 or IMD3 are over 10%. If not, you are done. If either is over, back off the voltage until the highest IMD is 10%.

PS, it took me a while to find the distortion setup in ARTA. It's in the somewhat obscure Setup / Spectrum Scaling dialog box once you've chosen the Spa (spectrum analyzer) button on the graph.

[brianpowers27]

Right at the beginning it's pretty much all spelled out: http://www.klippel.de/download/bin/A...erformance.pdf

So...we are measuring THD of F1 and IM2 and IM3 of F2. He doesn't seem to do two tests, but because of ARTA's limitation here we would do F1 first then two tone F1 and F2? Sounds about right? Just want to be clear on what's being measured and how.

Also F2 is specified as 4x amplitude. This is what? 6dB?

So something like this:
1) Apply a tone (F1) at the driver Fs
2) When THD equals 10%, note the excursion
3) Apply a second tone (F2) at 8.5Fs at 6dB? higher SPL
4) Raise input until either IM2 or IM3 (or is it IM2+IM3?) equal 10%, note excursion

Looking into SE a bit more there are a couple analyzers that I had forgotten about. I usually use the same one as John Krutke and the spectrum analyzer. There are two others. I had actually talked to John about this last year. At the time he was hoping to do write up on one of them as it was pretty similar to Klippel's parameter based method.
.

You are on go!

Side note: It would be informative to consider the composition of THD when you acheive x-max. ARTA steps can do this for you in a distortion as a percentage figure...

For Multitone testing in ARTA, the system lets you specify the 4:1 ration so there is no need for figuring the math.

I have done both of these test in ARTA before. If you have any questions regarding the execution, let me know.,