Practical Use and Understanding of the Klippel Distortion Analyzer

[Neil]

In preparation for Klippel testing, I think it is important that we review what the Klippel is, what it does, and how it does it. I know many members on the forum have no idea what the Klippel Distortion Analyzer even looks like, and it's time to get everyone on the same page.

I will be covering everything you need to know about the KDA, and hopefully in a logical, understandable method. Later this evening, I will add some pictures of the machine itself and its cables, which should make things even clearer. First, though, we need to get some preliminary information out of the way.

We can break-down driver performance into a couple of categories that will make it easier to understand (and predict) what is happening. First, we should identify what happens with a small input signal, meaning how the driver behaves with very little power applied to it. Once we understand how it behaves with a small signal, we can increase the power flowing through the coil and start to capture what happens with increasingly larger signals. Our understanding of behaviour at small signals relates to something you've probably heard before: Thiele/Small Parameters. It is here that we will start.

Thiele/Small Parameters - History
---------------------------------
When the electrodynamic loudspeaker was first invented by Kellogg and Rice in the 1920's, there was very little engineering or science behind its design. For as much 50 years, very few who designed drivers knew exactly what to expect when they started putting parts together. Alas, a series of scientific discoveries have now made designing an accurate, low-distortion driver predictable once you understand the concepts at hand.

Essentially, a driver transforms electrical energy to mechanical energy, which is then converted to acoustic energy. In the 1940's, the legendary Harry Olson helped develop analogous electric circuits which aided low frequency analysis of drivers in a system.
The driver is modeled as an electrical circuit with resistors, inductors, and capacitors representing various parts and aspects of the driver. With an equivalent electrical circuit, it is easier to model the transformation from one energy type to another. Olson gave complete electrical circuits for sealed and vented loudspeaker systems in 1943.

The original circuits weren't perfect, though, as they ignored the frequency dependence of some of the acoustical elements. As such, incremental improvements continued from many important audio engineers, including Leo Beranek and J.F. Novak. It was in 1961 that the future of small signal understanding began to really take shape, when A.N. Thiele published a paper titled "Loudspeakers in Vented Boxes" which detailed how to match driver parameters and the enclosure volume/tuning to an equivalent electrical filter response, or what is often referred to as an "alignment". Equally important, he introduced a method of measuring some aspects of the driver that made the design process possible.

Still, these advancements were made before everyone and their dog had email. What some discovered in a lab in Australia often weren't known in another lab in the US. J.E. Benson made further improvements and published a three part series titled "Theory and Design of Loudspeaker Enclosures." Like Thiele, Benson's papers primarily saw circulation in Australian journals. Thankfully, Richard H. Small published nine articles in the Journal of the Audio Engineering Society (JAES) that related all previous work and expanded upon it even further, allowing a designer to find the proper enclosure volume and tuning for a wide range of driver parameters. And with that, we had what are now referred to as the Thiele/Small parameters.

Understanding Thiele/Small Parameters
-------------------------------------
It is very important that we understand exactly what Thiele/Small Parameters describe. First, the purpose of Thiele/Small parameters is to measure physical aspects of the driver, and then use these parameters to describe the low frequency performance in a system. Though there are some extrapolations that can be made based on these parameters, their sole purpose is to describe how a driver behaves in an enclosure at low frequencies.

I don't intend to describe in detail all of the Thiele/Small parameters. If you wish to know more, I recommend reading the article on Wikipedia (http://en.wikipedia.org/wiki/Thiele/Small). What is important is that we identify a few important physical parameters from which all others (including Qts, Qes, and Qms) are derived. This includes:

Sd - The effective surface area of the diaphragm
Mms - The moving mass including acoustic load
Cms - The compliance of the drivers suspension *NOTE: Compliance is the inverse of stiffness; in other words, a driver that is highly compliant (ie. high Cms) has a soft suspension, and a driver that is not very compliant will have a stiff suspension.*
Rms - The mechanical resistance of a drivers suspension
Le - The inductance of the voice coil
Re - The DC resistance of the voice coil
Bl - The product of the flux density in the voice coil gap and the length of wire that cuts that flux

Note that since Thiele/Small parameters describe the behaviour with small signals, we may now proceed to describing large signal performance. First, though, we must understand why a driver would behave differently with a large signal based on these important parameters we identified above.

It stands to reason that Sd, the effective surface area, will not change. Likewise, the mass of the driver (Mms) will not change, and although there are small changes in Rms (not to be confused with what is often mistakenly called "RMS" power handling), these changes are not considered integral to understanding large signal performance. With that understood, let's keep delving into this beautiful science. I'll pick this up a bit later this evening.

If something is unclear or incorrect, please share this with everyone. I don't care if I'm right or wrong...it is just important that we all understand.

[Neil]

Large Signal Problems
---------------------
Now let's understand why the other parameters we identified change.

Cms - As the coil moves through the gap, the suspension (which consists of the spider and the surround) will stretch in the positive (forward) and negative (backwards) direction. Imagine an elastic band: stretching the elastic band is easy at first because it is highly compliant (not very stiff). However, the elastic band becomes harder and harder to stretch the further you pull it: it is becoming less compliant (more stiff). The same thing happens with your suspension. Since larger signals move the coil greater distances and stretch the suspension further, we recognize that the compliance and stiffness of the suspension must change with these large signals.
Bl - Let's revisit what exactly this is. This is the product of the flux density in the gap (B) and the length of wire residing in that flux (l). By the way, when we say flux density, we mean magnetic field strength. We'll ignore, for a moment, the possibility that the magnetic field generated by the magnetic system could change, and we'll simply focus on the length of wire residing in that magnetic field. As more power is applied to the coil, and as the frequency of this signal decreases, the further the coil moves forward or rearward. With enough power, the length of wire that is residing in the magnetic field begins to decrease. As such, the product known as Bl begins to decrease as well. *NOTE: Bl is sometimes referred to as the "motor force" but it is more appropriately called the motor force factor. The appropriate term for motor force can be represted by Bl(i) where i is the input current. We must, after all, have current in the coil to have real force.
Le - The coil itself is an inductor which means inductance is at play. The inductance and resistance of a coil forms a 1st order (6dB/octave) low-pass filter. The current through the coil produces a magnetic AC field which will depend on the position of the coil. The magnetic flux is much lower in free air than when in the gap where the surrounding iron path has lower magnetic resistance. Also, the magnetic field strength H and the flux density B have a non-linear relationship, which causes variation of the permeability with varying voice coil current. Simply put, the inductance will vary with both position (x) and current (i).
Re - The resistance does vary with current as well. With increased current comes increased heat, and it is known that electrical resistance of a metal varies linearly with the temperature. Due to the increase in resistance, the driver encounters thermal power compression where output is lower than predicted given an increase in power. Eventually, no output is gained and the coil is at risk for irreparable damage.

Having identified the reason why we have changes in the parameters, we still categorize the potential symptoms we wish to address.

Bl(x) - We must minimize variation of Bl with position because non-linear Bl values will generate significant harmonic distortion and intermodulation distortion.
Cms(x) - We want to minimize variation of Cms with position because non-linear Cms values will generate significant harmonic distortion and intermodulation distortion.
Le(x) - We want to minimize variation of Le with position because non-linear Le values with position will generate moderate harmonic distortion and high intermodulation distortion.
Le(i) - We want to minimize variation of Le with current because non-linear Le values with current will generate moderate harmonic distortion and moderate intermodulation distortion.

Lastly, I want to explain variation of resistance with current. The decreased output is considered a negative consequence, but generally unavoidable. As long as the coil is capable of handling enough power to reach Xmax, it is not often considered a big concern. In SPL competition, this is a bit different story, and there is something to be gained by managing the heat in the coil as efficiently as possible. Thermal management is something to be discussed in a little while. But you may have noticed an important term for the first time in this thread: Xmax. Quite an interesting (and controversial) term it is.

Defining Xmax
------------------
Xmax is, in essence, a fairly simple idea: it is the maximum distance the coil can travel from rest while producing an acceptable level of distortion. How we define "acceptable" and what practical use this is can be a pretty interesting discussion, though. For many years, the accepted of determining Xmax was strictly determined by coil and gap geometry, with no consideration of the suspension. Xmax was given by the difference between the coil and gap height, which was then divided by two.

For an overhung driver:
Xmax = (VCh - Gh) / 2

For an underhung driver:
Xmax = (Gh - VCh) / 2

However, it was discovered that the effective height of the flux extends beyond the height of the gap. Depending on the geometry of the "fringe field", the coil may be able to travel further (or shorter) than the conventional method would permit. Instead, it is appropriate to accept a distance where the measured Bl value at position x is a percentage of the rest Bl value. The position we select, according to Klippel, should be 82% of the rest Bl value, which is where approximately 10% distortion has been generated. We will call this Xmag. Likewise, we have Xsus, which is the distance where the measured Cms value at position x is 75% of the rest Cms value.

You'll notice that this definition does not include Le(x) non-linearity. Truthfully, inductance non-linearity is a complicated issue and the distortion is not often considered exceptionally offensive. It is still important to manage, though, if your goal is a wide bandwidth with low distortion. Regardless, the current accepted definition of Xmax is the lesser of Xmag and Xsus. If the driver has an Xmag of 15 mm and an Xsus of 18mm, then the resulting Xmax would be 15 mm. We know that the further the cone moves, the higher SPL we will measure. Thus, a high Xmax value indicates that the driver is able to move a great distance before reaching offensive distortion levels, and potentially delivering enormous SPL. Isn't Xmax great?

The Value of Xmax
-----------------
It would be an understatement to say that there is great debate in almost all circles about the value of Xmax. Particularly in car audio, it is not uncommon to see SPL competition vehicles generate enormous SPL using drivers with Xmax less than 20 mm. Meanwhile, other competitors can't compete using drivers with 30 mm of Xmax or more. Why not?

In engineering, there are always trade-offs that range from price to performance. Designing a speaker is no different. With a conventional overhung driver, Xmax can be increased by increasing the coil height, or by decreasing the gap height. Increasing the coil height has two negative effects:
1. Increased inductance - As inductance increases, the driver will begin its high frequency roll-off at increasingly lower frequencies.
2. Added mass - An increase in Mms will result in decreased efficiency.
Similarly, decreasing the gap height may negatively effect efficiency. Both efficiency effects can be seen in the formula for efficiency on the Wikipedia (http://en.wikipedia.org/wiki/Thiele/Small) page I referenced earlier.

There are similar trade-offs in all approaches that seek increased Xmax, although the level of sacrifice varies with each approach. That's a favourite topic of mine. What is important to see now is that a tradeoff does exist. What can be seen in some drivers is that thermal power compression is reached before the driver is able to reach Xmax. Unfortunately, the lowered efficiency means more throw is required to reach a certain level of output, and if that excursion cannot be achieved before the coil is in danger, the increase in Xmax has awarded you very little.

Xmax is, however, extremely important at low frequencies. For every halving of frequency, the excursion must increase four fold to maintain the same SPL. At frequencies below 30 Hz, high output is, for the most part, only achievable with large Xmax drivers and a large enclosure with a low resonant frequency. The size of the enclosure will be dictated by the Thiele/Small parameters.

For the sake of low distortion, it is also important to pay attention to the values of Bl and Cms all the way from rest to Xmax. It can be said that the more constant the Bl and Cms values are vs. position x all the way out to Xmax, the lower distortion you will encounter.

We should also take a moment to distinguish between Xmech and Xmax. Xmech generally means the farthest the driver will travel before encountering mechanical damage to the parts of the driver. This will be larger than Xmax, which is the farthest the driver can travel in a linear fashion (as defined above). Some manufacturers refer to Xmech as Xmax in their product literature, which is misleading to say the least. We also need to distinguish between one-way Xmax and what is sometimes called "peak-to-peak" Xmax. Sometimes a manufacturer will specify the Xmax as the distance the coil can travel in a linear fashion going forward, plus that same distance going rearward. Others rate it as the maximum distance the coil can travel linearily in the forward or rearward direction. There is obviously a lot of confusion and, unfortunately, it isn't necessarily best to trust the manufacturer.

At this point, we can identify a few things that we would like to measure. We will want to measure the value of Bl, Cms, and Le at any position x in the forward and rearward direction. We will also want the value of Le with any current i flowing through the coil. It is very important to recognize that measuring these aspects will capture what is driving distortion in a driver; measuring the actual distortion requires a microphone that will capture the sound pressure created by the driver.

There have been two important methods of linearity. The first was the DUMAX machine by Dave Clark of DLC Audio. The DUMAX machine and associated patents are now property of Alpine Electronics. The direct competitor, and now border-line industry standard, is the Klippel Distortion Analyzer from Dr. Wolfgang Klippel. We'll contrast these two in a moment, but first, let's take a look at the Klippel Distortion Analyzer.

[Neil]

Now a few pictures of the Klippel Distortion Analyzer.

First, some documentation.

http://www.diymobileaudio.com/gallery/data/523/Klippel_001.jpg

- Some summary documentation of the KDA

http://www.diymobileaudio.com/gallery/data/523/Klippel_002.jpg

- The binder that contains the manual. The manual is pretty thick, too, with all the important modules available covered in full.

http://www.diymobileaudio.com/gallery/data/523/Klippel_003.jpg

http://www.diymobileaudio.com/gallery/data/523/Klippel_010.jpg

- The front of the KDA. You have a simple LCD screen, a couple selector keys, the Power button, a USB output to enable connection to a computer, and an input selector.

http://www.diymobileaudio.com/gallery/data/523/Klippel_011.jpg

- Now a shot of the rear. We have a connection slot for the power cord, a laser input, 2 input connections that support connecting a mic, two outputs that connect to the amplifier, two Speaker ports where the included Speaker cable can be connected, and lastly...the port for the Amplifier cable.

http://www.diymobileaudio.com/gallery/data/523/Klippel_008.jpg

- The Power connector

http://www.diymobileaudio.com/gallery/data/523/Klippel_004.jpg

- The Speaker cable; this can be connected to either of the two Speaker ports on the rear of the KDA. The probes are simply attached to the terminals of the driver.

http://www.diymobileaudio.com/gallery/data/523/Klippel_005.jpg

- The Amplifier cable, which is to be connected with the output signal of the power amplifier. The sginals supplied to pins 1- and 1+ are provided by the Speaker cable, which is connected to the Speaker 1 output. I'll get some better shots of those in a few.


This pretty much sums up the included parts. Next, we will review exactly how we can measure and understand the non-linear performance of drivers.

[denim]

Great topic Neil. :)

[bikinpunk]

So, you're back on for testing? Any idea when you would be able to accept drivers? I've got a couple I will gladly send in.


Thanks for the preface. I honestly don't have the time to 'learn' what you're talking about right now but will look at it soon and try to absorb it all.

[low]

nice.

[squeak9798]

Don't have time to read it all right now, but plan to hop back in later tonight to read the overview given so far. From what I skimmed, it looks well written, organized and informative.

Thank you for all you contribute Neil.

[BLD MOVS]

Awesome. This will be great to follow and learn. A great topic for sure.

[Nelson de Leon]

Great. I'm beginning to earn more!

[reindeers]

Wow! This is real technical stuff... Makes for good reading. Thanks mate :D

[critofur]

Can we put all the replies like "good job!" in a seperate thread, and keep this thread for just reference posts by Neil, and perhaps anyone else who might contribute with useful info?

[DS-21]

One minor point, which may just be an example of a lacuna in my knowledge. You write the following:

"What can be seen in some drivers is that thermal power compression is reached before the driver is able to reach Xmax. Unfortunately, the lowered efficiency means more throw is required to reach a certain level of output, and if that excursion cannot be achieved before the coil is in danger, the increase in Xmax has awarded you very little."

I think your main point is correct: that an LF driver with very poor efficiency probably won't be able to use all of its specified excursion absent ever-more-insane amounts of power.

However, my understanding is that there is a proportional relationship between volume displaced and SPL, at least at LF. As I understand it, which may be entirely wrong - is that what power compression actually does is limit the ability of the motor to move the cone. That is to say, it reduces BL(x). So it's not that more throw is required to reach a given level, it's that more power is required to reach a given level of excursion, and thus the (paper) increase in xmax has still awarded you very little.

[ngsm13]

Subscribed.

nG

[Ricci]

Seems like there hasn't been anything tested in awhile. Are things going to start back up at some point?

Neil,
What amp do you use with the Klippel system? Could you describe the linear displacement testing? I'm interested in what signal is used to cause the driver excursion. Is it pink noise, sine wave, or perhaps something else? I wonder if a situation could arise where the amplifier negatively influences or limits a measurement?

[Megalomaniac]

can i ship the puppy to you yet neil?

[tard]

One minor point, which may just be an example of a lacuna in my knowledge. You write the following:

"What can be seen in some drivers is that thermal power compression is reached before the driver is able to reach Xmax. Unfortunately, the lowered efficiency means more throw is required to reach a certain level of output, and if that excursion cannot be achieved before the coil is in danger, the increase in Xmax has awarded you very little."

I think your main point is correct: that an LF driver with very poor efficiency probably won't be able to use all of its specified excursion absent ever-more-insane amounts of power.

However, my understanding is that there is a proportional relationship between volume displaced and SPL, at least at LF. As I understand it, which may be entirely wrong - is that what power compression actually does is limit the ability of the motor to move the cone. That is to say, it reduces BL(x). So it's not that more throw is required to reach a given level, it's that more power is required to reach a given level of excursion, and thus the (paper) increase in xmax has still awarded you very little.

his point there, is the thermal issue. you are correct in the cabin pressure aspect for power of compression. just note, what he said in regards to thermal is different than what you encounter with air pressures on the cone.

there is a relationship between volume displacement and SPL. although there is also other factors that belong in that equation. the equation is not accurate, nor is it complete, if the other factors are not taken into consideration. i'm not referring to differences in box or vehicles, that also plays part, but is not what i'm referring to.

[a$$hole]

Would like to see subwoofers that are limited by power tested ! [ not by excursion limit ]