Loudspeakers, the secrets of distortion

This article is about the challenges of collecting all the data needed to determine the actual performance of a driver through measurements, and how we developed an alternative method that quickly gives far more information than has previously been possible to review.

Way back in 1978, when the cobalt prices skyrocketed, manufacturers were forced to move on to ferrite ceramic magnets to replace the old aluminium-nickel-cobalt alloy magnets. This lead to a noticeable reduction in performance in drivers designed with alnico to begin with. Some engineers worked on new designs, and ended up with undercut pole piece in an attempt to make the gap more symmetric. They were probably surprised when the new ferrite design outperformed the old alnico designs.

The difference between the two was off course related to some kind of distortion. However, as the force factor in relation to the position of the coil [Bl(x)] was an apparent goal of this project, they may well have saturated the narrow part of the pole piece in the process. This again would lead to a reduction in inductance and a more stable flux field. The effect is quite similar to the relationship between force factor and position, but instead of position this relates to current [Bl(i)].

Lowering distortion in general is all that counts when it comes to allowing clean reproduction of music. Many would argue there are other important factors to consider too, but distortion is allways the correct term for describing everything that alters the recorded sound.

Both of them cause intermodulation distortion, but while one is in phase with the position of the diaphragm, the other one is out of phase with pretty much everything. It is affected by the impedance, and both electrical inductance and some electromechanical components interfer with the relationship between voltage and current. This changes the phase relationship between the original signal and the resulting distortion. The familiar Bl(i) curve does not give us much to go on to understand what really happens in the motor.

This tends turn up as a very bad type of audible distortion rarely documented and not widely understood. This is quite strange as information is easily available, and at the same time, relationship between BH-curves and sound quality has also been well documented for at least 5 decades. So despite not being caused by any hidden effect, this type of distortion is not widely documented. We can tell for sure that it is some kind of amplitude intermodulation distortion but that is pretty much where it stops.

There are lots of information fragments in a measurement, but we do not allways know where they belong and what they mean. That prevents us from seing the complete image.

In order to understand this at a deeper level we need some kind of graphical way to show it and make the performance of the driver intuitively understood. I have discussed this matter with several of my good colleagues in the industry, but over and over again I found myself struggling with showing enough data at the same time. We could for example make a standardized method that selects a few frequencies and currents, and plots the resulting distortion. That would really allow for some drivers specialized to fit those measurements and at the same time maybe not perform that well in real life.

Another problem surfaced in the process. If this requires so many measurements and such a large amount of processing to pick out the relevant parts of the measurements, what would be the interesting bits when we are reviewing sample drivers that are not working well, and how can we get an understanding of what we need to change to improve the performance?

That is when it hit me, the simulations we had made were so extremely close to the finished product, what else could they hide? Can we process them further? Can we even plot curves in a way that would be impossible to measure? This last question rises an even more interesting question, would it be interesting to plot non measurable data? Would it represent any real life scenario? As it turns out, the answer to this question gave us the answer to everything.

By picking the correct pieces and make them fit together we can get a relatively simple and far more complete picture that intuitively highlights any error.

When we measure the performance of any product we measure the result of several interacting systems. By focusing on the particular parts of the motor, collecting data, processing it, and putting it together the correct way, we were suddenly able to illustrate the actual performance of the drivers motors individual parts separately. We could limit this to show data within the working range of the driver. This enabled us to plot up to more than 100 different curves showing in depth performance details on the inner workings of the motor.

Among these curves we have several different AC profiles for both the magnetic material and the forces between the coil and the rest of the motor. We can not only see the formation of eddy currents, but also how they actually affect sound. We can see how every individual part affects the phase relationship between current and voltage. We can study how different parts even affects the relationship between current and force over time. We can collect so much useful data that we have to limit it to a handful of the most useful diagrams. In the development process of a driver we also limit the number of data points significantly until we know we are on the right path.

To illustrate how this works I have a very simple diagram here that shows the interaction between current, excursion and force factor. Just by plotting these three together it is very easy to see how Bl(x) and Bl(i) plotted individually reveals very little of the performance of a given driver.

This shows a very expensive and widely used woofer. Notice how current and excursion adds up exponentially.

Here is our ferrite motor for the Tonalab 15 inch woofer for comparison. This design both has improved Bl(x) and Bl(i), but the most noticable difference is in the corners where the driver appears to be totally unaffected by the sum of current and excursion related distortion components.

The beauty of this is that it is extremely hard to figure out what signal to use to expose these effects in a measurement. One would off course find them, but the required signals and processing would differ from driver to driver. At the same time it would be difficult to know what to look for, and what causes the distortion in the first place. Without knowledge of what might be a weak spot in a particular driver we will really have to guess what type of signal could be of interest.

Using this method we can get extremely precise answers with general validity even before we build the driver. This is off course the point of simulations in the first place, so this appears to be something we already knew. However, in simulations we have typically tried to mimic the properties we would normally measure. By plotting data that can only be indirectly measured the simulated data is suddenly far more useful than any of the indirect measurements.

This actually gives us a far more precise picture of reality than a large amount of measurements would. After all, measurements are a theoretical exercise too. It is all about selecting the tool that reveals all the details.

Jørn Rune Kviserud
Tonalab
April 28, 2022