Tech Talk

Improving Woofer Motor Linearity with Finite Element Analysis

George Short | Senior Principal Engineer

Even a simple woofer motor, well executed, is capable of remarkable performance. But with attention to detail, it gets a lot better.

Bottom left is a traditional woofer motor. This is a nominal 6” woofer, built around a very nicely sized ceramic magnet. The first iteration of this motor, the pole piece in the center is the same height as the rest of the motor, so the top plate and pole top are flat.

A simulation of the magnetic field through the right half the motor is shown below right. The bright magenta color is the region of the strongest flux, and as it gets weaker the colors fade through orange and yellow and finally to green. The black box represents the voice coil at rest, which resides in the magnetic gap (hereafter referred to as the “gap”) fully immersed in the magnetic field. The extended blue boxes represent the voice coil’s maximum inward and outward motion limits.

When alternating electrical current flows through the voice coil, the current and hence the voice coil experience an accelerating force directly proportional to the sum of magnetic flux crossing the voice coil. The voice coil moves forward out of the motor and then rearward into the motor, which moves the woofer cone, which moves the air, which makes sound.

The magnetic flux wants to stay in the steel as much as possible, so mostly it jumps straight from the top plate across the gap and into the pole piece. But some flux, called “stray flux”, will always spread out as it crosses, and because in this motor design the magnetic flux is not identical above and below the magnetic gap, the voice coil is immersed in an asymmetric magnetic field.

Below is a close-up of this magnetic gap showing the stray flux crossing the voice coil, and a graph of the motor force vs coil excursion is below. There are two key features:

The motor force drops off rapidly beyond a certain amount of voice coil excursion;
Motor force asymmetry. In fact, this motor exhibits peak strength when the voice coil moves about 3mm inside the motor.

#1 is what one would expect; the woofer can’t move backwards and forwards an infinite distance, so at some point it must run out of juice. More on that later…

#2 – Asymmetry – is the real problem. Asymmetric motor force means the woofer cone behaves differently when moving in vs moving out, which causes audible distortion.

Improving Magnetic Field Symmetry

Through the years, we have learned that the easiest and most effective way to correct the motor asymmetry is to extend the pole piece above the top plate, easily accomplished with a small change to the pole casting.

The new size and shape is optimized via CAD Finite Element Analysis (FEA). A graphical representation of the FEA is shown at right. In a nutshell, the designer (me) instructs the computer to break down the motor into a large but finite number of triangular elements, then analyze the physics within each triangle. One can see that when the physical surface becomes complicated, such as a corner or arc, the analysis also gets complicated and requires more calculations per unit of space. That is why the triangles get smaller. The amount of math in each triangle is actually the same.

Very quickly we can come up with an optimized size and shape (compared to building and testing physical prototypes). Below left is the magnetic field simulation of the same basic components as before, but with a 5mm extension added to the pole, as well as a close-up of this gap.

One can immediately observe the magnetic flux as it crosses the gap is both equal and balanced. So, one simple change to our motor design symmetrizes the magnetic field and eliminates this source of distortion, and with no increase in complexity or cost.

Does this mean that we have eliminated all distortion (yippee!)? Well, not quite, but we’re getting there. In the case of our 6-Inch woofer, its application defines a performance envelope within which the woofer excels, and beyond which it makes more sense to just add more woofers.

Based on the work of HARMAN alumni Dr. Wolfgang Klippel¹, we know the objective criteria of symmetric motor strength distortion becomes subjectively audible when the motor force at excursion is less than 82% of the motor force at rest. This is our performance envelope.

Looking at the Motor Force vs Cone Excursion graph again, the red box denotes the 0% to
-18% Motor Force window. The data line exits the envelope at ±6.5mm, meaning because of a little extra time and effort and a lot of computing power, our little woofer cone can move 13mm - more than half an inch – peak-to-peak, clean!

How does all of this translate to sound quality? Well, one only needs a quick listen to the JBL Stage II. They are amazing!

Footnote (1)

Dr. Wolfgang Klippel was Senior R&D engineer at HARMAN International, Inc., Northridge, CA, USA (1993-1995); responsible for the project “Nonlinear Control of Loudspeaker Systems“;

Dr. Klippel went on to form Klippel GMBH, creator and manufacturer of the well-known Klippel Acoustic Analyzer and Software products.