Loudspeaker 'Back EMF'

The subject of "back-EMF" from speaker drivers is one that has surfaced from time to time across many decades of audio engineering, and it always seems to get much discussion, much disagreement, and not a lot of conclusions reached. Atmasphere brought this up in the related thread of "why amps sound different", and it inspired me to do a couple of experiments.

First of all, what is "back-EMF"? EMF stands for "Electro-Motive Force", and in this case "back" means backwards, from the speaker to the amplifier. The idea is that if an amplifier can send electrical power through a speaker voice-coil and cause it to move, then a moving speaker can also generate electrical power and send it back to the amplifier. And since a speaker diaphragm is made of matter and has inertia, then it stands to reason that should the electrical output of an amplifier demand a particularly complex waveform, the speaker might, at certain times, send back electrical power that's in opposition to that produced by the amplifier. It is this opposing power that is commonly refered to as "back-EMF".

Whether or not EMF is generated at a given instant is determined by two opposing forces. On one side is the inertial energy of the loudspeaker diaphragm - its mass, direction and speed. This is counteracted by the mechanical damping - the air in the speaker box and/or the springiness of the speaker's suspension (and horn loading if applicable), and the electrical damping - the production or absorption of electrical power from the crossover, cables, and amplifier. EMF then becomes "back-EMF" in the amount that it is in opposition to the amplifier's output.

So why do we care? All of these electric and electro-motive forces interact with each other to determine the energy that transfers between amplifier and speaker, so they are essential for us to understand why different amplifiers behave the way they do. Traditionally, EMF is analyzed as part of the "load" on the amplifier versus the frequency, with back-EMF contributing to the load's phase angle. This is handy as the behavior of the loudspeaker can be summarized, or "modeled", as a network of resistors, capacitors, and inductors - and a big aspect of an amplifier's performance can be measured in terms of its linearity into this network. For the most part, I subscribe to this traditional view.

In the previous thread mentioned above, Atmasphere alluded to another viewpoint that I have seen on occasion - that there is other, "special" back-EMF generated that does not conform to traditional loudspeaker load modeling . . . and that it is this extra back-EMF that helps explain the sonic shortcommings of a particular approach to amplifier design. He also speculated that older, high-sensitivity horn drivers with large magnetic structures did so in particular . . . which I interpreted to mean "Atmasphere feels that i.e. a JBL 375 compression driver produces significant back-EMF". Hopefully he'll chime in and do a better job than I can of articulating his view.

Anyway, this is point which I differ with . . . but I just happen to have some 375s lying around. And how 'bout some woofers . . . I also have some JBL D130s. Perfect.

Enter the experiment. The broader question being, does "special" back-EMF exist? Specifically, do the EMF characteristics of the 375 and the D130 deviate from that anticipated by traditional analysis? For the 375, there should thus be virtually no back-EMF at all, and for the D130, the back-EMF should correspond exactly to the phase angle predicted by its Thiele-Small parameters. To answer this, I conducted two sets of measurements, both with a pair of drivers coupled together by placing them face-to-face and sealing the airspace between their diaphragms. The first measurement would be with a sinewave input to one driver, and measuring the output power and phase angle on the second.

The second measurement will be with a squarewave input from a high source impedance, with the voltage at the speaker terminals viewed on an oscilloscope. The electrical load on the second (undriven) driver would be changed between 0, 4, and 8 ohms - any high-frequency back-EMF will appear as ringing, changing the leading-edge profile of the squarewave as the load is changed. This allows the driver load behavior resulting from purely electrical load characteristics (voice coil inductance and resistance) to be seen separately from the electro-motive load behavior.

And the results - first the D130s. I will admit I was quite impressed and surprised with the sheer effeciency of their electromagnetic motors - even in free resonance with a 16-ohm driver, these make lots of sound! And with no load, the undriven speaker produced a voltage only 1.7dB lower than the input! With a 4-ohm damping load, the power transfer was -13.3dB/mW. The listed free-air resonance for the D130 is 40 Hz, and the expected 180-degree phase shift occured at 41.6Hz. (Thiele-Small parameters predict a phase-shift of 90 degrees per driver at the free-air resonance point.) I found a 45-degree shift at about 228Hz . . . the Thiele-Small parameters predict this at 217Hz. Turning to the square-wave response (47 ohm source). . . the only observable change is amplitude, no change in overshoot resulted, and there was no ringing at all.

Turning to the 375s - again, incredible sensitivity - I performed these tests at a low 150mW (375s don't grow on trees, after all), and needed hearing protection until the drivers were set face-to-face, at which point the sound was almost inaudible. Power generated by the undriven driver was in this case -10.3dB/mW. But the real difference was the phase angle - zero. At any frequency between 500Hz and 12KHz. Again, the square-wave test (470 ohm source) revealed no ringing or change in overshoot, in fact, the opposite was true - the presence of the second (undriven)driver actually dampened some of the supersonic energy that was put into the (driven) driver, rounding the top of the squarewave. Output from the undriven 375 was visually perfectly sinusoidal. This indicates that the mechanical damping completely halts the generation of any back-EMF.

So here's my conclusion . . . these classic drivers are extremely efficient at producing sound vibrations from electrical energy, and are thus impressively efficient at producing electrical energy from sound vibrations. But the amount of back-EMF they can put into an amplifier is still similar to more modern designs, because the generation of back-EMF is related to the diaphragm resonance, not to sensitivity. For woofers, the Thiele-Small parameters can reliably predict the EMF characteristics. And for tweeters, domes, and compression drivers, their resonant peak is generally outside the frequency range of use, their movements are small and well-damped, and the amount of input power is comparatively low . . . which makes their contribution to back-EMF completely insignificant.

Similarly, the effects on amplifier stability are well-known . . . many volumes have been written about properly stabilizing tube amplifiers at low frequencies, where back-EMF is likely to cause non-linearity. At the other end of the spectrum, the mechanical characterics of a tweeter or compression driver are highly unlikely to affect the phase margin of any reasonably well-executed conventional solid-state amplifier.

Of course, opinions abound and I welcome them. I also understand the level of inaccuracy inherent in many aspects of my testing . . . after all, this is just a couple of hours on a weekend. I do not present this as any sort of definitive, highly scientific study . . .