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 . . .
You need to listen to some music, otherwise your EMF may back up on you and then you'll have to see a doctor! Good luck and Godspeed my friend.
You probably have observed the passive radiator used in some speaker systems. It moves just about as much as the active driver. If you replace the passive radiator with a driver (having a magnet and voice coil) it will generate voltage as you have observed. An interesting experiment is to put a capacitive or inductive load on the undriven driver and see how you can tune the speaker system. A short circuit will prevent (or minimize) cone movement. A capacitor will allow movement at low frequency but not high. An inductor will prevent cone movement at low frequency.

Have fun.
Back EMF is a phenomenon that has been used often for marketing reasons: to praise one's product (let's say a poweramp), because of it's handling of back EMF. But what does it actually mean? Nothing. Back EMF is a highly overrated phenomenon that doesn't correlate well with actual sound quality, like skin effect with audio cables (skin effect is almost non existent within the audio frequency band).

Chris - portion of Back EMF generated by the speaker can get to the other speaker (tweeter to midrange). Amplifier would "short it" but there is about 5uH inductance of the speaker cable in between (and amp's output impedance is higher at higher frequencies). I use shotgun biwired cables and have slightly cleaner sound with more "air".
Fascinating discussion, and one that does not deserve only four replies before it is consigned to the Audiogon archives. Thanks for bringing it up, Kirkus.

Dazzdax please correct me if I am wrong, but my understanding is that the current flow across a transistor depends on the potential difference between the collector and the emitter. If the potential difference is dropped (by a negative voltage applied by back EMF to the emitter, for example), then current flow would be less. My understanding also, is that the magnitude of back EMF is fairly high, particularly in active setups where there is no passive crossover in between the amp and speaker.
Amfibius, you should address this question to Kijanki, because he is the expert in this field. The current flow through a transistor is related to the current between base and emitter. This way I don't see why a negative voltage generated by back EMF could alter the collector flow. This is a highly technical matter. I've read somewhere that back EMF could be used to increase the efficiency of an electromotor!
To me back EMF has no significant meaning in case of home audio. Unless you need multiple speakers that have BIG woofers, like in the PA setting.

Amfibius - It does interfere with an output to some degree. Most of amps contain negative feedback, forcing desire voltage on the output in spite of the current fluctuations. In one way it is beneficial helping with things like back EMF or intermodulation (linearizing output devices) but often creates other problems. One problem mentioned before was puting more power (by holding voltage steady) when speaker impedance drops to few ohms (resonanse) at certain frequencies, the other is transient intermodulation (TIM) when feedback is not fast enough (delays in the signal path) to respond to higher slew rate at the input - causing transistors to go into saturation. Small charge is trapped at semiconductor junctions and transistors need more time to recover making unpleasant sound.

How real or serious is effect of the back EMF? I have no experience - we have to ask speaker people.
Hi Amfibius . . . Dazzdax is correct in stating the classic analysis of a bipolar transistor's operation, as being based on the current flow from the base to the emitter. I happen to agree with Douglas Self's assertion that this is quite a useless view, because in application it's the base-to-emitter VOLTAGE that really matters. But this is a digression, and it means absolutely nothing to the end user of a finished audio product.

Where I feel that the typical audiophile arm-chair analysis of back-EMF becomes absurd is a complete disregard of the frequency component of the energy in question. It's not like while your're relaxing to some Brahms, your errant woofer suddenly gets a hankering to jump back and forth for a few cycles at 10,000 Hz, and your amplifier better be prepared to short out that energy! Assuming that you'd care, because you'd hear such abberant behavior so clearly from the driver itself, that any effect on the amplifier stability is a moot point.

Thus, the problem with Kijanki's point about back-EMF getting from the woofer into the other drivers is that if the crossover is doing it's job, the back-EMF will be too low in frequency to ever make it to the tweeter. And if it's not, the tweeter has so much more to worry about with the low-frequency energy coming from the amplifier, than with the woofer's low-frequency back-EMF.

However, if we view back-EMF simply as a contributor to amplifier load, rather than as a mysterious external force that the amplifier must dampen, than subjects such as the current through the output transistors, and especially that touchy subject of negative feedback, can be properly analyzed, rather than simply conjectured about.
Dazzdax, thank you for the correction. I meant to say base to emitter, just got my terminologies confused for a moment :) My question really is - if back EMF applies a negative voltage to the emitter, AND if amplifier current flow depends on the voltage across the base and emitter - is it possible for back EMF to reduce current flow? Or do I have it wrong again?

Kijanki your answer went over my head a little. Reading your response carefully, it appears to me as if you were describing conditions that cause a transistor to go into saturation. That is fine, I understand that. But I am not sure how back EMF fits into the picture?

Kirkus, my understanding is that back EMF is only detrimental to amplifier load. I was not even aware that some people argue that back EMF causes high frequency aberrations :)
Assuming the most conventional (emitter-follower) output stage, then yes, energy that's applied at the amplifier output will affect the current flow through the output transistors. If this wasn't true, then the amplifier would have an infinately-high output impedance, and could never transfer any power to the loudspeaker. So the real question is, what exactly are the current requirements of the amplifier . . . so we can effectively design it to work well to fulfill those requirements.

There is really only one mechanism that allows ANY solid-state amplifier to be coupled directly to a loudspeaker: negative feedback. Even in a supposedly "zero feedback" design, there is intrinsic local negative feedback in the output topology. Think about it . . . if the output is derived from the emitters, and signal is applied to the bases, and the output current is determined by base-to-emitter voltage . . . then applying a signal "backwards" at the output will attempt to change the base-to-emitter voltage as well . . . which will in turn cause the current through the output devices to change in an opposite fashion.

So if we're to understand fully how to make amplifiers work correctly, we MUST have a coherent, duplicatable model of the loudspeaker as a load, otherwise the only thing we can use to design with is whimsey, credo, and dogma.

Oh wait, this the high-end audio world. Just ignore all of the above . . . . sorry.
Kirkus - crossover is far from being perfect and Back EMF from tweeter to midrange or midrange to tweeter at the frequency close to crossover point (probably around 2.5kHz) gets thru. Amplifier's DF is limited at higher frequencies and cable inductance brings almost 0.1 Ohm (2.5kHz). I am not talking about major effects - just enough to make biwired connection to sound more "airy" and cleaner.

Amfibius - I mentioned TIM only to show that making amplifier 100% imune to back EMF and other loading effects is not a good thing.