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Jan 7th, 2020

Does negative feedback cause TIM?

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Actually, “TIM” is not so much a type of distortion as a test method to detect Slew Induced Distortion. Nobody calls it that though, and if I need to be pedantic, what we call the animal may not be the right hill to die on. So I’ll fold and call it “TIM” just like everyone else.

TIM is a form of distortion caused by the gradual overload of the input stage of “miller” type amplifiers when driven at high frequencies. This type of amplifier includes most op amps, but also most linear power amplifiers. They consist of a differential input stage followed by a gain stage and an output stage.

Incidentally, class D amplifiers don’t come into this discussion. They are structured totally differently and don’t have an inherent TIM mechanism.

Anyhow. The idea behind the Miller circuit is to put in a lot of gain so the input voltage is negligible. Suppose the amplifier has an open-loop gain of 100. That is the gain you get when you remove the feedback network. Suppose now you’re making it put out 20V. That means that the input stage sees 200mV. This is much more than the input stage can handle without distorting. It pretty much breaks the feedback loop because the gain stage sees a signal that’s already distorted. The gain stage ends up amplifying the wrong signal. The problem isn’t that the feedback loop is causing distortion. The problem is that the amplifier hasn’t got enough gain to allow the input stage to stay linear. 100 is not “a lot” then.

Now I hear you ask, haven’t feedback amplifiers got much, much higher open-loop gain? They do, but only at DC. At 20kHz, 100x was a normal value for a typical 1970’s solid state amplifier. That was why in those years Matti Otala had to draw attention to the fact that at high frequencies distortion from the input stage couldn’t be ignored. By contrast, at 1kHz the same amplifier would have an open-loop gain of 2000, and for the same 20V output the corresponding 10mV across the input stage was unproblematic.

So how do you solve this? Simple: more open-loop gain. Not just at DC of course but over the entire frequency range. Of course, “more open-loop gain” is the same as “more feedback”. TIM isn’t caused by too much feedback. It’s caused by not enough feedback. That’s the exact reverse of what most people believe. If you see a lot of TIM it means you’ve tried, and failed to build an amplifier with a lot of feedback.

This gives you a handy shibboleth to see, whenever someone is holding forth on amplifiers, which end of their anatomy they’re talking out of. Simply ask them whether feedback causes TIM. If they say yes, you can safely ignore anything else they might have to offer on the subject.


A much more detailed version of this story was published under the title “The F word”, and is available here:


Dec 20th, 2019

SPK5 – App Note (Replaces SPK4 – App Note)

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SPK5 is intended as demonstration platform for the PTT6.5W04-01A transducer.
The design is deliberately kept very simple: a small ported wooden box, traditionally shaped with a simple 12.5mm chamfer for management of edge diffraction, and a passive cross over at ~3.2kHz. Although extremely simple, with numerous possibilities for enhancement by the skilled speaker designer, the SPK5 design very successfully demonstrates the tremendous improvements in sound quality which is possible to achieve when using the long-stroke ultra-low-distortion PTT6.5W04 woofer from PURIFI Transducer Technology.


Dec 12th, 2019

Low frequency harmonic distortion is almost inaudible. So what’s the point of low distortion drivers?

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Decades of research has shown that we’re not very sensitive to distortion at bass frequencies. I doubt if anything has happened to our species recently that would change that. Consider the science settled. The problem with scientific findings is, it’s frightfully easy to miss the fine print and draw the wrong conclusions.

I’d like to propose a simple demo to illustrate this. I’ve simulated two highly simplified woofers, both of which are ideal except that one has a nonlinear Kms (but a perfectly constant BL=1) and the other a nonlinear BL but a perfectly linear suspension (Kms=1). Never mind the units, it’s a simulation so I normalised as many of the values to 1 as I sensibly could.


Stiffness and Q are set for a 40Hz Butterworth roll-off. As you can see from the graph I’m not trying to make this demo at all subtle. After all, most of you will be using PC speakers or earbuds at best to listen to the sound samples.

The magnitude and nature of the two nonlinearities was chosen such that the resulting harmonic distortion is about equally bad in either case:


The armchair psychoacoustician will conclude that any audible differences between these two drivers are going to be very subtle indeed.

Let’s run some audio through them and listen to the result. For good order I’ve inserted a 2.5kHz low pass filter to make the sound samples representative of midwoofer use. I’ve also included a third one where both Kms and BL are set to a constant value of 1 so you have a distortion free reference to listen to as well.

Driver with only nonideal suspension stiffness Kms: (kmsdist1.flac)

Driver with only nonideal force factor BL: (BLdist1.flac)

Fully distortion free driver: (nodist.flac)

I hope you’re duly startled. Just to show that I’m not cheating, here’s a plot of the cone position of both simulated drivers, between seconds 6 and 8 of the clip.


It’s basically the same cone movement. Give or take. The bass distortion is also fairly similar, and very large. What happens though is that the “give or take” includes midrange content which doesn’t move the cone noticeably, but which is clearly much more affected when the force factor changes compared to when stiffness changes. The reason is that only low frequency forces are working to overcome the suspension. From the resonance frequency upward, the cone mass is a much greater drag on the voice coil than the suspension. Transducer designers say that at high frequencies “the system is mass controlled” (further expanded on in another blog post about moving mass, “speed” and bandwidth). So, if Kms is the only cause of low frequency distortion, it will not cause distortion at higher frequencies. If BL is a cause of low frequency distortion, it will also amplitude modulate higher frequency components (i.e. produce IMD, intermodulation distortion). We don’t so much hear distortion levels as distortion mechanisms. You need to understand the mechanism before you can design a test that will quantify it sensibly.

Fortunately it’s not all that complicated here. Just apply a low-frequency sine wave and a mid-frequency sine wave together and look at the spectrum that comes out in either case:



Well that’s something the harmonic distortion plot didn’t tell you: the harmonic distortion may be comparable between both versions but the IMD products around the 1kHz tone are very, very different.

I should add here that the simulation only includes the position dependent component of BL. In practice, BL is usually current dependent as well as our AES paper on force factor modulation shows.

So what conclusions can we draw from that? Quite a few.

  • Similar distortion figures can hide very different manifestations.
  • Intermodulation measurements are indispensable for evaluating loudspeaker drivers.
  • BL as a function of position is a critical performance specification that should never be left out of a data sheet.
  • The same goes for BL as a function of current or its equivalent, position dependent self-inductance (see AES paper).
  • The stiffness curve of the suspension of a woofer can be designed purely based on practical requirements of robustness and power handling.
  • For pure subwoofers, low distortion is optional.
  • With their limited control bandwidth (200Hz or so), motional feedback (MFB) systems can only improve distortion in the subwoofer frequency range but are powerless against midrange distortion, including IMD. This explains the limited take-up of this technique.
  • Anyone asking “can we ever hear distortion mechanism x when elsewhere in the signal chain distortion from mechanism y is so much greater” should look at what types of distortion either mechanism can and cannot produce. Only then can they know if one distortion mechanism is likely to mask the other.

The science was right: even gross bass distortion is remarkably difficult to hear. The fine print says yes, provided it stays in the bass.


Hearing the simulated audio of the BL nonlinearity immediately took me back to the bus station in Kibuye, Rwanda, where they’d mounted a pair of 12” prosumer speakers on poles. Through them Afrobeats music was blasted all day. It was loud and the tweeters were blown. I just had to redo the samples using the track they were actually playing when I passed through. Apologies to the artist, whose music I quite enjoy.


Dec 10th, 2019

A fast driver needs a light cone. Or does it?

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Intuition can play us tricks. Take this simple example: how does a speaker cone move when you try to make it produce a “pulse”? I’m willing to bet quite a few of you will guess it will rapidly move forward and then equally rapidly return to its rest position. And from that it’d be quite reasonable to conclude that a heavy cone would be pretty bad at doing this. Quite reasonable but sadly also quite wrong.

You see, acoustics doesn’t work like that. If it did, you’d be able to produce constant pressure by moving the cone forward and keeping it there. What really happens is that the air simply gets out of the way of the cone and life goes on.

You couldn’t even produce constant pressure by keeping the cone moving at a constant speed. You’d get what we call wind, but as soon as that wind gets going, pressure settles back to normal. In short, the only way you can get pressure from a moving piston is by making it push on the air, accelerating it. Making a short pressure pulse then simply amounts to pushing (accelerating) for a very short time.

That just shows you how fallible our intuition is. Sound pressure doesn’t correspond to cone position. Not even to cone velocity. It corresponds to acceleration. So now we can answer the question: what movement does a cone make when you ask it to put out an acoustic pulse? It accelerates during the pulse and then keeps coasting:blkms(Wait, isn’t the amplifier supposed to stop cone movement? Eventually, yes, but not nearly as fast as the damping factor myth would have it. We’ll devote another blog post to that.)

Basically, what we’re saying is that fundamentally, moving mass only affects sensitivity, while what folks call “fast” or “slow” amounts to bandwidth. And that does not relate to mass, but mostly to how real cones flex and spring back when you push on them. How much depends on material type and geometry but not directly on mass. A case in point: diamond tweeter domes are fabled for their “speed”, i.e. bandwidth, but as it happens, they are also the heaviest domes in regular use. This is reflected in diamond tweeters’ lower than average efficiency. But even though diamond domes are much heavier than their aluminium counterparts, they’re much, much stiffer too.

There’s little point in elaborating the intricacies of membrane design here because you can simply look at the frequency response graph. If a driver’s response is smooth and continues a long way, it’s ‘fast’.


Dec 7th, 2019

Doppler distortion vs IMD?

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Let’s get this out of the way first: Doppler distortion is a form of IMD. This is interesting because IMD in general tends to get little interest on loudspeaker forums, whereas Doppler distortion is often made a big deal of.

Any distortion process will cause both harmonic and intermodulation distortion. After all, harmonic distortion is nothing more than a single sine wave modulating itself. Sometimes you get phase modulation, sometimes amplitude modulation, often a mix of both. As demonstrated in another blog post, a drooping Bl curve will cause a mid-frequency signal to be amplitude modulated by a low-frequency one. Doppler distortion will cause the mid-frequency signal to be phase modulated.

The problem is, you can’t easily see from a spectral plot which of the two is actually the case. In fact, you can’t see it at all. That is because spectral plots don’t show phase information. It’s often assumed that this information doesn’t matter i.e. that you can simply gauge the audibility of distortion products by looking how tall they are compared to the signal.

I’d like to offer up a small demo to caution against this form of Popular Psychoacoustics. Below are two signals whose power spectra are completely identical. Only the phase relationships are different. One is a pure amplitude modulated signal, the other is its purely phase modulated counterpart. The carrier frequency is 1.38kHz, the modulation frequency is 43Hz. The phase modulated signal (labelled FM on the graph, it’s the same thing) corresponds to the Doppler distortion caused by a cone excursion of +/-12.5mm. That’s right: a peak to peak displacement of an entire Imperial Carpentry Unit, give or take a gnat’s whisker.

Pure AM modulation: (PureAM.wav)

Pure FM modulation: (PureFM.wav)


Put on a pair of headphones and listen to both. I’ll leave you to draw your own conclusions.


Nov 11th, 2019

SPK4 – App Note

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SPK4 is intended as demonstration platform for the PTT6.5W04-01A transducer.
The design is deliberately kept very simple: a small ported wooden box, traditionally shaped with no particular management of edge diffraction, and a passive cross over at ~2.5kHz. Although extremely simple, with numerous possibilities for enhancement by the skilled speaker designer, the SPK4 design very successfully demonstrates the tremendous improvements in sound quality which is possible to achieve when using the long-stroke ultra-low-distortion PTT6.5W04 woofer from PURIFI Transducer Technology.


May 2nd, 2019

Distortion, The Sound That Dare Not Speak Its Name

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Read any discussion about loudspeakers and you get the impression that distortion as a topic is eagerly avoided. If it is mentioned, it is done sotto voce, implicitly. For instance: “you can’t get good bass out of a small long-stroke driver. There’s no substitute for cone area when you want to move air”. Doesn’t sound like it is about distortion at all, does it? Let’s unpick the statement a bit: there is no substitute for cone area. Of course there is: displacement. If you want to move 100 cc of air, you could move a 500 cm2 cone by 2 mm or you can move a 200 cm2 cone by 5 mm. At the wavelengths we’re talking about, there’s no difference between the two. So if the bigger driver sounds better, it must be because it’s managing that 2 mm movement much more precisely than the smaller driver is managing its 5mm. And that is a statement about distortion. If we can crack the question why a short-stroke driver is more accurate over short strokes than a long-stroke one over long strokes, it should enable us to build a long-stroke driver that’s just as accurate as a short stroke one for the same acoustical output. More accurate in fact, because once you understand the problem, there’s no reason why you couldn’t reduce distortion even further. This is what PURIFI set out to do.

Identifying the Problem

Loudspeaker drivers are coupled problems. They consist of a motor, a suspension and a diaphragm that interact with each other mechanically. All three parts cause distortion in different ways, and those distortion components add up in unexpected ways. A HD measurement done on a complete driver tends to show a complicated jumble of frequency and amplitude dependent distortion products. An IMD
measurement shows another jumble. Figuring out what distortion component in the reproduced sound is produced by what element is remarkably hard.
Getting round this requires decoupling the problem again and trying to predict what each part will do on its own. After following the evidence with quite some rigour, PURIFI identified two significant distortion mechanisms that have gone mostly unnoticed: Force Factor Modulation (FFM) and Surround Radiation Distortion (SRD). Together they explain practically all low-frequency distortion that currently remains in otherwise well-designed drive units.
For something as notoriously complex as a loudspeaker driver, this list is startlingly short. Really? Just those two? And nobody has noticed before? Things become less mysterious when you look at the distortion signatures of FFM and SRD. They are very similar in nature and magnitude. For someone with an experimental penchant (and let’s be honest, that’s all of us in the speaker industry) it’s easy to hypothesise one of these problems and try a fix. Only to find that distortion has barely budged. So that wasn’t the problem we think and move on.
Once you know what to look out for, you’ll find various products that have indeed attempted to solve one problem or the other. None of them made history: it’s only when you address both that distortion plummets and sonic magic happens.


When we talk about distortion, there’s often a distinction made between Harmonic Distortion (HD) and Intermodulation Distortion (IMD). These aren’t two different types of distortion per se, but different ways in which the same distortion mechanism can manifest itself more or less saliently. Take for
instance a woofer whose BL curve droops progressively with excursion. Tested with a single 30 Hz sine wave, this will only manifest itself as a form of soft limiting. This sounds like a change in tonal quality, but little more. The effect of the suspension progressively stiffening (Kms increases) with excursion would sound more or less the same in a single sine wave test. A HD measurement is not helpful in telling you which of the two effects is happening.
By contrast, imagine what happens if you add a 1kHz tone to the bass tone. The added excursion caused by the 1kHz component itself is negligible. But now the two distortion mechanisms show very different signatures. As BL rises and falls throughout the 30 Hz cycle, so does the sensitivity of the motor. The 1 kHz tone gets amplitude modulated. You can hear the 1 kHz tone wobble. BL droop manifests itself not only as harmonic distortion, but also as intermodulation. The variable stiffness of the suspension however has no such effect. The 1 kHz tone will not be modulated by suspension stiffness. Why should it? 1 kHz is well above the resonance frequency, so there the mass of the cone completely dominates how the 1kHz component makes the cone move. The difference between the two distortion mechanisms is plainly audible on any genre of music that has both bass and midrange content. And as a distortion mechanism, the droop of the BL curve is much more audible than the progressive stiffening of the suspension.
This is rather important. One often encounters drivers where two different distortion mechanisms are precisely orchestrated to make their harmonic distortions cancel. Such drivers look great on paper but this sleight of hand actually worsens IMD.
Even though there are no standardised methods of presenting loudspeaker IMD measurements on paper, it is quite crucial to learn to think about loudspeaker nonlinearities in terms of intermodulation rather than harmonic distortion.

Force Factor Modulation (FFM)

The impact of position dependent force factor BL(x) and the position dependent suspension stiffness Kms(x) have been well publicised. These parameters aren’t nearly enough to predict real life distortion performance though. They only predict distortion when excursion is large, which you only get when you play bass heavy music very loud. If the BL(x) and Kms(x) duo are to be believed, all speaker drivers ought to have the same negligible distortion under normal listening conditions. This we know is not the case.
PURIFI has extended the purely statistical concept of BL(x) into a dynamic one that includes time and voice coil current. The new mathematical model correctly predicts motor force for an arbitrary combination of applied voltage signal and movement. The model reveals that all motor distortion that can’t be explained by BL(x) can be explained by something called Force Factor Modulation. FFM happens when the magnetic field created by the current in the voice coil adds itself to the magnetic field created by the permanent magnet. Ideally, the magnetic flux in the air gap is only determined by the magnet and the geometry. In practice, it varies strongly because of the current in the voice coil. The problem is exacerbated in longstroke drivers because a larger portion of the coil is creating this unwanted magnetic field without actually producing useful drive force. This goes some way in explaining why short stroke, large diameter woofers have such a faithful following. It also tells you exactly what problem to solve to get the same sound out of a compact long stroke design.
The distortion takes the form of the signal being multiplied with a filtered version of itself, so it is predominantly second order in nature. Now, there is a common misconception that second order distortion is innocuous. This may be largely true of harmonic distortion where a second harmonic is easily masked by the fundamental, but in the case of intermodulation distortion it is patently false. Second order IMD generates difference frequencies which are below the signal frequency and don’t get masked at all. They audibly clog up the bass region in a manner which becomes extremely obvious once you remove the distortion. Also, amplitude modulation of mid frequency signals by the bass is very audible as burbling.
A second important insight was that Force Factor Modulation isn’t just linked to position dependent inductance and to reluctance force (=the attraction between the coil and the iron parts), but that all three phenomena are actually one and the same thing. This insight has driven the design of PURIFI’s new motor which is virtually free from force factor modulation.
Additionally, the new motor allows FFM and BL(x) droop to be optimized independently. It wouldn’t help much to remove FFM and then to find distortion dominated by classical BL droop, so additional refinements were made that make the static BL(x) curve extremely flat over a large excursion range. The linearity of PURIFI’s motor is significantly better than what was historically possible with shortstroke designs.
With Force Factor Modulation comes a side order of Magnetic Hysteresis Distortion. If the magnetic flux in the gap varies with current, any iron in the gap will be subject to that varying flux. Magnetic hysteresis is quite different from saturation. Saturation is a fairly benign, soft-limiting type of distortion that happens at very large signal levels. Hysteresis by contrast happens at all signal levels and lends a grainy, hazy type of distortion to almost any transducer that contains iron. In terms of measurements, hysteresis distortion tends to dominate the midrange (well above resonance and below breakup) outright. Hysteresis distortion is worst in underhung drivers because of the sheer volume of iron surrounding the voice coil.
This explains the recent arrival of so-called “iron free” drivers. Such drivers do address the problem, but at enormous expense. PURIFI’s motor combines
the performance advantage of iron-free while retaining the economic and technical benefits of using iron to shape the magnetic circuit.

Surround Radiation Distortion

The surround is generally considered part of the suspension, and as such only its contribution to Kms(x) is noted. Its contribution to sound output is rarely noted. In modern (i.e. long-stroke) drive units the surround can easily make up 20% of the radiating surface. It would be optimistic in the extreme to expect that a piece of deforming rubber will end up radiating undistorted sound. Indeed, it does not – its distortion contribution exceeds that of the cone by orders of magnitude. Again the distortion is second order in nature and most obvious at low frequencies. But again that introduces intermodulation distortion affecting the entire frequency range of the driver. SRD is the second reason why large diameter, short stroke drivers have a leg-up. The surround simply takes up a smaller percentage of the moving area. Clearly though, that is only half a solution. The real solution lies in finding a design whose acoustical output is distortion free.
This is what PURIFI has done. Depending on the application PURIFI deploys differently shaped surrounds to neutralise SRD. The precise shape is determined by numerical optimisation, but the result is that across the full excursion range, the surround moves an amount of air that’s precisely proportional to excursion.


It is possible to build compact long-stroke matching or bettering the audio performance of short-stroke, large-area drivers. Doing so requires addressing two very specific distortion mechanisms: Force Factor Modulation and Surround Radiation Distortion. PURIFI’s drivers put these insights into practice.


Sep 29th, 2016

Force Factor Modulation in Electro Dynamic Loudspeakers

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The relationship between the non-linear phenomenon of ’reluctance force’ and the position dependency of the
voice coil inductance was established in 1949 by Cunningham, who called it ’magnetic attraction force’. This paper
revisits Cunningham’s analysis and expands it into a generalised form that includes the frequency dependency and
applies to coils with non-inductive (lossy) blocked impedance. The paper also demonstrates that Cunningham’s
force can be explained physically as a modulation of the force factor which again is directly linked to modulation
of the flux of the coil. A verification based on both experiments and simulations is presented along discussions of
the impact of force factor modulation for various motor topologies. Finally, it is shown that the popular L2R2 coil
impedance model does not correctly predict the force unless the new analysis is applied.