Subwoofer feedback topologies

[SSassen]

As some of you know, see my other topic in the Class-D forum, I've embarked on another subwoofer project. This one however will be a no-holds-barred approach and hence I'm using the Adire Tumult 15D4 woofer in the design.

In order to have maximum control over the response curve, THD and excursion I'll be using feedback from the actual woofer. The obvious approach is to mount a piezo or MEMS accelerometer onto the woofer cone and put that in the feedback loop for the amplifier. I've been calculating the requirements for such a device and asked for feedback from Dan Wiggins at Adire and he commented there's another, potentially more interesting, relation that could make for a simpeler yet just as effective approach.

I'm however not 100% sure how to approach this so thought I'd post a few questions here to see how my fellow DIY-ers would approach this or whether anybody has any good suggestions. But let's first look at the maximum g force generated by the woofer, and then go from there.

The position of the cone with respect to time, assuming sine wave stimulus, is:

X(t) = Xpk sin(w t)

Xpk obviously is the peak excursion (not peak-to-peak, so it's 33mm here), w
is 2 pi f, and t is time.

The velocity is the first derivative of this:

V(t) = w Xpk cos(w t)

and acceleration is the second derivative of excursion:

A(t) = w^2 Xpk -sin(w t)

Maximum acceleration occurs when -sin(w t) is either 1 or -1, thus we are
left with the maximum acceleration being:

A(max) = w^2 Xpk

Let's assume the system has its largest Xpk at 20 Hz,

w = 2 pi 20 Hz
w = 125.6/s

and thus w^2 is:

w^2 = 15775/s^2

and since Xpk = 33mm, or 0.033m, then:

Apk = 0.033m * 15575/s^2
Apk = 514 m/s^2

and since g = 9.8 m/s^2, then:

Apk = 52 G

Dan commented that acceleration is also given by current times BL divided by mass (BL * i / m). So monitoring the current into the voice coil, as long as you have a constant BL and m, will give you acceleration. This got me thinking that in order to make this work all I'd need to do is to design a voltage controlled current source of sufficient power to drive the woofer and it will automatically flatten the curve, lower THD and keep excursion within acceptable limits.

My question obviously is how to approach this from the amplifier end, do I use a low-resistance sensing resistor in series with the woofer? Or something else? How exactly would I design a voltage controlled current source around the woofer? Anybody got any suggestions? Or a few pointers maybe?

Best regards,

Sander Sassen
http://www.hardwareanalysis.com

[Mr Evil]

Current amplifiers like you describe are occasionally seen. As you have calculated, they do eliminate some sources of distortion (because force is proportional to current), but not as much as much as proper motional feedback.

One problem is that you lose all electrical damping, which raises the overall system Q by a lot. On the plus side you don't have the stability problems of MFB.

You would implement this the same as a normal current feedback amplifier: by taking feeback from a small current-sensing resistor in series with the speaker. You can also mix current and voltage feedback to achieve a specific finite output impedance, mixing the properties of both, allowing control of Q.

[darkfenriz]

Originally posted by SSassen

Dan commented that acceleration is also given by current times BL divided by mass (BL * i / m). So monitoring the current into the voice coil, as long as you have a constant BL and m, will give you acceleration. This got me thinking that in order to make this work all I'd need to do is to design a voltage controlled current source of sufficient power to drive the woofer and it will automatically flatten the curve, lower THD and keep excursion within acceptable limits.

I think it is not true.
Or only a half of truth.

acceleration=force/m=Bl*i/m
is an inertia of the cone, but other phenomenons occuring are:

resilience:
force(t)=Bl*i(t)=-(1/Cm) *x(t)
where Cm is a Thiel-Small parameter of stiffnes of a membrane

friction
force(t)=-b*V(t)

where b is constant

move of the cone is a superposition of these principles

best regards

[SSassen]

Darkfenriz,

Thanks for the reply, but didn't you just give me a half answer

Best regards,

Sander Sassen
http://www.hardwareanalysis.com

[darkfenriz]

well, probably I did.
and the conclusion is:
I will insist that the best way to drive a speaker is voltage source, because as long as Bl is constant the voltage is proportional to coil's velocity. And velocity is propotional to acoustic pressure as long as adiabatic thermodynamic process is linear.
With current source you produce force, which may be 'wasted' on resilience, inertia and friction depending on mechanical parameters.
Remember that pressure is what we actually hear and mechanical velocity is the result we want, not the fact that speaker 'did its best' and wasted much force on it.
Problems like temperature-induced compression aren't that crucial in my point of view so no real pros for current source.
hope I didn't make any brainfart here.
end_of_second_half
regards

[SSassen]

Darkfenriz et al,

I’ve given the current sensing subwoofer feedback idea some more thought and came to the conclusion that current sensing is not the way to do it. Why? Simply because what we try to accomplish is to create an ideal loudspeaker which has a superconducting voicecoil, hence can be controlled exactly by changing the voltage across the voicecoil. In this case speed is directly proportional to the voltage applied.

In our case speed is only directly proportional to the voltage applied when BL is indeed fixed, but in reality it isn’t. When the woofer is pushed hard part of the voicecoil will leave the linear part of the magnetic field and hence BL changes. This will reduce the feedback voltage of the current sensing resistor we’ve opted to use, hence the amplifier will push even harder effectively forcing the cone further out of the magnetic field. Hence distortion increases and we’re quickly approaching Xmax. Obviously this is not the way to go.

So how about the accelerometer approach? The output voltage of an accelerometer is the derative of speed and hence below the frequency where its wavelength is smaller than he cone diameter there’s a linear relation between sound pressure and speed. Because we’re using a 15” woofer that frequency is upwards of 400Hz, and we'll only be operating it to about 120Hz, hence we’re well within the limit. So acceleration will be our feedback signal. So what we’ll then end up with is that the acceleration will be tracking the input voltage of the amplifier. The only thing we should watch out for is that for very low frequencies the cone will have very large excursion, hence a high-pass filter (+/- 10Hz) should be used to limit excessive excursion at sub-sonic frequencies.

Any suggestions? Did I miss anything?

Best regards,

Sander Sassen
http://www.hardwareanalysis.com

[darkfenriz]

hmm...
I don't understand your point.
A signal from accelerometer is derative of velocity abd thus derative of ouput voltege, so you need to integrate the accelerometer (e.g. with first order lowpass). Putting a differetialamplifier into feedbackloop isn't a good idea
what do I miss?
regards

[Pigale]

Hi,

Have you ever heard of the 3a Triphonic 1200 subwoofer? It used a microphone to "listen" to the outcoming signal from the four 11'' loudspeakers and then compared it with the incoming signal from the source. Of course, it had its own servo amp of some 150 WRMS which was fed with the resulting signal. An active crossover system separated frequencies above 120 Hz to send them to full range speakers. One of the advantages of this design was the size of the enclosure used. Because of the very nature of the servo system, size was kept to a minimum, something like a 0.8 cubic foot enclosure and distorsion figure was very low.

This system was designed in the early '70 and never really caught up with the market for pricing reasons and maybe because the market was not yet ready to accept it. We have to remember that in those days, bass this low (we're talking 20 hertz here) was more a source of distorsion than of music for the turntables, tonearms, cartridges and amps of this era. But still, this technology should still be considered today as it is very actual and seems to be suitable for your project.

[dblab]

Hi,
I know a system that use the topology you said;
it's Subsonice Manger. For us it's very "fast and clean".
A microphone is directly mounted on the diafram (10"Vifa) and it's in the feedback of the internal amplifier.
Best Regards

[megajocke]

Originally posted by darkfenriz
well, probably I did.
and the conclusion is:
I will insist that the best way to drive a speaker is voltage source, because as long as Bl is constant the voltage is proportional to coil's velocity. And velocity is propotional to acoustic pressure as long as adiabatic thermodynamic process is linear.
With current source you produce force, which may be 'wasted' on resilience, inertia and friction depending on mechanical parameters.
Remember that pressure is what we actually hear and mechanical velocity is the result we want, not the fact that speaker 'did its best' and wasted much force on it.
Problems like temperature-induced compression aren't that crucial in my point of view so no real pros for current source.
hope I didn't make any brainfart here.
end_of_second_half
regards

Actually, no. Acoustic pressure is proportional to acceleration below a frequency proportional to the circumference of the cone. Thats why you need 4x (12db) more excursion when you go down an octave for the same SPL. The inertia of the cone nicely cancels out this above resonance when driven by a current source.

The voltage over the "motor" part of the circuit is miniscule compared to the voltage over the voice coil resistance and inductance above the resonance of the driver so the "motor" is driven by an approximation of a current source.

Increasing the motor strength or lowering the dc resistance would give a lower Qes which makes the response above resonance rise. If you could make Qes = 0 the response of the driver would be rising with 6dB/octave because the velocity is the same at all frequencies.

As I have understood it, the advantage of using current drive is that the effects of inductance and inductance modulation are canceled out. 3rd order distortion created by eddy currents is also canceled out. (Not totally sure it was eddy currents though)

The disadvantage is that the Qts becomes Qms = very high. Huuuge peak at resonance. Has anyone tried lowering it back with a damping basket? (damping material compressed against the back of the basket)

This stuff is something i read in an old post by Kuei Yang Wang who seems to be very knowledgeable in the area. The theories do make an awful lot of sense!

/Joakim