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Old 3rd May 2010, 09:14 PM   #41
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Amazing stuff, Steph!

I have to read my pspice book by Paul Tuinenga again!
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Old 3rd May 2010, 09:23 PM   #42
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Attached you will find the continuation of posts #30 and #39 about modelling a loudspeaker in fee air, using LTspiceIV.

I have followed bentoronto repeated advice "get a feedback signal and use it" instead of playing with equations and models for trying to synthezise the pure motional voltage.

Bentoronto method provides a very good result, especially when pre-equalizing the signal at the input. Thanks for opening our eyes, bentoronto !

In order this circuit to compute, you need all the subcircuit and symbol files posted on post #39.

P.S. 1
In a real circuit, the two coils located into the pre-equalizer need to be implemented using a gyrator, like we have in analog graphic equalizers.

P.S. 2
If somebody can suggest some spice directives enabling a faster .DC operating point calculation, that would be very welcome. As is, the .AC directive computes in 80 seconds. This is on the slow side when doing fine-tuning.

P.S. 3
I have not calculated nor measured the effective DC coil resistance suppression provided by this circuit. I have no idea if we are close to or above the 80% DC coil resistance suppression quoted in the Werner-Carell experimental work at RCA described in the AES paper dating back from Oct 1957. Later on, I'll try to embed a suppression percentage measurement in the schematic, as design help.

Cheers,
Steph
Attached Images
File Type: jpg Loudspeaker in free air - servo-sound equalized.jpg (292.2 KB, 227 views)
File Type: jpg Loudspeaker in free air - servo-sound equalized (Bode plot).jpg (74.5 KB, 217 views)
Attached Files
File Type: zip Servo-Sound.zip (205.7 KB, 48 views)
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Old 4th May 2010, 08:11 AM   #43
Elvee is offline Elvee  Belgium
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This is almost identical (conceptually) to the circuit I physically made and tested.
The amount of negative resistance can be computed easily: If G is the voltage gain seen from the shunt resistor Rs, then (-R)=(G-1)*Rs
I have convergence problems with your power amp sub, and I had to bypass it.
I deducted from the graphs its gain was about 27.5dB.
This means that (-R)~= (24/2.5-1)*0.33= 2.84 ohm.
This is about 72% of the coil resistance, which is OK without any compensation or precaution.
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Old 4th May 2010, 09:31 AM   #44
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Here you can see the behaviour when changing the value of the feedback resistor from 999k (almost no feedback) to 18k (exagerated feedback).

Note how different the output looks when going from 22k to 18k. Things are getting critical when the feedback resistor is less than 22k.

I don't know what is the optimal feedback resistor value. I would say between 27k and 22k. With such a value, the native 100 Hz resonance doesn't show anymore, and the 100 Hz to 700 Hz response tends to become a symmetric bandpass, something that won't be too difficult to pre-equalize.

Personnaly, empirically, I would use the following rule for determining the optimal practical feedback resistance : in case of a 3% error in the nominal feedback resistor (resistance tolerance, aging, coil DC resistance variation over temperature), I would allow a 2dB variation in the acoustic response.

Anyway, the acoustic response if not yet satisfactory. Pre-equalization is needed.

Obviously, if we use a feedback resistor in the range 27k to 22k, there is a 5th order correction needed :

- 2nd order for raising the amplitude between 40Hz and 100 Hz (steep pass-band boost)
- 2nd order for flattening the amplitude between 100 Hz and 1kHz (damped notch)
- 1st order for getting the 1kHz -> 10kHz response horizontal (kind of high-pass shelving)

This is the pre-correction strategy I've used in the previous post. I think that a 5th order pre-equalization scheme is an acceptable complexity in 2010.

Please note that it may be possible to reduce the complexity of the pre-equalizer, if one has access to the feedback network of the power amplifier. This is the situation we are facing inside a Korn-Macway (aka Servo-Sound) arrangement. I think that we'll still come up with 5th order correction, but splitted between the pre-equalization and the action chain. The overall complexity may thus decrease, like if the pre-equalizer is 3nd order, and the action chain is 2nd order. Need to investigate. Potential stability issues.

Anyway, now that we are playing with current sensing, optimal feedback adjustment and a 5th order equalization scheme, it may be time to see the kind of mechanical complexity and electronic complexity we may face when opting for a dedicated acceleration sensor like used in Philips Motional Feedback systems (MFB) RH541, RH544 and RH545. We shall remember that the accelerometer solution is superior in distorsion reduction, and less sensitive to temperature effects.

We also need to remember that any existing driver may be converted to a Philips MFB arrangement, glueing a small piezo transducer (like used in miniature buzzers) on top of the voice coil, under the dust cap.

For running the simulation files, you need the subcircuits and symbols provided in my previous posts.

Cheers,
Steph
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Old 4th May 2010, 10:37 AM   #45
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Please have a look to the attached pictures.

The circuit has not changed. The only change is that we are now zooming on 47k to 27k feedback resistors. The green curve is the one with the 999k resistor (say, no feedback). There you see how it is peaking, without feedback.

The 33k curve is remarkable. I missed it in the previous post. It provides a "straight top" acoustic response, however not horizontal. The "straight-top" feedback strategy may require less pre-equalization efforts :

- 2nd order for raising the amplitude between 40Hz and 100 Hz (steep pass-band boost) (like before)
- 1st order (actually, less than 1st order) for getting the 100 Hz -> 1kHz "straight top" horizontal
- 1st order for getting the 1kHz -> 10kHz response horizontal (kind of high-pass shelving) (like before)

We may thus say good-bye to a gyrator (that's one opamp less) and if there is some access to the feedback network of the power amplifier, the pre-equalizer may only consist on the 40 Hz to 100 Hz steep pass-band boost followed by a simple RC shelving arrangement for getting the "straight top" horizontal.

This being said,

1 - Before making more refined simulations, one must ask ourselves if there will be a tweeter used, and a crossover filter used. What is the effect of the feedback sensing the two currents together (woofer + tweeter) without being able to isolate the woofer current ?

2 - After having answered this, one must ask ourselves if it is a good idea to let the system feed the drivers with a reduced copper resistance, for frequencies above 1 kHz. Knowing that loudspeakers, and tweeters especially, see their sensitivity decreasing because of their coil inductance, I would say that above 1 kHz, we should change the feedback arrangement for increasing the virtual output resistance of the amplifier. Above 1 kHz, the coil inductance is not the sole ennemy. There may also be some short term variations in sensitivity like compression caused by thermal modulation. Driving the transducer using current (forcing a current into it instead of imposing a voltage on it) may add some other benefits, in this area.

For running the simulation files, you need the subcircuits and symbols provided in my previous posts.

It's quite funny, reinventing Thiele-Small and the amplifier-to-speaker interface ! Hope you enjoy like me.

With points 1 and 2 coming at the table now, we are not yet finished !

Cheers,
Steph
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Old 4th May 2010, 11:04 AM   #46
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I never realized you could have so much fun with numbers. I guess there may be some future to this modeling stuff (kidding... but my respect for Steph's deft handling of the simulation is sincere).

The question of choice of sensor is very important. For a long time, my impression has been that for small excursions, a quality driver's motor is pretty linear. Moreover, some of those non-linearities are zero'd away when used as feedback backwards, if you know what I mean.

In contrast to some cheap accelerometer glued to a paper dustcap.

Are cheap accelerometers really as linear as the motor in a good driver?
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Old 4th May 2010, 11:56 AM   #47
Elvee is offline Elvee  Belgium
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Quote:
Originally Posted by steph_tsf View Post

It's quite funny, reinventing Thiele-Small and the amplifier-to-speaker interface ! Hope you enjoy like me.
I certainly do.

Before proceeding, I think the numerical values of the speaker's parameters should be refined: I plotted the simulated speaker's impedance, and the resonance is obviously too sharp. It is probably necessary to increase the value of R2 in your model, but I don't have the expertise to give meaningful advice on this point.
If the data of an actual speaker could be found, it would be a good starting point.

Please, don't see my remark as a criticism, I think you do a fantastic job.
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File Type: jpg LSimpedance.JPG (109.3 KB, 55 views)
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Old 4th May 2010, 12:17 PM   #48
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hi bentoronto,

I guess we need a more elaborate feedback, still using the voice coil and no other sensor, for getting rid of the 5th order or 4th order pre-equalizer. What we want now is a feedback arrangement allowing us to get a flat horizontal acoustic response from 35 Hz to 8 kHz. What if we now introduce the concept of the feedback bridge for extracting the coil back EMF and use it as feedback ? Would it suit you now ? Or, are there important things we missed regarding the "pure negative resistance drive" approach ?

Cheers,
Steph
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Old 4th May 2010, 12:23 PM   #49
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Quote:
Originally Posted by Elvee View Post
I think the numerical values of the speaker's parameters should be refined: I plotted the simulated speaker's impedance, and the resonance is obviously too sharp.
I did it on purpose for pedagogic reasons. If you look to the compliance value, you'll also see that it is more representative of a closed box system, than a free air system where resonance is less pronounced. I wanted to see a clear contrast between open-loop and servo-driven. Starting with such parameters also makes quite obvious that we need a strong extension below 100 Hz. All in all, this "worst case" initial choice gives us some headroom : if we succeed with such data, then certainly we'll succeed with all possible drivers.

What kind of driver would you advise, that is well documented, decent, not expensive and available both in Europe, Canada and USA ? Here in Europe we have Visaton and Monacor as main affordable suppliers. What's the choice in Canada and in USA ? Okay for selecting one European driver and one USA driver, and making all the simulations with them starting from now.

Steph

Last edited by steph_tsf; 4th May 2010 at 12:37 PM.
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Old 4th May 2010, 06:23 PM   #50
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Here is a brief bridge feedback description, as simple as possible. The idea is to create a feedback signal that's more elaborate than just the current in the coil. The aim is to get a more useable acoustic response than the one we've got using the negative resistance drive arrangement. No more potato-shaped acoustic responses, and no more declining trend in the medium range, those are the objectives now.

1. The expedite bridge feedback

The voltage available at the shunt gets compared with another voltage created by an extra branch. That other branch is a static x 100 scaled copy of the immobile loudspeaker impedance. The 3.9 ohm copper of the coil becomes 390 ohm. The 200 microhenry coil inductance becomes 20 millihenry. The 0.33 ohm shunt becomes 33 ohm. In this x 100 scaled branch, there is of course no back EMF developing. That's the very important point.

The branch current, over there, is thus maximum, always more than 1/100 of the real loudspeaker current. The current is always more because in the x 100 scaled branch, there is no back EMF decreasing the overall voltage. Let's call this current the immobile speaker current.

An inexpensive way to extract something close to the back EMF is to compute the potential difference developing on each shunt. If the back EMF is considerable, like at speaker resonance, the real current and the immobile currents will be considerably different, and a considerable potential difference will exist between the two shunts. Such approach has the advantage of simplicity. Let us call this approach the expedite bridge feedback arrangement.

2. The accurate bridge feedback

How would you extract the back EMF, in a perfectly accurate manner ? There are not thousand different ways. Say there is a 0.33 ohm shunt measuring the current in the loudspeaker. There is thus a voltage developing, proportional to the coil current. Let us now multiply this current by the DC coil resistance plus the coil inductance. In a scaled manner. Like 1/1000th of the current in x100 impedances. Then we get an accurate image of the immobile voltage inside the loudspeaker. We know that the total voltage on the loudspeaker is the sum of the immobile voltage plus the back EMF. A simple difference amplifier can thus do the job, working on a 1/10 scaled down voltage. The difference amplifier delivers a voltage equal to 1/10th of the back EMF.

3. Driving at constant coil speed - the consequences

Anyway, being the expedite way or the accurate way, we realize that the loudspeaker current is still used as positive feedback (like in the negative resistance drive), but in a more elaborate way. This enables us to say that the bridge feedback approach is a negative resistance drive with more concern about the linearity of the acoustic response, because this time, we force the amplifier to drive the loudspeaker at constant back EMF.

But wait a minute ?
Isn't there an issue ?
In the bass range, with massive bridge feedback applied, we will drive the loudspeaker at constant back EMF. However, back EMF is proportional to the coil speed inside the loudspeaker. If you operate a loudspeaker at constant coil speed, knowing that constant SPL is constant coil acceleration, what kind of acoustic response will we get ?

Constant coil acceleration, determining a flat acoustic respoonse, is the derivative of constant coil speed. So, if you drive at constant coil speed, the acceleration (determining the acoustic response) is a 1st order increase with frequency.

We need to realize this before putting bridge feedback in action. Otherwise we'll get troubled by the results. In the bass range, the more we apply bridge feedback, the more the bass response will show as 1st order highpass ! The bridge feedback is thus eating the bass response.

Actually, this is a great feature because pre-equalization will simplify a lot. A 1st order bass boost may suffice, in theory, as pre-equalizer. The more bridge feedback we apply, the simpler the pre-equalizer may get, simplifying down to a 1st bass boost arrangement.

Cheers,
Steph
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