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Driver operation & E-mails

Posted by tomservo on September 12, 2003 at 09:52:06:
Hi Wayne
You sound sincere so I will explain again about acoustic phase, please read this all carefully before rejecting it.
Several data points:
For anything traveling in a sine wave motion, the velocity and acceleration are always 90 degrees apart.
Sound power radiated from a small point source is proportional to its Volume Velocity (Ud)
For a radiator, which is less than about Â¼ wl in diameter, it feels a radiation resistance which changes with frequency. That is when the frequency increases, it radiates increasing sound power with a fixed radiator Velocity.
In this case, a constant velocity radiator produces a +6 dB /oct rising frequency response.
A highly loaded horn on the other hand presents the radiator with a constant resistance, which is a significant magnitude. Being a resistance, the power radiated is proportional to radiator velocity (voltage). In this case, a constant velocity produces a constant power.
This need for a constant velocity is why horn drivers typically have so much more motor strength per radiator area than a direct radiator has
Unlike electrical analogues used in equivalent circuit models (and the reason they may not be â€œexactlyâ€ right modeling a loudspeaker) , this â€œfrequency variableâ€ radiation resistance is a changing resistance without the corresponding phase shift that reactive components provide when an amplitude is changing. Hence, electrical models which are used to approximate this action can include a phase shift which the real acoustic property does not have.
To make the output of a small point source flat, the changing radiation resistance must be compensated for, so the acoustic pressure is constant.
An alternative way of saying this is that the radiator velocity must fall with increasing frequency in order to deliver a constant power into a changing resistance.

For an electrodynamic motor such as a VC motor in a loudspeaker or even a DC servomotor, the force per amp and back EMF are always exactly related.
In the rotary motor, the force factor is Kt or torque per amp with Kv being the voltage constant, in the VC motor is it BL (Newtons of force per Amp) and Voltage constant is un specified in the loudspeaker case.
In order for the acoustically small radiator to have flat frequency response (in the face of a changing radiation resistance), it must have a Velocity which FALLS at a rate which compliments the change in radiation resistance as above..
This fall off or slope is produced by the drivers moving mass which is reflected through the motor as a capacitance which is in series with the Rdc.
This part is what the technical references I gave you in a previous post are talking about and is what they mean by â€œmass controlledâ€.
This R / C forms a 1 pole low pass filter whoâ€™s corner F is the low cutoff of the speaker.
The speaker operates on the sloped part of the velocity curve not on the flat part.

A real speaker:
Taking the simplest case, a sealed box, one can follow how the speaker works and why.
Starting way below box resonance, one has a spring dominated system, it is the compliance which governs the motion and when a fixed voltage is presented, the motion of the radiator is constant with frequency.
This is because a fixed voltage produces a fixed current across the Rdc, the fixed current produces a fixed radiator force on the spring and so a fixed displacement results.
This produces an acoustic output, which decreases at 12 dB per octave with decreasing F.
Looking at the drive currentâ€™s phase, one can see that is leads the voltage.
Measuring or modeling a sealed box below cutoff, one can see the output falls 12 dB /oct AND the excursion or displacement is constant with decreasing F.
At a higher F, at Fb, the spring and mass are equal but opposite reactanceâ€™s. , they form a parallel tank L/C/R tank circuit which at resonance, one seeâ€™s is a resistive impedance which represents the Rdc in series with the acoustic load paralleled with the mechanical losses, L and C.
For a direct radiaor, this is a high value as the acoustic load is insignificant and mechanical losses typically are fairly low (a high parallel R).
Those quantities are factored by the motor strength with a more sensitive motor (force per amp) producing a higher impedance value with a broader curve for a given set of physical properties..
Above Fb, the spring has a decreasing influence and the mass becomes the dominant controlling element (the effect described in the technical references a few posts back).
In this range the radiator Velocity is falling 6 dB per octave due to the Rdc / mass (R / C) filter needed to off set the radiation resistance.
If one plotted radiator velocity (its â€œVoltageâ€) vs frequency, one would see that at say 1 Hz the impedance is Rdc, then it increases at about 6 dB per octave to a maximum at Fb, then above Fb, it decreases at 6 dB per octave.
Remember that it is the range when the velocity is falling 6 dB per octave that the acoustic output is flat.
This falling velocity is the result of being now an R / C (Rdc / reflected moving mass) and that filter which causes the fall off HAS a nominal â€“90 degree phase shift above Fb.
AS the frequency in increase further, the secondary element begins to play a part, this is the series inductance.
This L is in series with the mass â€œCâ€ and as the frequency increases the phase is shifted towards 0, at some frequency, these are equal but opposite reactanceâ€™s and cancel out.
Now the impedance is at resistive minimum being the Rdc in series with the acoustic load which is a small R.
Above Rmin, the impedance goes positive again, well above Rmin, it is nominally +90 degrees.
Above this point, radiator geometry and a host of other effects begin to show up adding more phase shift.

Because back EMF and force per AMP are precisely linked, it has been possible to derive the radiator motion from the impedance by electronically removing the component of it proportional to the voltage across the Rdc which is proportional to current.
Once the Rdc drop is removed, one can determine the motor Velocity (as it is exactly proportional to Voltage through its Voltage constant) and / or the force or current through the Force constant (BL in the speaker).
In motor control it is common to use a negative output impedance to produce a much better velocity control than open loop because by electronically removing the Rdc, one has a direct connection to the part whoâ€™s velocity is exactly proportional to Voltage.
Conversely, when torque control is required, then the current is what is controlled.
Alternatively, since a mass controlled system is also a constant acceleration system (constant force against constant mass equals constant acceleration), one can use an accelerometer on the radiator and use its output as a feed back signal for an amplifier to correct from.
This feedback can pertly overcome the compliance corner, pushing the response downward and since it is acceleration, also can partly correct for motor nonlinearities.

Please before rejecting all this, look into it further, while it may not be the way your used to seeing it, it is the way they work and Iâ€™m not pulling your leg..

So far as your e-mails, the only one I got was the one I posted, the ones that Pat got at work were the ones, which caused the issue.
I had received a call from her saying â€œwho is Wayne and why is he so mad and threatening us with legal action ?â€.
Then I got one from Brad saying to stay off A.A until Mike has a chance to look at the letters, it took him a couple days to get to it I guess. His assessment ultimately was there was no real threat and Brad said it was OK to go back on A.A.. The Lawyer however also suggested it might make better business sense to be more secretive about how things work etc.
You do sound genuine here as well, I left a message with Pat to find the e-mails she sent to Mike to look at.
Depending which comes first (the mail server being up and running again today or not) I have to go to the shop Monday or Tuesday anyway, I will get the e-mails from Pat and post them.
Tom