altering T/S parameters?

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Hi,
I want to alter the Q and Fs of a bass speaker to make it more suitable for sub-bass use.

If one adds mass to the cone to lower Fs, what other Thiel Small parameters change with the added mass. eg. No.(efficiency).
Please post formulae for these other changes?

If a series resistor is added to the driver to raise the Qts, do any other T/S parameters change?

Again formulae would help.
 
Hi,

It should be possible to change the TS parameters (especially Qes and Qts) of a dual voice coil driver by putting a variable resistor over one of the voice coils (only one voice coil is driven). This should allow changing parameters continuously; haven't got the equations, though :-(

Regards,
Dirk
 
adding cone mass will make a big difference to Vas. To make the VAS smaller you would have to tighten the suspension(maybe a DVC with the 2nd coil shorted togetheer would help?) Stiffening up the suspension will increase the fs again.

i would think halving fs(double mms) should square the Vas. The easiest way to play with this it to put a small magnet on each side of the cone and have them evenly distributed around the center.
 
Adding mass lowers Fs and increases Vas. By how much depends on the original cone mass. I think it's a square law in both cases.

Adding resistance raises Qes, thereby raising Qts. No other parameters change. I'm just going to try and find the link for how you can work out the change.

EDIT: here is the formula from Weems.

R = [(Qrequired / Qmeasured)Re] - Re
 
Hi all,
so far we have

added mass lowers Fs, increases Vas, raises Qm leading to raised Qts, increases BL,

Added resistance raises Re => Qe => Qts.

No change to BL,

Any more?

Richie thanks for the formula. You have confirmed the calc that comes out of Bullock.
 
There is a lot of incorrect information so far in this thread.
Most notably, adding mass does not change Vas or Bl at all.

Adding mass causes the following changes:
Because Cms=1/((2*pi*Fs)^2*Mmt)

Fsm/Fs=sqrt(Mmt/(Mmt+Madd))

Fs is the original resonant frequency
Fsm is the new Fs with added mass
Mmt is the original moving mass (including air load)
Madd is the amount of mass added.

Then:
Qes'=2*pi*Fsm*(Mmt+Madd)*Re/Bl^2
Qms'=2*pi*Fsm*(Mmt+Madd)/Rms

These can be simplified but I am lazy this AM.

Sensitivity is reduced by 20*log10(Mmt/(Mmt+Madd))

-------------------------

Adding series resistance increases Qes and reduces sensitivity by 20*log10(Re/(Re+Radd))

Qes'=Qes*(Re+Radd)/Re

Series resistance does not affect BL or Vas or anything but Qes (and of course Qts).

----------------------------------

I am sure I have posted all of this in the past, as well as the effects of shorting or resistively damping a dual voice coil woofer. Search for RDO (Resistively Damped Operation)
 
Hi AndrewT,

"Basic Acoustics" by Donald Hall discusses pretty much the theory behind loudspeaker drivers (in fact the book centers on loudspeakers and boxes). Although I don't have the book in my hands at the moment, I recall it has the formulas that would have answered your questions...

Cheers,

Clem
 
Hi,
there is an Re and Q in the formula, maybe they cancel out.
To confirm that, BL is a physical entity. B is the magnetic flux in the gap and L is the length of voice coil in the gap. So adding an extra external R to Re should have no effect.

My problem is that a large number of the T/S parameters don't have an easily visualised physical entity and the formulae inter-relating them do not obviously show when changed terms cancel out. Thus leading to my original post.
 
Mistaking the T/S parameters for fundamental parameters is a common mistake.

The parameters that really matter are
Sd, Mmt, Re, Bl, Cms

You can't change anything here except Mmt and Re without rewinding a coil or changing cone diameter, etc....

Bl is the length of wire inside the gap multiplied by the magnetic field strength. This doesn't change unless you change magnets (or add a bucking magnet). This is changeable in a DVC driver....

Cms is the stiffness of the suspension, which doesn't change no matter how much mass you add.

Remember, T/S params are measured at very low excursions.
 
Yes, it is true that B and l do not change with added series resistance, but it is well known that damping changes (this is analogous to amplifier damping factor) and this is because Qe is calculated assuming a zero source impedance.

The force produced by the motor is give by Bli(t) where i(t) is the current, i(t) is lower for a given input voltage when series resistance is added, and therefore adding resistance is like having a weaker motor, effective Qe goes up, system efficiency and voltage sensitivity go down, etc.

It was mentioned that Vas changes with changes in mass. This is not true, Vas is simply the suspension compliance, expressed as the volume of air having the same compliance.

The Q's change with mass change because the free air resonance changes. The value of the mass and spring reactance at resonance changes and since Q is reactance over resistance (resistance obviously constant with f) the Q's change. Remember that Fs is inverse square law with changes in mass and compliance, and efficiency goes down as 3rd order with increased mass, IIRC.

Pete B.



AndrewT said:
Hi,
there is an Re and Q in the formula, maybe they cancel out.
To confirm that, BL is a physical entity. B is the magnetic flux in the gap and L is the length of voice coil in the gap. So adding an extra external R to Re should have no effect.

My problem is that a large number of the T/S parameters don't have an easily visualised physical entity and the formulae inter-relating them do not obviously show when changed terms cancel out. Thus leading to my original post.
 
Ok, here we go:

-Increasing Mms lowers fs, increases Qes (and Qts) and lowers efficiency.
-Adding a series resistance increases Qes (and Qts), and lowers efficiency.

Neither of them modify Vas or Bl. Vas is essentially a way of expressing the compliance of the cone suspension;
Cms=Vas/(rho0*c^2*Sd^2), neither of Re or Mms is in that equation.
Bl is the motor strength, "how many newtons of force do I get for an ampere of current through the voice coil". That does not change for increased Re or Mms. It is true that
BL = SQRT((2 * PI * Fs * Re * Mms) / Qes)
but Mms/Qes remains constant if Mms is changed. And if Re is changed (by a series resistance) Re/Qes remains constant.

Hope that clarified some... ;)

If one wants to change the mechanical parameters by electrical means Audio Pro's ACE (or Yamaha's YST) is the way to go. With that technology, both the apparent mass, compliance and resistive loss can be altered, or if you wish fs, Qts and Vas.
 
Svante said:
Ok, here we go:

-Increasing Mms lowers fs, increases Qes (and Qts) and lowers efficiency.
-Adding a series resistance increases Qes (and Qts), and lowers efficiency.

Neither of them modify Vas or Bl. Vas is essentially a way of expressing the compliance of the cone suspension;
Cms=Vas/(rho0*c^2*Sd^2), neither of Re or Mms is in that equation.
Bl is the motor strength, "how many newtons of force do I get for an ampere of current through the voice coil". That does not change for increased Re or Mms. It is true that
BL = SQRT((2 * PI * Fs * Re * Mms) / Qes)
but Mms/Qes remains constant if Mms is changed. And if Re is changed (by a series resistance) Re/Qes remains constant.

Hope that clarified some... ;)



I will agree with the parts that I can check. I was using Bass Box Pro and the auto calculate of other parameters but your added Mms definition works. Where did you get your formula's from? I would like more to try to make a "better" speaker or at least a better simulation:D
 
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