CHANGED TITLE: TS parameters and how physical changes alter them

[John D]

I read Dickason's book about loudspeaker design. In one chapter he describes how physical changes affect TS parameters and make the driver more suitable for a particular concept (BR, CB, TL etc.). However, still some of my questions have not been fully answered.

- What means are at hand to lower the fs of a driver?
- Which physical changes affect Qms and Qes?
- How are Qts and fs related to VAS?
- Why are high BL en low Qts regarded as being a good thing, while higher values of Qts enable lower bass? Low damping is said to be bad, but isn't quality bass about frequency response and distortion?

I'm sure a couple of you guys understand the mechanisms at work here. Please shed some light ;x( .

[servicetech]

Zaph recently did an article regarding xmax on woofers, well worth the read:

http://www.zaphaudio.com/lowxmax.html

Generally what I've found is the smaller the box a woofer is designed to go in the most expensive and less efficient it is.

[John D]

Zaph recently did an article regarding xmax on woofers, well worth the read:

http://www.zaphaudio.com/lowxmax.html

Generally what I've found is the smaller the box a woofer is designed to go in the most expensive and less efficient it is.

I've read that article before. It has been on his site for quite a while already.
However, this article doesn't actually answer my questions.

Thanks anyway

[Dennis H]

http://en.wikipedia.org/wiki/Thiele/Small shows how to calculate Fs, Qms, Qes and Vas.

About high Qts drivers, they need huge boxes to work well. In practice a sub with a slightly drooping low end response will sound best in a room because of room/boundary gain. And room effects are so huge that almost everyone uses an EQ with a sub anyway.

Try ISD Online to get a quick feel for what changing things does. It's quicker to use than WinISD or Unibox because you only need to enter 3 numbers to describe the driver.

http://www.linearteam.dk/default.aspx?pageid=newdriver (requires Java)

[rc white]

The best way to illustrate this is to look at the relationships between T-S parameters and physical parameters..

Vas = poC^2 Cms Sd^2

Qts = (Mms/Cms)^.5 1/Rmt

Fs = 1/(2pi(Mms Cms0^.5)

Rmt = Rms + [(BL)^2/(Rs + Rvc)]

You can lower fs by increasing moving mass or Vas, high moving mass = low efficiency, high Vas = big box

compliance, Cms is implicated in both fs and Qts and Vas, the larger its value the larger Vas, smaller Qts and lower Fs., Qts and Vas are related by this.

If we want to design a sealed box for instance, Small showed that the optimum sealed box has a volume = Vas/ 3 in which f3 = 2fs And Qt = 2Qts, the practical lower limit to fs is around 20Hz. so f3 = 40Hz. and Qts = .354. for Qt = .707, the volume then depends upon efficiency, Vilchurs original AR-1 had an f3 of 43Hz. and efficiency was around 92db. for a 60 litre box.
From this we need a driver with fs = 20Hz., Qts = .354, and Vas = 180 litres
What the driver parameters are depend upon what you are trying to do and this is still a common spec. for drivers since it is a good spec. for a 30Hz. reflex alignment as well as a 40Hz. sealed one.

There is a lot of nonsense talked in the audio press about damping, except for a small region near its fundamental resonance the amplifier has no control at all over driver damping because a moving coil driver is an inherently unstable device.
Most of the other things such as distortion and excursion are entirely dependent upon the manufacturer and cannot be deduced from T-S parameters.
High BL and low Qts are good if you want maximum output for sound reinforcement etc. low Qts drivers are often supplied with a high output impedance to improve ther bass output, (Rs in the expression for Rmt).

[John D]

Thanks,

I'm still trying to see the bigger picture, and your explanations helped, RC.
Dennis linked to wikipedia. I had looked at the wikipedia site before, but I couldn't understand anything of it. It went easier this time.
I tried to do some simple calculations and for that I used the BMS 18N850 I've got in my subwoofers.



Cms = mm/N 0.140 or 0,00014 m/N
Mms = 0,303 kg

fs = 1 / (2pi (0.00014 * 0,303) ^.5) = 24.44 hz

Hey! That worked 8) !

Resonance frequency Fs Hz 24.4

So, to decrease fs, you either increase the mass of the system, or make the suspension lossier. That makes sense.




ρ is the density of air (1.184 kg/m3 at 25°C), and c is the speed of sound (346.1 m/s at 25°C).
To get Vas in litres, multiply the result of the equation by 1000.

Allright.
Sd = 0.1212 squared metres
Cms = mm/N 0.140 or 0,00014 m/N

Vas = 1,184 * 346,1^2 * 0,1212^2 * 0,00014 = 0.29167

That makes 291,67 liters

Equivalent volume Vas L 288

Ok, that's close enough.

So, bigger cones move more are, and thus Vas is higher for bigger cones.
Cones with lossy suspensions are easier to move, just as a larger amount of air is easier te compress. So high compliance leads to a larger equivalent volume and thus to higher Vas.

There's one thing I still don't understand:

Cms - Compliance of the driver's suspension, in metres per newton (the reciprocal of its 'stiffness').
Rms - The mechanical resistance of a driver's suspension (ie, 'lossiness') in N·s/m

What are the difference and similarity between these two. Can they be calculated into one another? To me, it seems like they tell me about the same thing, but that probably isn't true.
Anyone?

[John D]

After some further reading on the wikipedia page a couple of questions rose:

Measurement notes - large signal behavior
Some caution is required in measuring and interpreting T/S parameters. It is important to understand that the T/S parameters are linearized small signal values. An analysis based on them is an idealized view of driver behavior, since the actual values of these parameters varies with drive level. Cms increases the farther the coil moves from rest. Bl is generally maximum at rest, and drops as the voice coil approaches Xmax. Re increases as the coil heats and the value will typically double by 270 °C, a point at which many voice coils are approaching (or have already reached) thermal failure.

As a demonstrative example, Fs and Vas may vary considerably with input level, due to nonlinear changes in Cms. A typical 110 mm diameter full-range driver with an Fs of 95 Hz at 0.5 V signal level, might drop to 64 Hz when fed a 5 V input. A driver with a measured Vas of 7 L at 0.5 V, may show a Vas increase to 13 L when tested at 4 V. Qms is typically stable ±2%, regardless of drive level, but Qes and Qts drop >13% as the signal level rises from 0.5 V to 4 V, due to the changes in Bl. Because Vas may rise substantially (eg, >80%) and Fs drop considerably (eg, >30%), with only 3% change in measured Mms, the calculated sensitivity (η0) can drop by >30% as the test signal level changes from 0.5 V to 4 V. Of course, the driver's actual sensitivity has not changed at all, only a modeling variable shorthand for it. This example shows that the measurement voltage to be preferred whilst designing an enclosure or system is the one likely to represent typical operating conditions.

The result of most of these level-dependent nonlinearities is distortion and lower than predicted output. The level shifts caused by these nonlinearities are often collectively called power compression. Design techniques which reduce nonlinearities will generally reduce both power compression and distortion. Sophisticated magnet or coil designs attempt to linearize Bl and reduce the value and modulation of Le. Larger, more linear spiders can increase the linear range of Cms, but the large signal values of Bl and Cms must be balanced to avoid a phenomenon called dynamic offset.

"Cms increases the farther the coil moves from rest"

Is this true? I'd reckon it to be the other way around. When the cone moves away from rest, there will be more stress on the spider. Won't this lead to a lower compliance?

By this rationale the fs would not decrease, but rather increase.


"Qms is typically stable ±2%, regardless of drive level, but Qes and Qts drop >13% as the signal level rises from 0.5 V to 4 V, due to the changes in Bl. "

When the cone moves out of its rest, the Bl would drop. As Bl drops, the Qes should increase. Am I missing something here?

[Dennis H]

I think the equations in the wiki are correct but I agree that some of the author's conclusions don't make sense mathematically.

PS: I just fixed a goof where I said increase when I meant decrease. I'll bet the author did some of that too. Whoever he is, he does seem to understand how drivers work.

About Cms and Rms, think of Cms as a car's spring and Rms as the shock absorber.

"Cms increases the farther the coil moves from rest"

Is this true? I'd reckon it to be the other way around. When the cone moves away from rest, there will be more stress on the spider. Won't this lead to a lower compliance?

I agree. The spider's stiffness increases off center so the compliance (Cms) is less.

By this rationale the fs would not decrease, but rather increase.

I agree again.

"Qms is typically stable ±2%, regardless of drive level, but Qes and Qts drop >13% as the signal level rises from 0.5 V to 4 V, due to the changes in Bl. "

When the cone moves out of its rest, the Bl would drop. As Bl drops, the Qes should increase. Am I missing something here?

I agree again. Also the decrease in Cms would cause both Qes and Qms to increase. And his numbers don't mean much as they totally depend on the design of the specific driver. 4V on a heavy sub would hardly move it.

The changes in Q with excursion are really quite academic. The important thing is that distortion goes way up with excursion due to changes in Bl, Le and Cms. Which one of those dominates will depend on the driver. 10% distortion is pretty common at the published Xmax so you want to keep the excursion well below there. And, if you keep the excursion low enough to avoid distortion, the Q values aren't going to change much.

[John D]

Dennis,

Thanks for your reply. I'm happy you agree with me on the points I mentioned: then I DO understand!

I About Cms and Rms, think of Cms as a car's spring and Rms as the shock absorber.

Could you elaborate a bit on the part I qouted, though?

This is what the wiki says:

Rms
Units are not usually given for this parameter, but it is in mechanical 'ohms'. Rms is a measurement of the losses, or damping, in a driver's suspension and moving system. It is the main factor in determining Qms. Rms is influenced by suspension topology, materials, and by the voice coil former (bobbin) material.

Cms
Measured in metres per newton (m/N). Describes the compliance (ie, the inverse of stiffness) of the suspension. The more compliant a suspension system is, the lower its stiffness, so the higher the Vas will be.

I am now beginning to see the bigger picture here, but this is still one of the blind spots. I am sure Rms and Cms must be somehow related, but I haven't been able to find any explaining formulas yet.

The way I see it now Rms is the mechanical resistance to cone movement, while Cms tells us something similar: how far the cone moves when it encounters a force of one newton. This means Cms would have to be related to a restoring force, or resistance to movement.
Rms then again depends on the size of the driver. I'm not sure how exactly, though.

[Dennis H]

I'm not sure how to explain it any better than the mental image of the car shock + spring.

Smaller Cms = stiffer spring. A spring resists any movement away from center and restores to center when the electrical signal is removed.

Bigger Rms = bigger shock absorber. A shock provides damping (friction) of movement in any direction and has more effect on fast movement than slow movement.

[John D]

Ok, that makes sense.

That is why Rms is also dependent on the Sd of the driver: a bigger driver moves more air and the air poses a resistance to movement. Rms is about friction losses and Cms is about springiness, not accounting for any losses.

I don't mean to be a pain in the @$$, but do you have some formula's 8) ?

[cjd]

A spring rate (this includes surround and spider compliance) is not necessarily a progressive rate - it can be linear.

C

[Dennis H]

but do you have some formula's

Nope, I had to google to find that wikipedia page.

I think, in practice, Rms is calculated backward from Qms which can be measured with the impedance curve. If you want to get into the heavy math of calculating stuff from the impedance curve, the author of LIMP (impedance companion to ARTA) is very fond of math in his manuals. Have fun.

http://www.fesb.hr/~mateljan/arta/download.htm

[Dennis H]

A spring rate (this includes surround and spider compliance) is not necessarily a progressive rate - it can be linear.

C

If I understand you, by linear you mean the force to move 10mm off center is twice that to move 5mm. I think they mostly shoot for that but the suspension becomes nonlinear as you move toward the end of its travel and the cone doesn't move as far as you'd think it should so you get distortion.

[Xander]

About Cms and Rms, think of Cms as a car's spring and Rms as the shock absorber.

I'm in an electronic control systems class, and we're learning quite a bit that I can actually relate to speakers and amplifiers. Kind of interesting. It's hard stuff, but at least I have some interest.

I'm going to attempt to explain this a bit to see if I actually learned anything...

Like already stated, Cms is rated like a spring and Rms is rated like a damper. This is a very common system called a mass spring damper system that can be modeled a variety of ways.

One way to model is is with a physical object. Imagine a cart on wheels (frictionless...). It is attached to a wall with both a spring and a damper. Now there is a force pushing on the cart. When the force lets go, the spring and damper act together to settle the system back to neutral. A system is generally classified as underdamped, critically camped, or overdamped. You usually shoot for a critically damped system which has a quick return to neutral without any overshoot. An underdamped system will have a lot of overshoot and will wobble back and forth before returning to neutral. An overdamped system will take a looong time to return to neutral (too much damping).

You can also model it with an RC circuit, or an LCR circuit. but I have to go to class now...

[rc white]

Rms

Rms is the acoustic resistance of the suspension, this contains a resistance component that is multiplied by Sd^2 to get mechanical Ohms. In well designed woofers the Sd^2 term predominates and Rms has only to do with details of construction although there may be a relationship to Cms because of the materials being used.

As I posted before the major damping resistance in the system comes from the motor, this is the (BL)^2/(Rg + Rs) term in the expression for Rmt.

Mms, Cms and Rmt do represent the mass spring and damping of a damped mass and spring system and the acoustic output over its piston range represent solutions to the quadratic form equation that describes these systems if the rear radiation cannot effect the front radiation, i.e. the baffle is infinite, (a mass spring system in inherently second order).

The quadratic form equation can be put..

ax'' + bx' +c = f(y)

In this the coefficients can be replaced by electro acoustic analogue coefficients and the differential operators replaced by "s"

This gives the familiar critically damped Butterworth solution.

s^2 + s 2^.5 + 1

The constant group delay Bessel Thomson

s^2 + s 3^.5 + 1 etc.

Each of the terms containing s have a coefficient that can be derived from the T-S parameters of the driver, that is basically what Thiele and Small did, provided us with an easy way to solve this equation, in the reflex case two coupled resonant systems.
rcw

[stinems]

This may or may not be relevant, but here is a trick I find intriguing...

Sometimes you WANT your driver to have a higher Qts, like in the case of dipoles, or you want to up the resultant Qtc of your sealed box alignment without changing the box itself. If you're willing to give up some sensitivity, a 1 or 2 ohm resister (more in parallel for power handling) can be applied in series with the woofer to simulate a higher Qts. If I understand it correctly, doing this tweaks the electrical Q of the driver, and in RC Whites's equations above you would probably add the series resistance to the "Rs" term.

Sam

[Xander]

Rms is the acoustic resistance of the suspension, this contains a resistance component that is multiplied by Sd^2 to get mechanical Ohms. In well designed woofers the Sd^2 term predominates and Rms has only to do with details of construction although there may be a relationship to Cms because of the materials being used.

As I posted before the major damping resistance in the system comes from the motor, this is the (BL)^2/(Rg + Rs) term in the expression for Rmt.

Mms, Cms and Rmt do represent the mass spring and damping of a damped mass and spring system and the acoustic output over its piston range represent solutions to the quadratic form equation that describes these systems if the rear radiation cannot effect the front radiation, i.e. the baffle is infinite, (a mass spring system in inherently second order).

The quadratic form equation can be put..

ax'' + bx' +c = f(y)

In this the coefficients can be replaced by electro acoustic analogue coefficients and the differential operators replaced by "s"

This gives the familiar critically damped Butterworth solution.

s^2 + s 2^.5 + 1

The constant group delay Bessel Thomson

s^2 + s 3^.5 + 1 etc.

Each of the terms containing s have a coefficient that can be derived from the T-S parameters of the driver, that is basically what Thiele and Small did, provided us with an easy way to solve this equation, in the reflex case two coupled resonant systems.
rcw

Thanks for that description, it's a bit of a different way to look at it.

[rc white]

out put impedance

This is a link to an article at ESP that has details of how to increase amplifier output impedance withought power loss..

http://sound.westhost.com/articles/cscaling.htm