Air-spring non-linearity, causes?

[thadman]

Following some research on acoustic resonances, it was brought to my attention that the enclosure air-spring becomes non-linear beyond a certain level of compression. Therefore the Maximum SPL (below an arbitrary distortion threshold) attainable by a system is thus dictated by the volume of air within the enclosure.

Dennis H has provided a useful formula for determining distortion relating to air compression:

Distortion % = 140*(one-way driver displacement)*(1/enclosure volume)

What are the causes for this form of distortion? Is it due to the temperature decay or the pressure imbalance between sides of the diaphragm?

How can we decrease this phenomenon?

Thanks,
Thadman

[benchtester]

I assume they are referring to the difference between the cone going in and out. Going in: the spring constant is increasing and going out: the spring constant is decreasing.

As an exaggerated example: the box is tiny and the cone can move inward to half the internal volume. The resulting internal pressure would double (1 atmosphere gauge pressure). If the cone moved outward by the same displacement, the resulting pressure would be less by 1/3 (-0.33 atmospheres gauge pressure). So the change in pressure is 14.7 psi inward but only 4.9 psi outward.

For realistic displacements, I don't know how significant this effect is. One could do a spread sheet simulation. (It would be one way to verify if I am talking about the same thing as Dennis.) The air spring constant would be some exponential function.

Although the cause is fundamental, there are ways to avoid this distortion. Going to a bigger box would help some and there are various speaker configurations that reduce or eliminate this effect. I have heard of two configurations both called "isobaric". One vents the back of the cone to the other side of the wall, the other uses a second driver to depressurize the back of the primary driver.

[Dennis H]

Thanks benchtester. I was trying to think of an easy way to explain it and you nailed it. BTW, the formula I posted is from one of Linkwitz's spreadsheets with some unit conversion. I think we can all assume that he got the math right.

[benchtester]

Dennis, thanks for the compliment. I was shooting from the hip and got lucky.

Here's a big Linkwitz spreadsheet with a distortion calculator (cells V15 and V16):

https://www.linkwitzlab.com/closed-box1.xls

But this one is written differently with the effective surface area:
Distortion % = .014*(one-way driver displacement in mm)*(Sd in cm^2) /(enclosure volume in liters)

I like this one since the distance units cancel.

The air spring distortion looks like it can get significant although it will mostly be at loud/low frequencies where displacement is large.

Everyone should take a look at Siegfried Linkwitz's site. (He is the "L" in LR2 crossovers.) It is quite a resource. Also check out his rentals, you might be able to talk you wife into it (don't dwell on the sound systems too long). :W

[benchtester]

BTW: The air-spring effect would be a good argument for true servo sub-woofers (where the electronics measure the position of the woofer and adjust the drive voltage accordingly).

[thadman]

Now that we've established the Air-Spring non-linearity, what other factors contribute to its influence?

Air provides a damping coefficient, is there any reasonable way to calculate this?

[kirknelson]

Does the air spring effect still exist in a ported design?

If it doesn't does that mean ported designs will have lower enclosure induced distortion at low freqs/high SPLs?

There seems to be almost unanimous opinion that bass from sealed speakers sounds "better" or more natural. This seems counter intuitive if bass distortion is higher in sealed designs than in ported designs. I suppose it has more to do with the slope of the roll off in conjunction with boundary reinforcement and the distortion is typically low enough to be inconsequential.

However, what if we build the box large and tune the port very low to simulate the slope of a sealed design (I think this is called an LLT design)? Would this have both a natural sounding roll off and low distortion at the expense of enclosure size?

Finnally, a bit off the topic but, I have read that most sealed designs use a Qtc of .707 but that .5 is considered "transient perfect." What exactly does transient perfect mean? Does that refer to the transition from driver->enclosure->boundary reinforcement for low freq response?

Sorry for all the noobish questions.

[ThomasW]

Hi,

Qtc of 0.50 is 'critically damped', not transient perfect. Qtc of 0.707 is 'maximally flat'.

No driver or alignment is truly transient perfect. That's a theoretical concept, it doesn't exist in the real world.

The ego trip known as LLT, is nothing more than a rebranded EBS design given magical abilities that defy the known laws of physics. Beyond that it's not worth discussing...

Porting creates an air spring. It's the resonance of this column of air (the spring) that is the port tuning (Fb). The port increases output at Fb, but it can have a negative impact on transient response.

I suggest you build a box that can be used sealed or ported then experiment. There's no substitute for hands on experience when it comes to answering questions like those you're posting.

[dlr]

Porting creates an air spring. It's the resonance of this column of air (the spring) that is the port tuning (Fb). The port increases output at Fb, but it can have a negative impact on transient response.

This is not correct. The air in the port is the mass of the resonance. There may be some amount of compliance to it, but the primary characteristic is as a slug of mass. The air in the box is the compliance (the spring).

The last line should say that the port WILL have a negative impact on transient response, since reflex systems (ports, PRs) are 4th order. There are ways to reduce the impact, such as very low tunings, but that's for another thread.

Dave

[ThomasW]

selective serotonin reuptake inhibitor.....

[kirknelson]

Ok, so the port open wouldn't have any benefit to the current discussion.

I guess it makes sense considering how small and quick the driver movements are. The air doesn't really have a chance to obtain velocity only change pressure.

I think I understand the Qtc now...A Qtc of .50 is the point at which additional volume will no longer have an effect on the response of the driver and .707 is the volume at which the driver will exhibit a flat response to the lowest freq. Now that I think a bit more about it, the design equations don't consider the room size or placement so how could Qtc predict boundary gain.

Thank you Thomas!

[Piotr]

Although the cause is fundamental, there are ways to avoid this distortion. Going to a bigger box would help some and there are various speaker configurations that reduce or eliminate this effect. I have heard of two configurations both called "isobaric". One vents the back of the cone to the other side of the wall, the other uses a second driver to depressurize the back of the primary driver.

Bigger is better but isobarik does not solve this. Isobarik can reduce even order/symetrical distortion from the motor and suspension of the drivers though but the nonlinearity of the air spring of the box is still there.

If the box volume is 50-100 times the max displacement of the driver you can forget about this distortion.


/Peter