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 over on HTGuide 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
Dennis H over on HTGuide 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
It's due to air being not entirely linear when it comes to compression and rarefaction.
Don't use air. 😀
se
Re: Re: Re: Air-spring non-linearity, causes?
How about a transmission line? How would its attributes affect air non-linearity?
Fast1one said:
How about a transmission line? How would its attributes affect air non-linearity?
In most cases, the air in the box is more linear than your driver's suspension. It is when the driver volume displacement exceeds 10% of the box volume that it will become significant. Still, whether it is more significant than driver nonlinearity depends on the driver.
Transmission lines pressurize a box, so they are affected.
Transmission lines pressurize a box, so they are affected.
Ron E said:
Of course they do. It's rather elementary to describe the distribution of pressure in a line with a Cos wave. However, for the same volume of air and driver displacement, does the TL (driver at one end, opposing end open) wrt a closed line (driver at one end, opposing end closed) possess the same degree of air non-linearity?
It is really rather elementary stuff. Given the same SPL at the same frequency, the degree of pressurization will be the same in a sealed, vented, PR, TL, etc.... The proof is left to you as an exercise...😱
Re: Re: Air-spring non-linearity, causes?
I'm not so sure that it is due to non linearity of air. Even with an ideal gas which follows the completely linear ideal gas law PV = nRT, if we assume constant temperature (so nRT = C (constant))
P = C/V
thus dP/dV = -C/V^2
Since dP/dV is the spring constant this means that even an ideal gas is a non-linear spring.
Steve Eddy said:
I'm not so sure that it is due to non linearity of air. Even with an ideal gas which follows the completely linear ideal gas law PV = nRT, if we assume constant temperature (so nRT = C (constant))
P = C/V
thus dP/dV = -C/V^2
Since dP/dV is the spring constant this means that even an ideal gas is a non-linear spring.
Re: Re: Re: Air-spring non-linearity, causes?
A potential solution could then be to make the drivers suspension force the inverse of the air spring force. As far as I understand, the individual non-linear forces should sum to be linear as the total restoration force.
Is it then possible to accurately determine an enclosures air spring force and model it? Even with acoustic foam or rigid fiberglass present?
Mark Kelly said:
A potential solution could then be to make the drivers suspension force the inverse of the air spring force. As far as I understand, the individual non-linear forces should sum to be linear as the total restoration force.
Is it then possible to accurately determine an enclosures air spring force and model it? Even with acoustic foam or rigid fiberglass present?
You may be able to do that to some extent with some drivers by adding a small DC offset to the signal to compensate with the driver suspension linearity. Not really recommended.
thoriated said:
The air-spring non-linearity is dependent on level (ie displacement). If we were able to accurately model the air spring force on the surface of the diaphragm we could correct it through either mechanical or electrical means, but that assumes we know the air-spring force on the surface. The non-linearity in subwoofers is able to be corrected through servo feedback since motion can be considered one dimensional (assumes we are operating below the bandwidth where modes propagate in the cone and/or suspension) and is able to be measured since acceleration is independent of the point on the surface of the diaphragm, greatly simplifying the computational requirements. We cannot assume the diaphragm motion is one-dimensional at high frequencies and it would be prohibitively expensive to measure the acceleration at every point on the surface, thus feedback is an impractical solution to determining the air-spring force. We will have to create a model that describes the air-spring non-linearity and based on that information we could use DSP to correct it.
Besides the DC offset approach, you can shift the suspension restoration point a bit with some drivers by operating it with the cone facing downward or upward with a fairly large amplitude sine wave for a period of time. Of course, some significant measurement capability is needed to determine how much would benefit the situation.
DSP/motional feedback is a more sophisticated way to compensate, but would only be effective when the cone is in its pistonic mode. The good news, such as it is, is that the air nonlinearity would manifest itself significantly only in the lowest octaves of a bass driver's effective range (not counting horn thermal distortion which is more of a HF effect).
DSP/motional feedback is a more sophisticated way to compensate, but would only be effective when the cone is in its pistonic mode. The good news, such as it is, is that the air nonlinearity would manifest itself significantly only in the lowest octaves of a bass driver's effective range (not counting horn thermal distortion which is more of a HF effect).
Is it possible to accurately determine the air-spring force vs displacement? If non-linearity is present (as far as I understand) it should be able to be visualized in the same way that the Bl curve describes force vs displacement for loudspeaker motors. If we can determine this function, we can have a target function for the mechanical restoration force necessary to achieve a summed linear restoration force.
The main question then is: Is it possible to accurately determine the air-spring force function?
The main question then is: Is it possible to accurately determine the air-spring force function?
At LF assuming the process is adiabatic is reasonable. In this case, pV^gamma is constant where p is the pressure in the box, V is the volume of the air in the box, and gamma = 1.4 (ratio of specific heats). That is how you determine the force vs displacement.
Or you use 1.0 instead of 1.4 for the isotropic coefficient if the process is isothermal. This is the classic explanation of how stuffing works.
I coded this up into a spreadsheet 10 years ago. The fact that the air spring is more linear than most driver suspensions is the whole point of acoustic suspension. My spreadsheet bears this out as long as Vb is perhaps 1/5 of Vas (or so). I modeled compliance vs displacement as an odd polynomial...
John K more recently made a spreadsheet that calculates distortion percentage due to air spring nonlinearity....
I coded this up into a spreadsheet 10 years ago. The fact that the air spring is more linear than most driver suspensions is the whole point of acoustic suspension. My spreadsheet bears this out as long as Vb is perhaps 1/5 of Vas (or so). I modeled compliance vs displacement as an odd polynomial...
John K more recently made a spreadsheet that calculates distortion percentage due to air spring nonlinearity....
Here is a development of the nonlinear air compliance:
For the trapped air we assume the compression/expansion process is governed by a polytropic process,
PV^k = constant (14)
where P is the pressure, V the volume and k is the polytropic exponent. k = 1 for an isothermal process and 1.4 for an isentropic process. An isentropic process is assumed here. The variation in volume of the rear box is given as
V = Vo + Sd xr (15)
where Vo is the box volume when the driver is at rest. Thus the pressure in the box is
P = constant/( Vo + Sd xr )^k (16)
Without going through the details Eq (16) leads to the nonlinear compliance
Cabnl = Cab(1 + Sd xr /Vo) ^(k+1) (17)
You can download an Excel spread sheet that allows you to calculate the distortion for a given driver/box
here.
To see the effect of just air compliance turn off the suspension nonlinearity.
For the trapped air we assume the compression/expansion process is governed by a polytropic process,
PV^k = constant (14)
where P is the pressure, V the volume and k is the polytropic exponent. k = 1 for an isothermal process and 1.4 for an isentropic process. An isentropic process is assumed here. The variation in volume of the rear box is given as
V = Vo + Sd xr (15)
where Vo is the box volume when the driver is at rest. Thus the pressure in the box is
P = constant/( Vo + Sd xr )^k (16)
Without going through the details Eq (16) leads to the nonlinear compliance
Cabnl = Cab(1 + Sd xr /Vo) ^(k+1) (17)
You can download an Excel spread sheet that allows you to calculate the distortion for a given driver/box
here.
To see the effect of just air compliance turn off the suspension nonlinearity.
If we consider the motion of a diaphragm as a driven harmonic oscillator, we should be able to accurately define its motion. The equation requires the inclusion of the systems damping coefficient.
How are we able to calculate the damping coefficient of air? Would a relationship between the mass of the diaphragm and the mass of the air lead us in the correct direction?
How are we able to calculate the damping coefficient of air? Would a relationship between the mass of the diaphragm and the mass of the air lead us in the correct direction?
There are two issues of non-linear air in electro-acoustics, at first the one related to the source and at second the one related to transmission.
The one discussed here so far, the source issue, is visible, when movement of diaphragm depends on stiffness of air volume trapped within pressure chamber (say, dimensions of which smaller lambda/2Pi). As stiffness depends on diaphragm excursion, diaphragm excursion modulates itself via stiffness, causing distortion. This kind of distortion rises with diaphragm excursion which rises with inverse power of frequency. Hence this kind of distortion rises linearily with sound pressure level and inverse power of frequency.
The other issue are non-adiabatic effects, say power flow to and fro the sound transmitting air, say transmission distortions. Common issue is thermal messing with acoustic radiation. I cannot fully explain it, but this issue is, why sound running thru ports too small, resonating or not, and pressure chambers such as ones before horns tend to show distortions rising linearily with frequency and with higher power with sound pressure level.
Turbulence is a further source of distortion, an example are bassreflex ports with edges.
The one discussed here so far, the source issue, is visible, when movement of diaphragm depends on stiffness of air volume trapped within pressure chamber (say, dimensions of which smaller lambda/2Pi). As stiffness depends on diaphragm excursion, diaphragm excursion modulates itself via stiffness, causing distortion. This kind of distortion rises with diaphragm excursion which rises with inverse power of frequency. Hence this kind of distortion rises linearily with sound pressure level and inverse power of frequency.
The other issue are non-adiabatic effects, say power flow to and fro the sound transmitting air, say transmission distortions. Common issue is thermal messing with acoustic radiation. I cannot fully explain it, but this issue is, why sound running thru ports too small, resonating or not, and pressure chambers such as ones before horns tend to show distortions rising linearily with frequency and with higher power with sound pressure level.
Turbulence is a further source of distortion, an example are bassreflex ports with edges.
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