Effects Of Cabinet Size When DSP Is Being Utilised

[Gorgonzola]

I've done a few speaker design -- mostly on paper, granted. In any case, in these exercises I have preferred close-box designs because, (as I understand), they yield better transient response. Obviously this means to get the same -3 dB point as with a vented box, you've got to equalize; that's not some thing I've shied away from. Amp power is cheap these days.

To lower the overall speaker 'Q' below, the traditional optimal .707, (as I recall offhand), you must increase the size of the close-box. I've never shied from this either, within limits. What I have not done in my designs is aim for smaller cabinet size the yields less than the optimal overall 'Q'. (I'm content that closed-box volumes are smaller than vented-box volumes generally.)

 

[sarumbear]

So am I right by understaning your concluding take on all this is that once DSPed you got what the DSP FR and parameters are and that the cabinet volume has little to do with it? And if it does its mainly related to power or has a minor influence?

I am not concluding. Linkwitz showed us the math back in 1978. The new cabinet volume and the final f3 defines the new efficiency.

And that you also agree with Sigbergaudio comment on that you could potentially if done right make a 15inch mid woofer in 60 litre cabinet sound as large(of course large is purely subjective but you get my drift) as if it was in a 120 litre cabinet? And would this be the same for a subwoofer?

I don't know how you define a sound to be large but the SPL at low frequencies limited by the driver's excursion, Xmax. Nothing you do with EQ will change that.

Thiele and Small demonstrated how sound produced by the loudspeaker at low frequencies could be modelled by a simple circuit analogy. By using the T/S parameters in computer simulation models, users could design loudspeakers without having to physically build the enclosure. They showed us that drive units are high-pass filters. Linkwitz cascaded a new filter that move the poles and zeros of the inherent filter of the drive unit which created a new filter with its own F3 and Qt. He called it the Linkwitz Transform. It is all math, nothing else.

 

[bigjacko]

Put driver into smal box will make the air inside the box stiffer, so now there is not just Kms from driver, but also from air inside. The Kms vs excursion curve will likely become unfavorable, become not a straight line. This will add distortion to frequencies below fs. The sensitivity below fs is also controled by stiffness. The fs will increase as box volume decrease, this will increase the bandwidth of higher distortion and lower sensitivity.

I have some questions about Linkwitz transform and what controls group delay. Does Linkwitz transform change the fs and Qtc in a way that is no different to the native ones? What I mean is frequency response, phase response, group delay, sensitivity, distortion, resosnant time and any other thing if I missed are the same. If not the same which ones and why is that.

Another question is what determines group delay? I had played with WinISD, I compared ported and sealed eq to the same frequency response as ported, the group delay are the same. Is group delay purely controled by frequency response?

Last questions is if Qtc is higher than 0.707, does the driver resonant longer than other frequency? If increase Qtc further does resonant time increase?

Thank you for anyone that has any input to this post.

 

[sarumbear]

Put driver into smal box will make the air inside the box stiffer, so now there is not just Kms from driver, but also from air inside. The Kms vs excursion curve will likely become unfavorable, become not a straight line. This will add distortion to frequencies below fs. The sensitivity below fs is also controled by stiffness. The fs will increase as box volume decrease, this will increase the bandwidth of higher distortion and lower sensitivity.

Your worries and questions may seem valid for a layman but unfortunately mathematics and physics disagree. The stiffness of the air inside the enclosure is simply an element of the final speaker. If you think otherwise please show us some research to back it up.

I have some questions about Linkwitz transform and what controls group delay. Does Linkwitz transform change the fs and Qtc in a way that is no different to the native ones? What I mean is frequency response, phase response, group delay, sensitivity, distortion, resosnant time and any other thing if I missed are the same. If not the same which ones and why is that.
Another question is what determines group delay? I had played with WinISD, I compared ported and sealed eq to the same frequency response as ported, the group delay are the same. Is group delay purely controled by frequency response?

Last questions is if Qtc is higher than 0.707, does the driver resonant longer than other frequency? If increase Qtc further does resonant time increase?

Thank you for anyone that has any input to this post.

Linkwith transform simply moves the poles and zeroes of the filter. The new filter will have all attributes of that new filter.

PS. What do you mean by Kms?

 

[sigbergaudio]

So am I right by understaning your concluding take on all this is that once DSPed you got what the DSP FR and parameters are and that the cabinet volume has little to do with it? And if it does its mainly related to power or has a minor influence?

And that you also agree with Sigbergaudio comment on that you could potentially if done right make a 15inch mid woofer in 60 litre cabinet sound as large(of course large is purely subjective but you get my drift) as if it was in a 120 litre cabinet? And would this be the same for a subwoofer?

It will be the same with a subwoofer (I was actually thinking about a subwoofer when I wrote it). The volume has even less impact on a midbass.

For a subwoofer, a smaller cabinet will give you less output in the low-end, which can be EQed back up, until you reach xmax, assuming you have the power to do so.

 

[Tangband]

There is no free lunch. Optimal box = the best. A smaller box with Linkwitz transformer dsp = worse, but can reach the same f3. The price is:

1. Higher distortion coming from the air inside the smaller box.
2. The driver must be able to do more linear movement (xmax) in a small box.
3. More power is required with a small box.

There is no gain except the size of the box, with a smaller box than optimal.
Edit : One small gain though- its easier to construct a stable, small box.
You can make a box thats 25*25*25 cm with a 10 inch bass and no crossbracing using Linkwitz transformer.

 

[sarumbear]

There is no free lunch. Optimal box = the best. A smaller box with Linkwitz transformer dsp = worse, but can reach the same f3. The price is:

1. Higher distortion coming from the air inside the smaller box.
2. The driver must be able to do more linear movement (xmax) in a small box.
3. More power is required with a small box.

There is no gain except the size of the box, with a smaller box than optimal.
Edit : One small gain though- its easier to construct a stable, small box.
You can make a box thats 25*25*25 cm with a 10 inch bass and no crossbraces using Linkwitz transformer.

Please show us the science behind item 1 as there is no reason there should be more distortion.

Otherwise items 2 & 3 are correct.

 

[bigjacko]

Your worries and questions may seem valid for a layman but unfortunately mathematics and physics disagree. The stiffness of the air inside the enclosure is simply an element of the final speaker. If you think otherwise please show us some research to back it up.

I do think the stiffness from the air inside the box is an element of the speaker, but different speaker volume will result in different final speaker stiffness. There can only be one best stiffness vs excursion, all other stiffness with their corrosponding box volume will not be favorable. How much unfavorable would that be is another question.

Linkwith transform simply moves the poles and zeroes of the filter. The new filter will have all attributes of that new filter.

PS. What do you mean by Kms?

Ahh, that is nice. Thank you for this information. Kms is TS parameter, it is 1/Cms, invearse of compliance.

 

[bigjacko]

Please show us the science behind item 1 as there is no reason there should be more distortion.

Otherwise items 2 & 3 are correct.

Introducing Directiva - An ASR open source platform speaker project

Follow up to post#18 UPDATE: The simulated drivers are the 6.5'' Purifi woofer and the SB Acoustics SB26ADC tweeter. Cabinet is width x height x depth = 216mm x 406mm x 260mm The order of the graphs is always: 1. sketch of the loudspeaker 2. frequency responses of the tweeter without...

www.audiosciencereview.com

At post 35 by DDF there is a reference from Linkwitz. Not sure if it is final scientific answer or just a speculation from him.

 

[sarumbear]

I do think the stiffness from the air inside the box is an element of the speaker, but different speaker volume will result in different final speaker stiffness. There can only be one best stiffness vs excursion, all other stiffness with their corrosponding box volume will not be favorable. How much unfavorable would that be is another question.

You may think so but there is no reason for that to be. Stiffness affects Q. and air stiffness is just part of the resistance that defines the total Q.

Ahh, that is nice. Thank you for this information. Kms is TS parameter, it is 1/Cms, invearse of compliance.

Here are the links to Small's and Thiele's papers from the 70s. I see neither Kms for Cms listed there. Please explain those parameters further.

http://diyaudioprojects.com/Technical/Papers/Direct-Radiator-Loudspeaker-System-Analysis.pdf

The Thiele-Small Parameters Revisited

 

[617]

There has been some discussion about this but not enough to fully understand what is going on when DSP is used in a certain sized cabinet. In the thread "Does QTC Value Matter If We Use DSP" we kind of concluded that DSP overrides the cabinet's roll off but the question now remains how does the cabinet volume effect the chosen roll off with DSP? Has any research been done to understand the effects or general speaker quality say when using the same DSP or roll off in different cabinet volumes?

For example for subwoofer, if we use a low QTS driver in a mid sized cabinet (.7 QTC) vs a fairly large cabinet (.35 QTC) then rolling them both off with the same DSP filter say flat to around 30hz, does the size of the cabinet effect group delay or is the group delay purely related to the roll off regardless of size? Basically, was the cabinet used to determine that roll off and group delay prior to DSP technology and now thanks to DSP it overrides all this effort to perfect group delay and other parameters when choosing cabinet size?

My experience tells(subjective) me that cabinet size still has some effect on woofer control and although I agree that once DSP is implemented your technically changing the cabinet size to one that of the DSP's roll off but it seems box volume can still play a roll in some perceived parameters.

This is really simple to visualize.

A given woofer and cabinet (sealed, ported, bandpass, whatever) will have a maximum SPL it can achieve at any given frequency.

A smaller box, or a sealed box, will have a smaller maximum SPL. A large box with deep port tuning will have a greater maximum SPL. An 'optimum' sized box will be the smallest box which offers 100% of the output potential of the woofer.

See the following graph:

Optimal Vented, Sealed, Sealed Undersized, Vented Undersized

Basically, you can add as much boost or filter you want, but you will only get the output under the curve shown here. No matter what you do, for example, at 30hz, the Optimal Vented enclosure will be able to produce 12db more bass than the Sealed enclosure.

With DSP, you can get any response you want under these curves. You can get a response that is flat to 10 hz in a sealed enclosure...but you will only be able to get 71 db out of it.

Group delay is set by the slope of the bass roll-off. It is determined by the frequency response. The faster the roll-off, the more group delay:

The Vented enclosure rolls off the most steeply so the group delay is greatest. The group delay of the other enclosures with slow roll off is less. However, let's say we add bass boost to one of the sealed enclosures so that it gets the same extended bass as the vented enclosure:

Now the group delay is actually greater than the vented enclosure. Anyway, here are the takeaways:

Group delay is determined by frequency response. Low group delay does not make bass sound 'fast'. A 30hz tone has a period of 33ms, but for a bass tone to 'exist' in your perception it needs about five cycles, which comes out to 165 milliseconds. In 165 milliseconds, the bass wave will have traveled 50 meters. If your room is significantly larger than 50m you might be able to measure differences in group delay.

DSP can give you any response you want, but the box sets the magnitude of the output at all frequencies.

Regarding distortion I am not sure if an undersized box can contribute to distortion, but obviously a smaller box, boosted with DSP, will require higher excursion, which will in turn increase distortion. At low frequencies, excursion is typically the limiting factor. At higher frequencies, it's more likely power handling.

 

[sarumbear]

Introducing Directiva - An ASR open source platform speaker project

Follow up to post#18 UPDATE: The simulated drivers are the 6.5'' Purifi woofer and the SB Acoustics SB26ADC tweeter. Cabinet is width x height x depth = 216mm x 406mm x 260mm The order of the graphs is always: 1. sketch of the loudspeaker 2. frequency responses of the tweeter without...

www.audiosciencereview.com

At post 35 by DDF there is a reference from Linkwitz. Not sure if it is final scientific answer or just a speculation from him.

Is this the link you mention?

Pluto + subwoofer

If so, do you mind showing what part of it supports your assumption?

 

[sarumbear]

This is really simple to visualize.

A given woofer and cabinet (sealed, ported, bandpass, whatever) will have a maximum SPL it can achieve at any given frequency.

A smaller box, or a sealed box, will have a smaller maximum SPL. A large box with deep port tuning will have a greater maximum SPL. An 'optimum' sized box will be the smallest box which offers 100% of the output potential of the woofer.

See the following graph:
View attachment 158424
Optimal Vented, Sealed, Sealed Undersized, Vented Undersized

Basically, you can add as much boost or filter you want, but you will only get the output under the curve shown here. No matter what you do, for example, at 30hz, the Optimal Vented enclosure will be able to produce 12db more bass than the Sealed enclosure.

With DSP, you can get any response you want under these curves. You can get a response that is flat to 10 hz in a sealed enclosure...but you will only be able to get 71 db out of it.

Group delay is set by the slope of the bass roll-off. It is determined by the frequency response. The faster the roll-off, the more group delay:
View attachment 158425
The Vented enclosure rolls off the most steeply so the group delay is greatest. The group delay of the other enclosures with slow roll off is less. However, let's say we add bass boost to one of the sealed enclosures so that it gets the same extended bass as the vented enclosure:

View attachment 158426

Now the group delay is actually greater than the vented enclosure. Anyway, here are the takeaways:

Group delay is determined by frequency response. Low group delay does not make bass sound 'fast'. A 30hz tone has a period of 33ms, but for a bass tone to 'exist' in your perception it needs about five cycles, which comes out to 165 milliseconds. In 165 milliseconds, the bass wave will have traveled 50 meters. If your room is significantly larger than 50m you might be able to measure differences in group delay.

DSP can give you any response you want, but the box sets the magnitude of the output at all frequencies.

Regarding distortion I am not sure if an undersized box can contribute to distortion, but obviously a smaller box, boosted with DSP, will require higher excursion, which will in turn increase distortion. At low frequencies, excursion is typically the limiting factor. At higher frequencies, it's more likely power handling.

The Linkwitz transformation will only work with closed boxes. Ported speakers cannot be equalised to any satisfactory degree.

 

[617]

The Linkwitz transformation will only work with closed boxes. Ported speakers cannot be equalised to any satisfactory degree.

The linkwitz transform is just a bass boost with some clever calculation to end up with a response that looks like a different woofer/box. You can use filters to get any response you want out of any box, the issue is the maximum SPL set by the box/woofer combination.

 

[sigbergaudio]

Introducing Directiva - An ASR open source platform speaker project

Follow up to post#18 UPDATE: The simulated drivers are the 6.5'' Purifi woofer and the SB Acoustics SB26ADC tweeter. Cabinet is width x height x depth = 216mm x 406mm x 260mm The order of the graphs is always: 1. sketch of the loudspeaker 2. frequency responses of the tweeter without...

www.audiosciencereview.com

At post 35 by DDF there is a reference from Linkwitz. Not sure if it is final scientific answer or just a speculation from him.

But the link to Linkwitz refers to a page that does not say anything about distortion as far as I can see?

 

[sarumbear]

The linkwitz transform is just a bass boost with some clever calculation to end up with a response that looks like a different woofer/box. You can use filters to get any response you want out of any box, the issue is the maximum SPL set by the box/woofer combination.

You are wrong. A bass boost will continue to boost as the frequency lowers. A simpler definition is a shelving boost, but that will still not explain the Q changes at the "corners".

There is no need to argue or rename what is an universally accepted method. Mathematics is solid and zillions of tests were done to show that it is working.

And, the maximum SPL is not set by the box. Efficiency is.

 

[617]

You are wrong. A bass boost will continue to boost as the frequency lowers. A simpler definition is a shelving boost, but that will still not explain the Q changes at the "corners".

There is no need to argue or rename what is an universally accepted method. Mathematics is solid and zillions of tests were done to show that it is working.

And, the maximum SPL is not set by the box. Efficiency is.

I understand what you're saying. You can get pretty close to a linkwitz transform with a high pass and a couple of boosting filters. It's obvious you understand more about how the LW transformation calculation works than I do.

My point is that for all practical purposes, an undersized box will limit output potential, regardless of the shape of the frequency response you achieve with filters.

 

[sarumbear]

My point is that for all practical purposes, an undersized box will limit output potential, regardless of the shape of the frequency response you achieve with filters.

I’m afraid I have to correct you again. The box has no play in limiting the output potential. Max SPL is limited only with the Xmax of the driver, nothing else.

The box size affects the efficiency, which is SPL/Watt.

 

[617]

I’m afraid I have to correct you again. The box has no play in limiting the output potential. Max SPL is limited only with the Xmax of the driver, nothing else.

The box size affects the efficiency, which is SPL/Watt.

No need to apologize for correcting me in a technical conversation. I'm confused, however, doesn't the addition of a vent to a sealed box create the opportunity for greater output given the same woofer?

When WinISD calculates graphs of Maximum SPL, it's taking into account the box, the excursion capability, and the power handling.

 

[bigjacko]

You may think so but there is no reason for that to be. Stiffness affects Q. and air stiffness is just part of the resistance that defines the total Q.

My saying was about stiffness vs excursion graph from klippel measurement, not about Q of the speaker. I don't know if Q of speaker can affect distortion. I have to admit I don't have any proof from my end, just from my basic physics derivation.

Is this the link you mention?

Pluto + subwoofer
If so, do you mind showing what part of it supports your assumption?

But the link to Linkwitz refers to a page that does not say anything about distortion as far as I can see?

Sorry, I was just quoting somebody else, I don't have the right link too..... Maybe @DDF can help here.