The importance of Kms(X) and BL(x) for mid-ranges

In context of your first post?

- Low excursion by design > reduces many suspension / motor-related artefacts
- No tuning necessary
- Very high efficiency > always good imo.

Yes, you'll need to cross slightly above Schroeder, but most 15" (sub) woofer drivers are perfectly capable of doing so.
You'll need 2 per mid, which further improves low freq. performance > spreading the load.


So for loudspeakers there are basically three dominant factors creating distortion/non linear behavior.

- The non-linearity of the compliance (1 / stiffness), Cms(x)
- The non-linearity of the BL vs displacement curve, BL(x)
- The non-linearity of the inductance. Le(x)

So the BL(x) and Cms are both dominant for the lower frequencies, around the Fs up to roughly 2 x Fs.
From that point on the inductance Le(x) is starting to be the more dominant factor.

So let's assume we have a mid-woofer with a Fs around 50Hz.
We are gonna cross this driver (actively) around 100-120Hz (2nd order highpass).

As long as we keep the cone excursion to a minimum, which is most cases is fine since most speakers will run into there max power at this point with a cone excursion of just 1-3mm or so.
 
In context of your first post?

- Low excursion by design > reduces many suspension / motor-related artefacts
- No tuning necessary
- Very high efficiency > always good imo.

Yes, you'll need to cross slightly above Schroeder, but most 15" (sub) woofer drivers are perfectly capable of doing so.
You'll need 2 per mid, which further improves low freq. performance > spreading the load.

Still doesn't say much.
You mean for home hifi purposes or PA purposes?
2-way, 3-way ?

I assume the first one.
Looking at the impedance graphs, I see a lot of blips, which is never a good sign.

I don't really understand the low excursion by design?
We are not interested in the excursion, although depending on SPL levels, a little excursion is always needed.
Depending on the motor design, but in general speakers with higher excursion will have a more linear low excursion, compared to speakers that naturally already have a limited excursion.
But you have to see the Klippel measurements for that (not a set and stone rule)

But the biggest question mark I have with these speakers, is that we don't know the free-air resonance.

In the end of the story, it wouldn't be my pick, unless there is an absolute need for having a included enclosure.
For hobby purposes that is really seldom an issue I think.
There are much better (mid) woofers out there.
 
Getting back to the 2 x Fs rule of thumb

The last couple of weeks I have been looking at multiple measurements from Hificompass, VoiceCoil Magazine as well as from Hobby Hifi (German magazine).
At the same time trying to predict the performance looking at just freq resp and impedance as well.

I would say, 2 x Fs is bare minimum, but it really depends per woofer.
Which makes me believe in my other little theory, that sometimes the Fs is created with just added mass (and maybe improving BL to compensate), but without an optimized Cms.

For example, there are 6 inch woofers with an Fs of around 30-35Hz, but their distortion starts to rise at 3-4 x Fs.
Whit other woofers, you can clearly see the THD going up at 2 x Fs.
It is a bit like just adding mass to an existing driver.
Like we concluded before, below the Fs the non-linearity of the Cms is going to bahve unpredictable.
Boy, would it be handy to have one of these engineers on board who manufacture these things...........

The vast majority of 6 inch woofers seem to rise in distortion below 80-100Hz.
There isn't much difference between 5,25 inch vs 6 inch except for absolute maximum SPL.

(Good performing) 4 inchers all seem to rise below 120-200Hz
With 8 inch speakers there seem to be a big step in improvement all of a sudden again, starting to distort significantly below 40-70Hz.
Even the just decent ones seem to outperform most expensive 6 inch woofers with ease.

Bit by bit this appears to become almost a literature research project, so maybe at some point I will see if I have the time to put it all down on paper.
 
You have such a bias on those 8" units :p

From an aesthetic pov 8" and the accompanying baffle width is big for standard (European) living rooms. Heck, even 6" is hard to sell to the family (as in SWMBO...), but then again, a decent horn/waveguide often is 6", so options are limited.

So there we go again. It shall be a tradeoff.
 
I don't have a bias at all. :D

But no seriously,
I am actually more than happy to use a 4 inch or a 5 inch if I have to.

But I am just trying to streamline all those tradeoffs

Actually my whole message wasn't about promoting 8 inch woofers at all.
It was more wondering about why they have such a better performance.
The step seems to be much bigger compared to 5 inch vs 6 inch.
 
I always thought it was a 6 inch?

Since that fits in a decent size (book shelf) cabinet, BR will go down to 40-45Hz, decent sensitivity and SPL.

These days I very rarely advice any full-range BR anymore.
Amplifiers are so cheap, so a small little 4-6 inch closed cabinet will do just fine plus two small subs you hide somewhere. Everyone is happy.


Anyway, we are getting side tracked.
I had a quick glance on the loudspeaker database.
On average it looks like most 8 inch woofers don't really have much higher sensitivity.
With equal sensitivity but a smaller Sd, it means more has to come out of the motor.
And the motor is were all the non-linear trouble starts.

The difference in Sd between each size (4 inch -> 5.25 inch -> 6 inch -> 8 inch), is already roughly 3dB. Which already costs twice the amount of power to compensate.
 
Hoping to get responses from the guys in this thread, or any who feel inclined

What about the effects of Fb on midrange and BL??? Fb challenges BL with resistance and reactance... the pressure that Fb causes due to the increased air load, doesn't degrade midrange at all?
 
Hoping to get responses from the guys in this thread, or any who feel inclined

What about the effects of Fb on midrange and BL??? Fb challenges BL with resistance and reactance... the pressure that Fb causes due to the increased air load, doesn't degrade midrange at all?
You mean used in full-range/as a mid-woofer?
Or just only mid-range?
 
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You mean used in full-range/as a mid-woofer?
Or just only mid-range?
I mean midrange.....Its just that a midrange may cover more bass then others in another design...So for example in a two way design that used a 15" and a horn/waveguide.... the 15" is handling midrange as well as the Compression driver. Focusing on the woofer, lets say its a vented design tuned to 30hz..... Lets play some content that involves sub bass.....a 30hz signal is present simultaneously as the upper passband of the woofer, say to 800hz. The pressure is very high at 30hz, yet the loading keeps excursion low, though reactance is high, as well.

This complex of factors does not affect the midrange? How much pressure can the woofer take (for example, very small beginning CSA, still tuned to 30hz) before the midrange is affected?
 
The pressure is higher than an equivalent volume sealed cabinet, if I'm not mistaken...

The connection to the topic is BL.... I'm wondering is it possible for the motor to be challenged to the point of distortion... For example, an 18" used in horn loading, can destroy itself due to high throat pressures. Point being there can be a lot pressure on the woofer in vented
designs...

In the above purposed scenario, a 15" in a two way, is midrange and sub, if used as so.... when playing near or at Fb pressure is great... Im wondering is it ever an issue for the midrange when the woofer is playing near Fb, where excursion is kept low but BL is challenged the most.

I don't understand exactly how pressure affects performance within Xmax...but it would seem that Higher BL would deal better with higher pressure.

It would seem that as pressure becomes too high, sensitivity would suffer?...but what about above this point... maybe there are other consequences to frequencies above F during reproduction near F

We've talked about F in regards of keeping it away from the midranges passband. Fb of a 15" two way is easily kept away from midrange.... once again, could midrange suffer from the affects of the high pressures of Fb when the 15" is midrange and sub...

BL vs Pressure
 
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I mean midrange.....Its just that a midrange may cover more bass then others in another design...So for example in a two way design that used a 15" and a horn/waveguide.... the 15" is handling midrange as well as the Compression driver. Focusing on the woofer, lets say its a vented design tuned to 30hz..... Lets play some content that involves sub bass.....a 30hz signal is present simultaneously as the upper passband of the woofer, say to 800hz. The pressure is very high at 30hz, yet the loading keeps excursion low, though reactance is high, as well.

This complex of factors does not affect the midrange? How much pressure can the woofer take (for example, very small beginning CSA, still tuned to 30hz) before the midrange is affected?
In this case, were lower frequencies (< 2-3x Fs) are being used with higher/mid-range frequencies (> 2-3x Fs), we are still back to the original problem with Le(x) and/or inter modulation.

The only way to get rid of that, is to split the frequency band again so the 15" isn't effected by any cone-excursion.
How bad that is, also depends how much excursion that 15" woofer is doing.

As far as I know, these distortion elements are purely from (and on) the speaker itself.
(so yes, the cabinet itself also plays a role in that)

In a BR design this extra low "boost" is coming from the port, not from the speaker.
It even creates a dip in the cone-excursion.
The only thing to keep an eye on, is the excursion below this dip, because that will go exponentially higher.
Or in other words, if this 30Hz is like substantially lower than this "BR-dip", yes that obviously will effect the midrange, since it effects the cone-excursion.

So it good design it's wise to take this into consideration.
 
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Yeah, easiest way to reduce mid distortion is high pass filter :) even if it was dedicated bass, definitely highpass filter the excursion below BR tuning as there is barely audible output with huge excursion as sound from the port cancels it out. Basically its just distortion generator.
 
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Thanks for replying!
As far as I know, these distortion elements are purely from (and on) the speaker itself.
(so yes, the cabinet itself also plays a role in that)

Let me paint a picture and then you can say what you feel. Fb should never be placed above desired system cutoff. For this thought experiment lets focus on a 30hz Fb...... Are we saying that there are no consequences of the high pressure caused by the air mass loading, to midrange being produced at the same time?

With High excursion, from subbass....Midrange will create is own THD due to being produced while on the outer oscillation that was caused by the low frequency. The low frequency is the "carrier signal" bringing the mid range oscillations into excursion territory it would never have seen if not for the low frequency. Both the sub and mid range will now generate THD, correct?

Its almost like sympathy pains, is it possible that the distortions that happen at Fb, can cause the midrange to distort....GD and Decay come to mind, as well, The negative effects of pressure...if any.
 
Yeah, easiest way to reduce mid distortion is high pass filter :) even if it was dedicated bass, definitely highpass filter the excursion below BR tuning.
In sound-reinforcement (PA) this is often done at the BR tuning freq.
That way the theoretical cone-excursion will have two symmetrical humps, providing very high excursion levels as well as a sort of limiter at the same time. Resulting in that he max power of a speaker will be the more limiting factor.
(Which is much easier to deal with in an active audio compressor)

This doesn't work for people who suffer from group-delay anxiety though. ;)

I often like to put at least a 1st order HP on subs or active systems, which seems to be a good compromise.
But with cheap power available these days, and drivers with with good performance, I very rarely use BR systems.
Unless it's just like an ordinary 2-way system or so.
Which can still perform really nice obviously! :)
 
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Thanks for replying!


Let me paint a picture and then you can say what you feel. Fb should never be placed above desired system cutoff. For this thought experiment lets focus on a 30hz Fb...... Are we saying that there are no consequences of the high pressure caused by the air mass loading, to midrange being produced at the same time?

With High excursion, from subbass....Midrange will create is own THD due to being produced while on the outer oscillation that was caused by the low frequency. The low frequency is the "carrier signal" bringing the mid range oscillations into excursion territory it would never have seen if not for the low frequency. Both the sub and mid range will now generate THD, correct?

Its almost like sympathy pains, is it possible that the distortions that happen at Fb, can cause the midrange to distort....GD and Decay come to mind, as well, The negative effects of pressure...if any.
You could experiment with it, loop some synth chords for example, or a beat, or section of the song you linked to. Toggle highpass filter and try listen if you hear difference on the mids. Or something practical like that. Perhaps leave the highpass filter be but mix in some strong 20Hz or so sinewave and listen how bad the situation is with increased excursion.

If you are concerned about distortion then just highpass until sound is good, and use more woofers for lows. If you are concerned other issues then perhaps not, what ever is worse.

Anyway with some top shelf 15" drivers and casual home use I would say there is no problem with distortion. If you push it then it might be a problem but only you can find it out. I'm not sure if I hear any difference with or without below tuning highpass on my 15" BR cabs, but the levels are modest and they are part of three way speaker so no wonder :)

For sure, if you highpassed octave higher you've just lowered excursion to quarter what it was and down went distortion numbers for the whole bandwidth.

As I've understood it excursion makes the whole bandwidth distort as mechanical and electrical parameters of the driver change with voice coil position, title of the topic. Not sure how pressure affects. Pressure modulates with the tuning frequency, it can be more or less, when ever there is higher frequency content playing. 30Hz is so slow 800Hz had time to greet both high and low pressure backwave almost 27 times during one cycle.
 
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Thanks for replying!


Let me paint a picture and then you can say what you feel. Fb should never be placed above desired system cutoff. For this thought experiment lets focus on a 30hz Fb...... Are we saying that there are no consequences of the high pressure caused by the air mass loading, to midrange being produced at the same time?

With High excursion, from subbass....Midrange will create is own THD due to being produced while on the outer oscillation that was caused by the low frequency. The low frequency is the "carrier signal" bringing the mid range oscillations into excursion territory it would never have seen if not for the low frequency. Both the sub and mid range will now generate THD, correct?

Its almost like sympathy pains, is it possible that the distortions that happen at Fb, can cause the midrange to distort....GD and Decay come to mind, as well, The negative effects of pressure...if any.
My apologies, but I am struggle to follow what you're trying to ask really, sorry?

The "high pressure" you're talking about, always has influence on the loading of the speaker.
Linkwitz has a nice explanation on his website about this
(I am sorry, lost the direct link, but wouldn't be difficult to search and find that).

So the smaller you are gonna make this volume, relative to the Vd = Sd * xmax, the higher the "pressure", the higher the (asymmetric) loading on the speaker. This asymmetric loading will create quite some 2nd order distortion and probably also quite some IMD (inter-modulation distortion).

One of the reasons why it is NOT good idea to compare speakers in the same cabinet without compensating for this (like a linkwitz-transform). Because the paramters of the speaker will heavily influence this. (Fs, Qts etc).

I assume you mean just distortion in general with "THD"?
Because IMD and THD are technically not the same thing.

Since the box Fs (or Fb) is a product of the Mms, Cms and compliance of the box, this means that Fb is always still influenced by those as well. How much depend on the ratio of the Cms and compliance of the box I guess?
But I don't have the formula by hand at the moment.
In theory the compliance of the box can also change, since the walls etc are not ideal.
Meaning with more pressure, the compliance of the box will shift somewhat.

For a BR similar issues can occur (with also having a acoustic mass).
 
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