Linkwitz Stuff

[Guy Incognito]

Hey Guys,

Im new to much of this and im just trying to get my head around all of these new concepts.

As i understand it, Linkwitz crossovers are a great active filter to split a signal into high/mid/bass. The result of the crossover being flat with no peaks/dips or phase reversals.

Specifically for subs, a linkwitz transform can be used as a bass boost to increase the amplitude of low frequencies? So you might be able to extend flat response down another 10Hz or so before rolling off?

Is my current mode of thinking correct? I have noted that the transform and the crossover are different circuits and perform different tasks. Im just trying to picture how it might fit together. Is it something like:

For a sub, you would use a low pass on the input signal, linkwitz or otherwise, and then use the linkwitz transform to extend the gain at lower frequencies if desired. All of this occuring before the power amplification stage....

The advantage of this being, you would be able to reduce distortion by putting the speaker into a larger box but also maintain the same or better amplification at low frequencies by applying the transform?

Cheers all

[Greybeard1]

Originally posted by Guy Incognito
Hey Guys,


The advantage of this being, you would be able to reduce distortion by putting the speaker into a larger box but also maintain the same or better amplification at low frequencies by applying the transform?

Cheers all

The irony of it is that you will probably want to put the driver in a smaller box, not a larger one.

1) LT ccts require a decrease in system Q to allow for a decrease in Fb, therefore it is desireable to start with a higher Q than what you want to end up with.

2) it is EXTREMELY desireable to size the box such that the power applied is incapable of bottoming the driver(s)... keep in mind that a LT cct will mean high levels of power and excursion are being applied to the sub. It is more desireable to have an amp clip than a driver bottom, IMHO.

The sequence I went thru when building the system i built?

1) decide on driver and amp
2) make sure driver(s) can handle power of amp (thermal), revisit point 1 as required
3) size box such that Q can be reduced to allow LT cct to work.
4) reduce size of box to limit excursion to less than Xmax at full power.

If design meets the above parameters, then you can calculate an LT for it.


The last point I want to make is that there is no greater "efficency" to be had by using a LT cct. In fact, overall, a LT makes the overall sub less efficient, if you think about it.

e.g. If you have a sealed sub which is capable of 110dbspl at 30hz (full power or full excursion) and you apply sufficient 'LT" to get flat extension to 15hz, but at the cost of db gain in the LT, what you've really done is reduce the overall gain allowable on the sub to 100db at 30hz. You cannot apply the same drive levels to the sub that would give you 110 db spl at 30hz, at 15hz, or either your amp will clip or you driver will bottom (depending on how you've design the sub system)

Still... these LT-based systems have their place. The system i built used a set of 4 tempest classic drivers and a LT-capable ADA-1200 amp. The system is 95db spl 1w/1meter, and is capable of 126 db spl at full power above rolloff. I "threw away" about 14 db of that with a rather agressive LT. But the system is still capable of 110-112 db (ignoring room gain) at 16hz.

So if your initial efficency is high enough, or spl requirements are low enough, an LT can work well for you.
GB

[Wingfeather]

I'd like to add a couple of things.

Originally posted by Greybeard1
LT ccts require a decrease in system Q to allow for a decrease in Fb

The Linkwitz Transform uses zeros to cancel out the "natural" poles of the driver/box combination. It can do this whatever their Fc or Q-value is.

(Though, I recognise that you did say "LT ccts", which might mean that the specific circuit implementations that are floating around impose this limitation. I've only ever implemented my LTs digitally, so I don't know about that. My point is, the principle doesn't require the initial Q to be higher than the desired Q.)

Originally posted by Greybeard1
In fact, overall, a LT makes the overall sub less efficient

Well, that depends on how you define efficiency. It's not going to change the power-in/SPL-out ratio of the driver at any frequency, so I would argue that efficiency is unchanged. Having large amounts of gain at LF will just limit the maximum input you're able to give the driver at higher frequencies, so limiting your total system SPL.

Originally posted by Guy Incognito
The advantage of this being, you would be able to reduce distortion by putting the speaker into a larger box but also maintain the same or better amplification at low frequencies by applying the transform?

That should work. Using the larger box would mean you need less equalisation, reducing power input to the driver and so reducing distortion a little bit. However, I agree with Greybeard1 - this isn't the most common use of the LT. Most people employ it as a way to allow the use of a smaller-than-ideal box for a given driver - for cosmetic or logistic reasons, and/or to flatten a driver that would not reach a low enough cutoff in any box size.

I use the LT to equalise my woofers (2x8" per cabinet) flat to 20Hz in a box that's slightly too small (Q~0.85, IIRC). They also wouldn't reach 20Hz even if the box was dimensioned correctly. I ended up with around 15dB of gain at LF, which definitely needs bearing in mind. However, it works nicely and sounds great.

[Guy Incognito]

Thanks guys!

The amount of knowledge floating around is amazing. Its great to be able to have access to it.

I must admit, as i have read more about it, i have become more drawn to the idea. Primarily because i do want to make a sub with a relatively small enclosure.

Ive been torn between two peerless speakers - the 10" (830843) and the 12" (830845). The application notes recommend a 62L box with 65% fill for both drivers. This is okay but i would prefer something a wee bit smaller.

As this is my first project its unlikely i will be jumping into equalising the input, i want to concentrate on building a good sealed sub. However, its becoming very tempting to at least leave room in the design for adding this as an option later.

Im going to put pen to paper and see what comes up. I know its all trade offs but i never liked making them!

Any recommendations or comments are welcome,

Thanks again

[Greybeard1]

Originally posted by Wingfeather
I'd like to add a couple of things.

The Linkwitz Transform uses zeros to cancel out the "natural" poles of the driver/box combination. It can do this whatever their Fc or Q-value is.

(Though, I recognise that you did say "LT ccts", which might mean that the specific circuit implementations that are floating around impose this limitation. I've only ever implemented my LTs digitally, so I don't know about that. My point is, the principle doesn't require the initial Q to be higher than the desired Q.)

I'm not 100% sure about this...

There was a post over at the home theater forum where a fellow named Dave Alan posted the following, which was copied from a link at the Rythmic Audio site about their LT cct... the link no longer works, so I copied out the post... the part in quotation marks are from the Rythmic Audio site, the rest is Dave's comments.

"So far so good. Is there any limitation one LT circuit? Yes. The amount of fs and Qts one can change with LT turns out to be interdependent. That is, if one change the fs by a factor of X (that is old fs over new fs), one can only change Qts by a factor between X and 1/X. For instance, if one change the fs from 40hz to 30hz, one can change the Q value by a factor between 3/4 to 4/3. Therefore if one does not want to change fs by much, there is not a wide range that one can change Q value."

It makes sense that the L/T formula would have a numerator and a denominator involving the existing Fs and Qs and the desired new Fs and Qs, which would make Fs and Qs interdependent.

Also, since we're talking about the sound of a sub, which means in-room response, as you lower the existing Fs, the Qs will change with room gain and will be less of a factor in reproducing music program.

Basically, what that means in the real world app is that the more boost you apply (smallest box/largest amp that allows for optimal use of a given driver's excursion capabilities), the more control you have over the final Qs...no?

Anyway... I think my original comment is wrong. You don't have to force Q lower to lower Fs. But based on the quote above, changes in system Q and Fx are related.

GB

[Wingfeather]

Hi Greybeard,

Originally posted by Greybeard1
It makes sense that the L/T formula would have a numerator and a denominator involving the existing Fs and Qs and the desired new Fs and Qs, which would make Fs and Qs interdependent.

I'm 99% certain the person who wrote that has simply misunderstood the meaning of the maths behind the LT.

---

A quick overview for anyone who hasn't seen it before (I apologise for the mathsey nature of this, and also for how horribly hard it is to read - if anyone knows a good way of doing equations in text form I'd be very interested!):

The driver in a sealed box has a complex conjugate pair of poles determining the frequency and Q of it's LF rolloff, shown as the denominator in the following equation (the numerator is just 1 for now, so I'm ignoring the driver/box combo's zeros - but they aren't important for this stuff anyway):

H(s)driver = 1 / (s^2 + (Wc/Q)s + Wc^2)

Where Wc is the cutoff frequency and Q is, well, the Q.

The Linkwitz Transform introduces an electronic filter with a numerator that matches the denominator of the driver/box, and a denominator with the Fc and Q that we actually want, like so:

H(s)filter = (s^2 + (Wc/Q)s + Wc^2) / (s^2 + (Wc'/Q')s + Wc'^2)

Where Wc' and Q' are the desired system parameters.

When you cascade this electronic filter with the driver/box combination you're multiplying the two transfer functions together. The denominator of the speaker and the numerator of the filter cancel out entirely, leaving simply:

H(s)system = 1 / (s^2 + (Wc'/Q')s + Wc'^2)

You can see that you can choose Wc' and Q' to be whatever you want - there's no interdependence between them at all. Moreover, the parameters of the original driver and box aren't even present anymore, so they don't contribute at all.

What I'm wondering is if the mentioned interdependence is some kind of limitation with a common implementation of the LT. It's been a while since I designed my last Sallen Key filter so I can't say offhand...


(damn typos...)

[Daveis]

What does Linkwitz transform do to distortion (THD) measurements down low?

My gut says that you are operating the driver and amplifier much harder than normal so the distortion would have to go up.
But maybe the air damping starts to prevent that...

[Wingfeather]

Well, yes and no, I'd say.

Playing a sine wave at x Hz and y dBSPL out of a given driver/box system is going to require a certain amount of power and produce a certain amount of distortion. Whether you get up to y dBSPL at x Hz because of the LT or because you simply turned up the volume doesn't really matter.

Then again, if you're designing your system to use an LT from the outset (which you should be, really) then you may go with too small a box, reducing natural efficiency down low and thus requiring more power to actually reach y dBSPL at x Hz. In this case, the total system will probably have more distortion at LF than one without the LT, in a larger box.

The LT in itself is a low-level electronic filter (or a DSP filter) and isn't going to contribute very much (if indeed any) distortion of its own. The main worries with using one are either that input noise gets boosted a lot at LF or that you might end up with enough gain at the bottom end to clip things when playing back bass-heavy material.

[Guy Incognito]

Wingfeather,

I think you described it pretty well and linkwitz sums it up in a similar fashion:

A majority of drivers exhibit second order highpass behavior because they consist of mechanical mass-compliance-damping systems. They are described by a pair of zeroes at the s-plane origin and a pair of complex poles with a location defined by Fs and Qt. The circuit above allows to place a pair of complex zeroes (Fz, Qz) on top of the pole pair to exactly compensate their effect. A new pair of poles (Fp, Qp) can then be placed at a lower or a higher frequency to obtain a different, more desirable frequency response.

from http://www.linkwitzlab.com/filters.htm#9

So it seems you can place the poles either side of Fs (as already pointed out). I couldnt see any interdependence other than the restraints of equaliser voltage clipping and Xmax.


I know you can model excursion in CAD software but do you guys know the maths to do? Ive googled a fair bit and havent found much information. Its it a hard property to model?

I would like to model power consumption and excursion with an LT in a spreadsheet. So far ive only been able to find general relations:
For ever octave lower you need four times the excursion and sixteen times the power.....

cheers all

[Wingfeather]

I'm afraid I don't know the maths of it offhand. I'm pretty sure it's based on the T/S params of the drivers - from these you should be able to derive various aspects of performance. Presumably, the method is detailed in an AES paper from a while back. I'll have a look when I get the chance to see if I have it (I have access to a reasonably complete archive).

Alternatively, if the writers of such software as WinISD hang around here I'm sure they can give you far more information than me!