Linkwitz Transforms

Allen Ross · 07-09-2003, 09:53 PM

okay i have seen these mentioned with sealed subs, like so.

I am just wondering what they do, if my memory is correct it lowers the FS and something else.

Can a BFD do the same thing? i guess it couldn't if it isn't eqing it. How is it implemented?

So let me have all the juicy details on them cause i am thirsty for knowledge, thanks in advance

RichardHOS · 07-09-2003, 11:24 PM

A linkwitz transform is a way to electrically alter the final system Q and frequency response. It is an EQ of sorts... a specialized EQ designed specifically to counter the rolloff curve of a driver in a sealed enclosure.

I think a BFD (if it could cover low enough freuqencies, which it can't) type of EQ with appropriate filters could approximate a LT decently.

Read more about it here, here, and here.

Mark Hayenga · 07-10-2003, 01:25 AM

The frequency response of a subwoofer is defined by its transfer function. For a sealed subwoofer system, a transfer function is derived by analyzing the mass-spring-compliance system formed by the woofer/box combination. In the case of a sealed box, this mass-spring-compliance system is described by a second order differential equation. When you solve the differential equation using a mathematical technique called a Laplace transform, you can get a function that is the ratio of the system output (sound) to the system input (voltage), and express this ratio as two polynomials - one numerator polynomial and one denominator polynomial. If you factor these numerator and denominator polynomials, you end up with a product-of-sums representation for each. The individual 'sum' terms in this form define what are called the 'poles' and 'zeros' of the transfer function. The terms in the denominator define the poles, and these are what have the most effect on the frequency response of your subwoofer (in subwoofers, the numerator terms give zeros that all happen to be co-located at the origin of the s-plane for any subwoofer alignment you would want to build). So, to change the frequency response of the subwoofer, you have to change the location of its poles. A Linkwitz Transform circuit completely cancels out the effect of the natural system poles by making a filter that has the poles of the natural subwoofer transfer function as its zeros (ie the denominator of the subwoofer transfer function becomes the numerator of the Linkwitz Transform circuit). The Linkwitz Transform circuit uses as its denominator some made-up polynomial which just so happens to give your subwoofer that wonderfully flat, extended response you really wanted. Cascade the two and you get your final frequency response. Translate these numbers all back into electrical component values for an active circuit, and you can have a 15" subwoofer in a 5 liter cabinet that's flat to 0.1Hz if you so desire (theoretically, at least

)

Spoiler:

Allen Ross · 07-10-2003, 08:14 AM

hehehehe

Q
How does it work?

A
Magic

i love it

Mark_J_H_Jr · 07-10-2003, 11:39 AM

Mark,

Great explanation. I wish I had you to explain Laplace transforms when I was in school. I got the definition of a Laplace transform as, "serves as a device for simplifing the solution of ordinary and partial differential equations."

Then you somehow got some sort of 1/s and 1/s-a type solutions and were in another domain.

I never figured out how you went from one domain to another. Glad I don't have to worry about that anymore.

So without too much theory, is the LT circuit fixed or is it variable and you match it to a specific sub?

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Jack Gilvey · 07-10-2003, 11:59 AM

Quote:

So without too much theory, is the LT circuit fixed or is it variable and you match it to a specific sub?

Check out the links above. It's variable in that the component values are determined by the existing and desired Qtc and Fc.

Brian Bunge · 07-10-2003, 12:01 PM

Quote:

So without too much theory, is the LT circuit fixed or is it variable and you match it to a specific sub?

Mark,

The answer is...YES!

Most LT's are designed and matched to a specific driver/enclosure combo. But Marchand also sells the BASSIS, which is a variable LT.

If you ever get your sorry ass back to GA maybe you can come by and hear my Tumult with LT!

Dave Milne · 07-10-2003, 10:55 PM

Mark H

Nice explanation. So does it follow that one could make a "vented box LT" with four zeroes to cancel the four natural poles and four new poles to define the desired response?

Quote:

you can have a 15" subwoofer in a 5 liter cabinet that's flat to 0.1Hz if you so desire

Darn it that the real world physical limitations on amplifier power and driver excursion make this impossible.

RichardHOS · 07-10-2003, 11:46 PM

No, it's not impossible, but that flat response might occur at 50dB.

Brian_DR · 07-11-2003, 12:09 PM

Sometime it is not necessary to move all four poles in vented box or PR. First, a vented box/PR need 6th order roll-off to limit the excursion below box resonance freq. So it's not like in sealed box where you want to extended far below the box resonance freq. Second, for small box, those 4 poles most likely will split. That means one pair is located above box resonance frequency and one below.That is why those subwoofers may sound less bass. For comparison, Butterworth 4th order has all 4 poles located at the same frequency (ie box resonance frequency), but with different Q. Therefore, the task of LT is to move the pair above down to box resonance frequency. For us, we recommend using our extension filter as the extra 2 poles set to box resonance frequency so that the overall response is 6th or pseudo 6th (if the pair below resonace frequency is too far down). The advantage is the Q value can be now adjusted with this extension filter.... Everything plays very well.

Brian D.

Rythmik Audio