Linkwitz Transforms

Discussion in 'Home Theater Projects' started by Allen Ross, Jul 9, 2003.

  1. Allen Ross

    Allen Ross Supporting Actor

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    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
     
  2. RichardHOS

    RichardHOS Second Unit

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    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.
     
  3. Mark Hayenga

    Mark Hayenga Supporting Actor

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    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 [​IMG])

    Hey, I see a lot of DIY in here, I figured I'd give it a shot of 'Advanced' too [​IMG]
     
  4. Allen Ross

    Allen Ross Supporting Actor

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    hehehehe


    Q
    How does it work?

    A
    Magic



    i love it [​IMG]
     
  5. Mark_J_H_Jr

    Mark_J_H_Jr Stunt Coordinator

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    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?
     
  6. Jack Gilvey

    Jack Gilvey Producer

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  7. Brian Bunge

    Brian Bunge Producer

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  8. Dave Milne

    Dave Milne Supporting Actor

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    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?

     
  9. RichardHOS

    RichardHOS Second Unit

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    No, it's not impossible, but that flat response might occur at 50dB. [​IMG]
     
  10. Brian_DR

    Brian_DR Extra

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    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
     
  11. Allen Ross

    Allen Ross Supporting Actor

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    okay so i now know what they are, how do i calibrate it to a given box dimension? computer program? or freaky math by hand?

    Anyone got a link for the variable LT?
     
  12. RichardHOS

    RichardHOS Second Unit

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    Nice excel sheet to calculate LT values for a particular driver, enclosure, and desired response. Courtesy of Rod Elliot - hope he doesn't mind me direct linking to his downloads.

    Since I did, I'll give a plug for him and point out that he has PCB's available for a very low cost to build your own LT, complete with very detailed instructions on how to finish the project.
     
  13. Allen Ross

    Allen Ross Supporting Actor

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    okay so you can build one just like a cross over nice

    what site does Rod have, and how can i contact him?

    Anyone got a price for how much there's cost?
     
  14. Dan Wesnor

    Dan Wesnor Second Unit

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  15. Jack Gilvey

    Jack Gilvey Producer

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    Here's my favorite LT design program:

    http://www.pvconsultants.com/audio/eq/linktran.htm

    To Dan's point, it's amazing to watch the power requirements for a given frequency and SPL go up as you change Vb.

     
  16. Brian Bunge

    Brian Bunge Producer

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    Jack,

    I've noticed power requirements vary greatly when you hold everything constant except your resultant Q.
     
  17. Allen Ross

    Allen Ross Supporting Actor

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    WM8-B BASSIS single bare board with manual $ 20.00
    WM8-K BASSIS single board kit with manual and all parts $ 70.00
    WM8-A BASSIS single board fully assembled and tested $ 90.00
    WM8-KK BASSIS full kit with cabinet, stereo, power supply, etc $ 299.00
    WM8-AA BASSIS fully assembled in cabinet $ 499.00
    WM8-C BASSIS custom cabinet only $ 60.00
    WM8-EZK EZ Kit with manual and all parts $ 399.00

    sweet for 70 buck i get a nekid LT [​IMG] and another project


    oh wait i don't even have a sub that i need this for :b
     
  18. Jack Gilvey

    Jack Gilvey Producer

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  19. RichardHOS

    RichardHOS Second Unit

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    Allen, the first link I provided in my first post in this thread takes you directly to the LT portion of Rod's site. There's a link at the top of the page that takes you to the PCB section. The raw LT PCB is $15, and you'll need to put together a cheap power supply to power it.
     
  20. Allen Ross

    Allen Ross Supporting Actor

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    whoa even better, now to find a sub that i can use this on [​IMG]


    ahh the projects they pile up, i already have two pairs of monitors in the works, an speaker selector, and possible another pair of monitors and yet another sub [​IMG]

    who says this isn't addicting [​IMG]
     

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