[Bigus]

Another subject I need some polishing on. I understand the basics of how low pass and high pass work, how either can be done with inductors or capacitors (or both), and how "order" relates to slope.


I'm not at all sure what a Linkwitz-Riley transform function is or does though, and the use of "electrical crossover" and "acoustical crossover" in another thread had me scratching my head and thinking perhaps some expanding of my education is in order.


Other issues I know that I don't know... um, yeah... are how different crossover designs, including passive, analog active, and digital deal with phase issues. I'm reading Everest's master handbook of acoustics now, but I'm not sure if it's going to go very in depth into those topics.


Any useful comments, be they explanations or pointers to good reference material (that isn't insanely technical - I only had a couple of EE courses in my formal education)?

 

[hwc]

A Linkwitz-Riley 4th order crossover is two 2nd order Butterworth filters wired in series. You get a 24 dB per octave slope with -6dB point at the crossover frequency.


It is named after an HP engineeer named Sigfried Linkwitz, who has published many papers on mathematical modelling of filters that built upon the work that Thiel and Small did on mathematical modeling of speaker tuning.


The reason that 4th order Linkwitz-Riley crossovers have been so popular with high-end speaker designers for the last 25 years is that the drivers are in-phase across the crossover region, as opposed to a 2nd order Butterworth that has 180 degrees of phase shift.


When implemented digitally, the low-pass Linkwitz-Riley filter is simply two 2nd order digital Butterworth filters in series. Howver, the high-pass side in a Dolby Digital system follows the THX practice of using an electrical 2nd order Butterworth as half of the crossover. The second "2nd order Butterworth" is supplied "acoustically" by the natural rolloff of an acoustic suspension bass driver (q=.707) -- which just happens to roll off with exactly the same slope and curve shape (mathematically) as a 2nd order Butterworth high pass. Add the acoustic slope and the electrical slope and you get a 24 dB/octave high pass filter.


This means that, ideally, you would like your main speakers to have a q=.707 and be -3 dB at the crossover frequency.


The Linkwitz Transform function is another use of the mathematical models developed by Sigfried Linkwitz. It is basically a 4-pole shelving bass boost filter used to correct the roll-off characteristics of any sealed box woofer and replace them with new rolloff characteristics of a new target response. Two poles of the filter are used to correct the Q and roll-off of the existing woofer. Two poles are used to achieve a new Q and new -3dB point. For example, you could take a woofer in an undersized sealed cabinet with peak in the response and a -3dB point of 50 Hz and turn it into a low-Q woofer with a -3dB point of 30 Hz (if you have the amplifier power and driver excursion).


Sigfried Linkwitz has an incredible website that gives a good idea of the mathematical models that he has developed. His work, along with that of Thiel and Small, have really revolutionized speaker design by allowing very accurate computer modeling of speaker and crossover performance.

www.linkwitzlab.com

 

[Bigus]

Cool, thanks for the explanation.


Is the Linkwitz-Riley crossover the only design that has no phase shift across the crossover region?


What is the practical difference between a linkwitz transform function filter, and using parametric EQ to fix roll-off characteristics? You said the transform function can also modify the system Q... does EQ do that?

 

[hwc]

I don't know enough about crossovers to use the word "only". Let's just say that since Linkwitz published his Society of Audio Engineering papers on crossovers in the mid-1970s, Linkwitz-Riley crossovers have been very popular among pricier speaker brands.


The Linkwitz Transform Function is a shelving bass control. Instead of boosting symmetrically around a particular frequency, it boosts all frequencies below a particular frequency. It basically behaves like a low-pass filter.


One thing that makes it very useful is that it is the exact inverse of the curve the determines the roll-off characteristic of sealed box woofers.


The other thing is that it is a mathematic model with four parameters. When you model a woofer using the Thiel-Small parameters, you get two key numbers: the "Q" of the total system (the shape of the roll-off) and the "F" of the total system (frequency). You can plug these two numbers directly into the mathematic model as two of the four parameters and determine the resistor and capacitor values to cancel these characteristics. Then, you plug in the target "Q" and "F" for the desired result and the math models tell you the capacitor and resistor values you need.

 

[Bigus]

That sounds pretty interesting. In an ideal room with perfect or near perfect acoustical properties, that would be really great. It would seem that in a typical room with typical modal problems a parametric EQ might be more capable of giving a near flat frequency response. Perhaps the combination of the two would be appropriate... transform for general response shaping, and parametric control to treat peaks.


One other question: can the 24dB/octave Linkwitz crossover be used in both passive and active designs?

 

[hwc]

Quote:

Originally posted by Bigus That sounds pretty interesting. In an ideal room with perfect or near perfect acoustical properties, that would be really great. It would seem that in a typical room with typical modal problems a parametric EQ might be more capable of giving a near flat frequency response.

The Linkwitz Transform Function is not intended to address room response issues. It's designed to replace the low frequency characteristics of any real seal box system with any desired low freq. characteristics.


A graph is worth a thousand words. On the following web page is a sample graph:

http://www.marchandelec.com/wm8.htm


The trace "A" is the actual response of the woofer, which can either be measured or simply derived by plugging two Theil-Small parameters and the size of the box in a spreadsheet. This particular speaker is an undersized sealed enclosure (think Sunfire or some of the very small box B&W subs). It has a Q of 1.4 -- the big bump in the bass response. It would be boomy and poorly damped.


Trace B is the eq curve. Note that it completely cancels the peak in the original woofer and extends the bass response by nearly two octaves.


Trace C is the final response curve. In this case, the target appears to be Q=.707. However, you could also adjust this final curve to for Q= .5 which will give perfect transient response with no ringing.


This example is fairly extreme. In the real world, the 24 dB of boost required to extend the bass by two ocataves would be excessive. This would most likely drive any woofer into its excursion limits. But, used more judiciously (6 to 12 dB of boost), you can extend the bass response by half an octave to a full octave).

Quote:

One other question: can the 24dB/octave Linkwitz crossover be used in both passive and active designs?

Yes. You can use either passive or active. However, active crossovers are vastly superior. All mathematic models of crossovers assume a constant impedance of the drivers. But, real woofers vary from 3 ohms to perhaps 20 ohms depending on frequency. So it's really difficult to make a real crossover match the models. You've got to add impedance compensation circuists and, still, the best you can come up with is an approximation fo what you ideally want. With an active crossover, the impedance the crossover sees is the input impedance of the amplifier, which is nearly constant.


Plus, when you clip the bass amplifier in a bi-amped system, it does NOT distort the midrange and high frequencies. In fact, you may not even be able to hear clipping. In a full range system with passive crossovers, every time you clip a bass note, distortion products are sent to the midrange and tweeters. This is what makes clipping sound so bad and it's also what blows up tweeters.