User Name Stay logged in? Password
 Home Forums Rules Articles Store Gallery Blogs Register Donations FAQ Calendar Search Today's Posts Mark Forums Read Search

 Multi-Way Conventional loudspeakers with crossovers

 Please consider donating to help us continue to serve you. Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
 9th October 2004, 08:40 PM #21 diyAudio Member     Join Date: Nov 2002 Location: Grenoble, FR I've got some doubts, too Sallen Key filters are sometibes described with this transfer function: 1/(1+j*1/Q*(w/wc)-(w/wc)²) with a butterworth filter's equation, I managed to find the same thing (and Q is 0.707, that seems correct) but with a bessel, whos equation is 3/(3+3*j*(w/wc)+(w/wc)²) , it doesn't seem possible to have something like the first equation neither with a chebyshev whos equation is 1/(1+e²(2*(w/wc)+1)²) I tried to solve those equation all day long; now it's time to relax and listen a few cds __________________ Just remember: in theory there's no difference between theory and practice. But in practice it usually is quite a bit difference... Bob Pease
diyAudio Member

Join Date: Aug 2004
Location: Behind you
Quote:
 Originally posted by Svante Are you taking about second order filter only? Otherwise, what is your definition of Q? I don't agree that Q is the usual way of describing the difference, I even think it is inappropriate.
Q = resonant magnification factor, i.e. the ratio of magnitude at resonance to that at infinty or zero (for high-pass and low-pass respecively).

You're right, defining the filter responses by Q only works well at 2nd order. With higher orders, assuming they are constructed from multiple 2nd order sections, each section may have a different Q. Although the Q of each section is still fixed for each filter response, it's no longer the simplest way of describing them.
__________________
https://mrevil.asvachin.eu/

 10th October 2004, 07:55 AM #23 diyAudio Member     Join Date: Nov 2002 Location: Grenoble, FR from what I've seen, for orders>2, you decompose them into multiples of 2nd and 1st orders the total Q is Q1*Q2*Q3*.... and must be equal to the Q you want (0.71 for butterworth) Someone found a way to write a bessel or chebychev like this? 1/(1+j*1/Q*(w/wc)-(w/wc)²) __________________ Just remember: in theory there's no difference between theory and practice. But in practice it usually is quite a bit difference... Bob Pease
 10th October 2004, 10:10 AM #24 diyAudio Member     Join Date: Feb 2004 Location: Stockholm Ok, let's go through this. -A first order filter is described by a f0 only. f0 is the frequency at which the asymtotes for very low and very high frequencies cross. -A second order filter is described by A f0 and a Q. The definition of f0 is the same as for the first order filter. The definition of Q can be the amplitude at f0. Other definitions exist, but they give the same numerical value for a given filter. -A third order filter is a first and a second order filter in series. This filter has two f0:s and one Q. This Q is not the amplitude at either f0, but the Q of the 2nd order section. - A fourth order filter is two 2nd order filters in series. This filter has two f0:s and two Q:s. Neither Q is the amplitude at either f0, but the Q of the 2nd order sections. -etc, etc... The bottom line here is that many filters (almost all crossover filters) can be decomposed into a cascade of 1st and 2nd order filters. Each of these sections have a f0, and each 2nd order section also has a Q value. Trying to describe filters of orders >2 with a single Q value is doomed to fail, and will only add confusion. In the light of this: All first order filters of a given f0 have identical transfer functions. Filters of any order >1 are commonly described by a f0 (which may be different from those of the subsections) and a "family name", eg butterworth, bessel etc. The f0 can be defined in different ways, two common ways are by the -3 dB point, or the frequency at which the high and low frequency asymptotes cross. If the filter does not fit a well defined family, it is preferrably described by the f0:s and Q:s of all the subsections. Again, a single Q value will not tell the whole story except for the 2nd order filter. Butterworth filters have sections with identical f0:s, but different Q:s. These filters are 3 dB down at the asymtotic f0. Linkwitz-Riley filters are two cascaded butterworth filters and are therefore always of even order. These filters are 6 dB down at the asymtotic f0. Bessel filters filters have cascaded sections with different F0:s and Q:s. These filters are typically more than 3 dB down at the asymtotic f0. Tjebychev filters have cascaded sections with different F0:s and Q:s. These filters are designed to have a "ripple" of x dB in the pass band, and the f0 is usually defined as when the response goes below x dB. This f0 is lower than the asymtotic f0. For crossover filters, Butterworth filters produce a flat sum if and only if the filter is odd order, Linkwitz-Riley filters produce a flat sum for even orders. Bessel and Tjebychev filters do not produce a flat sum, so they are not principally interesting for crossover filters. PS. When I speak of cascaded filter sections, I think of active filter sections, where there are no interaction effects between from loading the previous section. HTH __________________ Simulate loudspeakers: Basta! Simulate the baffle step: The Edge
 13th October 2004, 02:56 PM #25 diyAudio Member     Join Date: Feb 2002 Location: The Netherlands (Friesland) Thank-you for the useful informative post Svante. __________________ We will pay the price, but we will not count the cost...
diyAudio Member

Join Date: May 2002
Location: Switzerland
Quote:
 Bessel and Tjebychev filters do not produce a flat sum, so they are not principally interesting for crossover filters.
2nd order Linkwitz is actually a 2nd order Bessel (with both branches having the same POLE frequency) with one driver wired out of phase.

Regards

Charles

 13th October 2004, 03:39 PM #27 diyAudio Member     Join Date: Jun 2002 Location: USA, MN phase_Accurate wrote: Just one addition: 2nd order Linkwitz is actually a 2nd order Bessel (with both branches having the same POLE frequency) with one driver wired out of phase. ------------------------------------------------- I don't think this is accurate. Bessel is a 2nd order TF with a Q of 0.577 and it is essentially a compromise between Butterworth and LR2. It has a compromise peak in amplitude to get a lower dip in power response. Butterworth Q=0.707 is -3dB at Fc and has a 3dB peak in the vector sum when both sections are at the same frequency, but has flat power response. LR2 is a Q of 0.5 and is -6dB at Fc and sums flat, but has a dip of 3dB in power response. People still argue whether on axis frequency or power response is important. There are pros and cons, but on axis frequency response is more important unless the environment is very reverberant. Getting hung up on alignments is not very useful, though. What we want is a flat sum and good off-axis behavior. Whatever gets you to that target on budget is what works. __________________ Our species needs, and deserves, a citizenry with minds wide awake and a basic understanding of how the world works. --Carl Sagan Armaments, universal debt, and planned obsolescence--those are the three pillars of Western prosperity. —Aldous Huxley
 13th October 2004, 04:40 PM #28 diyAudio Member     Join Date: Nov 2002 Location: Grenoble, FR I think I just have one thing to add to Svante's post Svante, you say that defining a >2 order filter with only one Q is wrong, but I'm not sure about that. Imagine a 4th order L-R. It's 2 Butterworth in series a LR's Q is 0.5 a Butterworth's Q is 0.707 0.707*0.707=0.5 so I think you can also put a Q=1 and Q=0.5 in series, that will end in a LR4 But this is yet to confirm __________________ Just remember: in theory there's no difference between theory and practice. But in practice it usually is quite a bit difference... Bob Pease
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Quote:
 Originally posted by Ron E phase_Accurate wrote: Just one addition: 2nd order Linkwitz is actually a 2nd order Bessel (with both branches having the same POLE frequency) with one driver wired out of phase. ------------------------------------------------- I don't think this is accurate. Bessel is a 2nd order TF with a Q of 0.577 and it is essentially a compromise between Butterworth and LR2. It has a compromise peak in amplitude to get a lower dip in power response. Butterworth Q=0.707 is -3dB at Fc and has a 3dB peak in the vector sum when both sections are at the same frequency, but has flat power response. LR2 is a Q of 0.5 and is -6dB at Fc and sums flat, but has a dip of 3dB in power response.
I was just about to say something similar. I think your Q's are right, Ron, but that you can say nothing about the power response in general. The power response will depend on the distance between the drivers, in relation to the wavelength at the crossover frequency. What you can say, though is that LR with swapped polarity on one driver is the only configuration that produces flat on-axis response (for 2nd order, given ideal drivers)

Quote:
 Originally posted by Bricolo I think I just have one thing to add to Svante's post Svante, you say that defining a >2 order filter with only one Q is wrong, but I'm not sure about that. Imagine a 4th order L-R. It's 2 Butterworth in series a LR's Q is 0.5 a Butterworth's Q is 0.707 0.707*0.707=0.5 so I think you can also put a Q=1 and Q=0.5 in series, that will end in a LR4 But this is yet to confirm
1+0.5 will not yield the same transfer function as 0.7+0.7. It is true that the amplitude at fc will be the same, but to the sides of fc, the responses will differ. The bottom line is, the definition of Q is not the level at fc, unless the filter is 2nd order. So 1+0.5 is not LR.
__________________
Simulate loudspeakers: Basta!
Simulate the baffle step: The Edge

 14th October 2004, 04:54 AM #30 diyAudio Member     Join Date: Nov 2002 Location: Grenoble, FR After looking at some exemple values; it seems you're right. The total Q is still the same as the 2nd order equivalent, but there's a defined order for the intermediate Qs LR is made of cascaded butterworth. But I've seen 2nd order LR, how are they made? __________________ Just remember: in theory there's no difference between theory and practice. But in practice it usually is quite a bit difference... Bob Pease

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post MarcMTL Multi-Way 41 23rd September 2008 05:47 PM jackinnj Multi-Way 17 14th March 2006 11:50 PM metal Chip Amps 1 26th June 2004 08:48 PM squidbait Multi-Way 7 7th April 2004 04:18 PM

 New To Site? Need Help?

All times are GMT. The time now is 06:26 AM.