dlin@prodigal.psych.rochester.edu (Daniel Lin) (01/23/91)
I am in the process of designing a crossover for a three way speaker system and have come across a problem concerning the proper crossover point. According to Weems' book on speaker building, the crossover frequency is defined as the frequency at which the output of a given driver is reduced by 3 dB. Weems then goes on to present formulas to determine the required components for that crossover frequency(i.e. both drivers are 3 dB down at the desired crossover frequency). However, other articles concerning proper crossover design have stated that both drivers should be 6 dB down at the crossover frequency in order to achieve a flat summed response at that frequency. Is there a contradiction here? If there is, which one is correct, and how does one determine the proper components for the crossover? Any tips concerning these questions would be greatly appreciated. Daniel Lin University of Rochester
hull%janus.Berkeley.EDU@ucbvax.Berkeley.EDU (Christopher Hull) (01/25/91)
In a x-over design it is neccessary that the vector sum of the acoustic pressures from the drivers be equal to 1. If the drivers are in phase than that implies that they are 6db down each (as in Linkwitz 2nd & 4th order x-overs). However for 1st & 3rd order butterworth x-overs, the drivers are in phase quadrature (90 degrees out of phase) and thus each driver is only 3db down at the x-over frequency. For x-over designs with even more phase difference it may be necessary for each driver to have full output at the x-over frequency (e.g. the "Quasi" second order filter). There are a number of design considerations that must go into choosing the x-over. For example, driver quality, actual x-over freuquncy, power level required, cost etc. Each x-over has a different set of trade offs. First order x-ovvers will only work with widenband drivers and are best for multi-way systems. Higher slope x-overs are expensive, tricky to build, but will allow use of fewer drivers over a wider bandwidth /driver. For two way sytems you may want to use 3rd or 4th order networks. For three way sytems first or second order networks will suffice. For four way sytems generally use first order networks. Also, their is the Bessel type network used in the Spica Tc-50 , which I have used myself. It is 4th order on low pass, and only first order on high pass. Chris Hull < hull@janus.berkeley.edu>
jroth@allvax.enet.dec.com (Jim Roth) (01/25/91)
-Message-Text-Follows- In article <9101@uwm.edu>, dlin@prodigal.psych.rochester.edu (Daniel Lin) writes... > Weems then goes on to present formulas to >determine the required components for that crossover frequency(i.e. both >drivers are 3 dB down at the desired crossover frequency). >However, other articles concerning proper >crossover design have stated that both drivers should be 6 dB down at the >crossover frequency in order to achieve a flat summed response at that >frequency. Is there a contradiction here? If there is, which one is >correct, and how does one determine the proper components for the >crossover? Any tips concerning these questions would be greatly >appreciated. This is a complicated issue that I can't really do justice to in a simple reply. But basically it depends on what type of crossover filter and the relative phases of the signals sent to the drivers at the crossover point. For example, if you use 3'rd order Butterworth filters, then they should be 3 dB down at the crossover frequency so that the summed power response on axis will be flat - the signals will be 90 degrees out to the drivers at the crossover point. On the other hand, a Linkwitz-Riley (cascaded Butterworth filter) crossover keeps the signals sent to the drivers in phase at all frequencies, so the -6 dB figure is correct. The advantage here is a better behaved polar response. Even this is oversimplifying things becasue you have to take into account the acoustic response of the drivers, as well as their electrical impedances (if a passive crossover is being developed) and modify the filter shapes and component values accordingly. It's not so simple when you "reduce it to practice". If you use the network and equations in Weems' book, presumably they will be for a nominal crossover phased 90 degrees at the crossover point. A really good way to learn more is from the Speaker Builder magazine, as well as the loudspeaker article anthologies available from the Audio Engineering Society. - Jim
dlin@prodigal.psych.rochester.edu (Daniel Lin) (01/28/91)
This business of designing a crossover is getting more and more confusing as I read into the literature. Many of the recent articles concerning crossover design in Journal of the Audio Engineering Society have focussed on high order crossovers, while providing little or no information on the optimization of "simple" first order designs. My initial query regarding the optimum crossover frequency required to obtain unity reponse at the desired frequency was answered (thank you) but several questions remain. Assuming that one is interested in designing an all first order network for a three-way speaker system utilizing "ideal" drivers- that is, the drivers are well behaved beyond their pass bands, show a smooth change in directivity across frequencies, and are free of contributions from the cabinet (e.g. diffraction loss). The literature suggests that equations used to determine low and high pass filter componenets cannot be applied to design the bandpass filter due to interactions between components. What kinds of calculations are required to determine the necessary adjustments? Are any adjustments needed for woofer's low pass or the tweeter's high pass crossover values? I suppose that once these questions are answered, I'll have to return to real world conditions to begin to optimize around driver limitations and cabinet effects. Thank you for your comments. Daniel Lin University of Rochester
jj@alice.att.com (jj, like it or not) (01/30/91)
In article <9172@uwm.edu> dlin@prodigal.psych.rochester.edu (Daniel Lin) writes: > > Engineering Society have focussed on high order crossovers, while > providing little or no information on the optimization of "simple" > first order designs. There are a few reasons for this. First, since the excursion of a driver falls off with the second derivitive, i.e. with f^2, you will find, in general, that you get insufficient excursion control with a first order high-pass filter. This can cause both bad sound (modulation by driver saturation or non-linear excursion at lower frequencies than you expect) and driver damage. > Assuming that > one is interested in designing an all first order network for a > three-way speaker system utilizing "ideal" drivers- that is, the > drivers are well behaved beyond their pass bands, show a smooth > change in directivity across frequencies, and are free of This means that all your drivers need to extend about 3 octaves beyond the cutoff frequency you've chosen. This is going to be a tough problem. What is the input characteristics of those drivers across the same frequency range going to be like, too? > The > literature suggests that equations used to determine low and high > pass filter componenets cannot be applied to design the bandpass > filter due to interactions between components. This is quite true, unless you figure the (complex) impedence of the driver into your equation. You will find out very quickly that you will then have no first-order functions anyhow. For instance, let us assume you use a direct-series-capacitor for a high-pass filter. Assuming you do this, what is the response of the system near the resonant point of the tweeter? It's WELL above what you expect, because of the order-of-magnitude peak in the magnitude of the tweeter impedence. Many, MANY first-order crossover designers haven't taken this into account, and have had nasty nasty peaks just below the crossover frequency. Now, given some need for efficiency equalization, this can be mitigated by absorbing most of the energy in the resistive pad, BUT you have to think of that first, and have appropriate efficiencies for your driver+box combo. > What kinds of > calculations are required to determine the necessary adjustments? It's not easy to say. Each type of driver (sometimes with drivers with bad QC, each DRIVER) has different characteristics. Furthermore, it's very hard to come up with an analytic model (pole/zero) for most drivers, because of the many delay components and non-linearities that are present, even if you have the appropriate equipment and necessary math calculation abilities. (And these are not easy to come by, either, nor are they cheap. In addition, you will have to decide level and frequency content for the model's applicibility, because you will find that drivers are (*&(*& non-linear.) > Are any adjustments needed for woofer's low pass or the tweeter's > high pass crossover values? Typically, the inductor for the woofer will need to be slightly larger thanyou expect, and the cap for the tweeter will be substantially smaller. These statements, however, are subject to much, MUCH qualification!!!! You'll be better off measuring SPL individually at each driver and then in sum, and making a guess as to what's happening, I suspect. > I suppose that once these questions are answered, I'll have > to return to real world conditions to begin to optimize around > driver limitations and cabinet effects. I think you'll find your life quite difficult. The design of passive high-level crossovers is by no means reduced to any reliable process. The loads for the crossovers are quite idiosyncratic, the parts accuracy is low, the manifacture of accurate parts is tricky, and so on. I've been predicting for years that people will start making integrated amplifier/speakers, with all the filtering done passively. So far, the integrated (circuit) amps aren't quite good enough (although they COULD be, the manifacturers don't see their market in quality), and the engineering (although well known and understood) hasn't been present in a place where it can be sold. -- -------->From the pyrolagnic keyboard of jj@alice.att.com<-------- Copyright alice!jj 1990, all rights reserved, except transmission by USENET and like free facilities granted. Said permission is granted only for complete copies that include this notice. Use on pay-for-read services specifically disallowed.
bill@vrdxhq.verdix.com (William Spencer) (01/30/91)
in article <9136@uwm.edu>, jroth@allvax.enet.dec.com (Jim Roth) says: > For example, if you use 3'rd order Butterworth filters, then they should > be 3 dB down at the crossover frequency so that the summed power response > on axis will be flat >From what I see in the common literature, this is not right in two ways. It's the summed pressure response (=voltage response), not the power. That does _seem_ wierd that power doesn't add. But the other problem is that "power response on axis" seems to be a non-concept. Power response controls the total energy in the room -- the response in a reverberant field. (Is there an acoustical law for this?) > - the signals will be 90 degrees out to the drivers > at the crossover point. Yes. Therefore at some angle relative to "on axis" the difference in delay between drivers results in in-phase operation and a 3 dB peak. The "polar tilt". > On the other hand, a Linkwitz-Riley (cascaded Butterworth filter) crossover > keeps the signals sent to the drivers in phase at all frequencies, so the > -6 dB figure is correct. You're presuming even order, which is of course the reason for the L-R. The combination of both drivers produces constant pressure on axis using half the power. But where does this increased "efficiency" come from? Yet we see the total energy in the room is the summed power response. Evidently this "increased efficiency" is not really that, it's a directional thing. The even-order can not be constant power and constant pressure at once, but the odd-order can. How? That polar peak off-axis adds more energy to the room. My understanding of all this is sketchy, but it's the result of other experts avoiding the subject entirely of trying to put together the pieces and explain what's really going on. Comment or clarifications? dlin@prodigal.psych.rochester.edu (Daniel Lin) writes... > The literature suggests that equations used to determine low and high pass filter componenets cannot be applied to design the bandpass filter due to interactions between components. What kinds of calculations are required to determine the necessary adjustments? Are any adjustments needed for woofer's low pass or the tweeter's high pass crossover values? Try Bullock's article in Speaker Builder 2/85 or the Loudspeaker Design Cookbook. The SB article may give you more options. From: jj@alice.att.com (jj, like it or not): > Anyone seriously considering "real" bi-amping >(which means a low-level crossover in front of the amps) >should probably look into various asymetric designs for >crossovers. Is there a way of explaining how these result in flat response other than the equations? Obviously I can see the equations sum. So what? That's _not_ understanding. >Which, you note, adds up to 1, with no phase-problems, >and no amplitude problems. What's the off-axis response? (Genuine interest, I don't know) Total phase shift? (see below) ----- Okay, with odd order crossovers you can connect drivers in either polarity. Does anyone want to volunteer which they think is better? I can see a few things. You can try both and see which compensates better for nonperfect drivers. The delay between drivers and the preferred up or down polar tilt can be considered. If the reverse polarity connection is chosen, which driver gets reverse absolute polarity? Seems that this depends on crossover frequency. However, also seems wierd that subwoofers could end up out of phase by this logic, I know they are in some designs. (This question applies to second order xovers also). In phase connection avoids this previous question. However, out phase suits typical quasi-first order designs due to the extra phase shift of the driver (not in all cases). With third order things get more complicated. In phase connection results in 360 degrees of phase shift going through crossover, not zero. So, a very complicated decision results, at least on principle. Luckily (?), most peaple claim the difference is inaudible. Due to the presence of the other considerations listed above, it's hard to truly test this factor in isolation. So, some answers and some questions. Let's get a discussion going. Bill Spencer
bill@vrdxhq.verdix.com (William Spencer) (02/01/91)
in article <9226@uwm.edu>, jj@alice.att.com (jj, like it or not) says: > In article <9172@uwm.edu> dlin@prodigal.psych.rochester.edu (Daniel Lin) writes: >> The >> literature suggests that equations used to determine low and high >> pass filter componenets cannot be applied to design the bandpass >> filter due to interactions between components. > This is quite true, unless you figure the (complex) impedence of the > driver into your equation. You will find out very quickly that > you will then have no first-order functions anyhow. [etc.] I believe you are answering a different question here. He (and Bullock) are saying a 3-way is not the same as two 2-ways in cascade. The crossovers interact with each other. (I'd like an explaination of why this happens, I don't get it, partially because I've stuck with 2-ways.) Anyway, good explaination of the need for impedance compensation or other techniques. Cookbook techniques for impedance compensation are availiable. With an oscilloscope and a sine wave generator you can experiment to further flatten impedance magnitude and phase. Connect a resistor, say 50 ohms, 10W between amp and the driver/compensation load. Changes in the load impedance will change the voltage response. >You'll be better off measuring SPL individually > at each driver and then in sum, and making a guess as to > what's happening, I suspect. It's also a good idea to check your transfer function at the driver terminals with that sine wave and 'scope. You will need to know what rolloff rate and phase characteristic to expect. > I've been predicting for years that people will start making > integrated amplifier/speakers, with all the filtering done passively. Not biamped? And you have to plug the speakers into the wall? Humm. I do think that for bi-amping to catch on some kind of standard is needed. Maybe amps with slots for crossover cards or something. Or ROM cards and digital crossovers! I can't believe I just wrote that :-). Digital does seem more illuminating when it replaces as much of the analog as possible. Even digital amps, but coming up with an amp that really uses digital to advantage requires some new approach. The digital could be used as an input to the power supply to intelligently prepare for transients, for example. Bill Spencer
michard@nuri.inria.fr (michard alain rsi) (04/29/91)
Could anybody give me a pointer to a document (book, article in a journal) which could be available in Europe, describing precisely 3-ways crossovers ? I need information about advantages and drawbacks of the various possible designs (Linkwitz,..) and the formulas that I can use to compute the value of the components. I have found in France a book on speaker design, with a good complete description of 2-ways crossovers, but for 3-ways the author just says that it is too complicated, and that readers should refer to directions-for-use published by loudspeaker manufacturers. A bit too short for someone who wishes to design his own speakers... Thanks for the help. Alain Michard I.N.R.I.A. - Domaine de Voluceau - BP 105 78153 LE CHESNAY - FRANCE michard@nuri.inria.fr