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  • #31
    Re: 6Db. crossovers????

    Originally posted by moron#99 View Post
    in this example the bessel is a highpass. your computer models should work out fine if you compare something like a 34hz second order butterworth to a 35hz third order bessel.

    No,no, no. You said you added a pole to the B2 HP (woofer) response. So the poles of the B2 remain fixed. So you are just cascading the B2 HP with a B1 HP to add the third pole. This will not ever yield a Be3 as the other point I was going to make was that a Be3 HP does not have poles at +/- 45. They are at +/-43.65. So adding a single pole doesn't result in a Be3 HP. Close, but not a BE response. You would need to shift the poles of the woofer alignment too by adding a zeros to cancel the existing poles and then new poles as required. By the way, the topic of canceling zeros and poles with poles and zeros was covered in my text books from back in 68. If they aren't teaching that at GT they must be slacking off.

    And again, you must be thinking of impulse response, not square wave. Further more, the truth is that the impulse response of a 3rd order Bessel HP will ring more than a 2nd order Butterworth HP, though neither is significant.

    Your 2nd to 3rd order conversion, as you are applying it is nothing more than cascading a B1 with a B2.

    Now, all these responses are under damped and therefore the impulse response is a damped oscillation that decays exponentially as time goes to infinity. It is not 2 cycles or 3 cycles. Further more, the true B3 as well as the B2 cascaded with a B1 initially undershoot and then overshoot more than the B2. I.e. they ring more than the B2.
    John k.... Music and Design NaO dsp Dipole Loudspeakers.

    Comment


    • #32
      Re: 6Db. crossovers????

      Originally posted by Pete Basel View Post
      There's an old saying that you'll learn is very true as time goes on, new ideas have most often already been invented, not always but most of the time. This is not to discourage you from coming up with new ideas, just do the background research to be sure and you'll probably learn more along the way.

      What you're suggesting has been covered in concept at least and for speakers by the Linkwitz Transform (LT). The LT has been around for over 30 years, the theory much longer than that. Further, any minimum phase EQ that reshapes a transfer function accomplishes what you are describing. The key point is that individual drivers are minimum phase systems, and if you apply minimum phase EQ matching the amplitude response to a new target, it will also have the same phase and transient response as the target. This has been known for a very long time, I would not doubt for 100 years or more. This is all basic theory behind signal processing - my graduate work was in analog and digital signal processing. Believe me there is much more advanced material than what you are describing.
      Linkwitz is after my time. He isn't mentioned in any of my old books or papers. I'll have to look go to the librabry and look for a book.

      I suspect what I am doing is a subset of his work in a more cookbook fashion. I am simply taking a polynomial and splitting it into two halves. Output = speaker * network. I know in advance that I want a bessel and therefore I can pick in advance a speaker alignment that results in the easiest possible network. two of the poles lines up by design and the "linkwitz filter" (?) ends up being as simple handful of passive components.

      i built and tested three different versions before quitting audio for computers. it was not a fancy test facility. spectrum analyzer, pink noise, a mic, a square wave, and a scope in the middle of a big warehouse. I was unable to figure out a way to generate pure impulse with the equipment on hand other than a square wave with smallest possible duty cycle. I felt lucky to have that. It was a bad time for US audio. just about everybody but JBL and Altec was going belly up.

      Comment


      • #33
        Re: 6Db. crossovers????

        Originally posted by johnk... View Post
        No,no, no. You said you added a pole to the B2 HP (woofer) response. So the poles of the B2 remain fixed. So you are just cascading the B2 HP with a B1 HP to add the third pole. This will not ever yield a Be3 as the other point I was going to make was that a Be3 HP does not have poles at +/- 45. They are at +/-43.65. So adding a single pole doesn't result in a Be3 HP. Close, but not a BE response. You would need to shift the poles of the woofer alignment too by adding a zeros to cancel the existing poles and then new poles as required. By the way, the topic of canceling zeros and poles with poles and zeros was covered in my text books from back in 68. If they aren't teaching that at GT they must be slacking off.

        And again, you must be thinking of impulse response, not square wave. Further more, the truth is that the impulse response of a 3rd order Bessel HP will ring more than a 2nd order Butterworth HP, though neither is significant.

        Your 2nd to 3rd order conversion, as you are applying it is nothing more than cascading a B1 with a B2.

        Now, all these responses are under damped and therefore the impulse response is a damped oscillation that decays exponentially as time goes to infinity. It is not 2 cycles or 3 cycles. Further more, the true B3 as well as the B2 cascaded with a B1 initially undershoot and then overshoot more than the B2. I.e. they ring more than the B2.
        you are right. the poles of a perfect 0.707 speaker are off. so to is the value of the B1 cap. change the cabinet volume or fill so that you Qtc hits 43 degrees. It is different again if you want to line up with 4th order.

        hmm. i think i best pull out my old notes and brush up. i can't even remember if the imaginary axis is drawn horizontally or vertically.

        Comment


        • #34
          Re: 6Db. crossovers????

          Originally posted by moron#99 View Post
          Linkwitz is after my time. He isn't mentioned in any of my old books or papers. I'll have to look go to the librabry and look for a book.
          http://www.linkwitzlab.com/filters.htm#9

          See "A Three Enclosure Loudspeaker System" from
          1980 for an early application of the LT:
          http://www.linkwitzlab.com/SB%20Mailbox.htm

          Comment


          • #35
            Re: 6Db. crossovers????

            Originally posted by Pete Basel View Post
            http://www.linkwitzlab.com/filters.htm#9

            See "A Three Enclosure Loudspeaker System" from
            1980 for an early application of the LT:
            http://www.linkwitzlab.com/SB%20Mailbox.htm
            Thanks, I'm going to bookmark this and read it in full during the course of my brush ups.

            yup. same thing.
            i'm just picking the box in advance so that I can do it passively without having to kill my SPL. He seems focused on extending the bass while I was focused on fixing up the impulse of a satelitte. similar thing though. Since mine requires purpose built cabinets then it would be a subset of his.

            Comment


            • #36
              Re: 6Db. crossovers????

              Originally posted by moron#99 View Post
              you are right. the poles of a perfect 0.707 speaker are off. so to is the value of the B1 cap. change the cabinet volume or fill so that you Qtc hits 43 degrees. It is different again if you want to line up with 4th order.

              hmm. i think i best pull out my old notes and brush up. i can't even remember if the imaginary axis is drawn horizontally or vertically.
              You still have not addressed my main point. You claimed that the BE3 rings less than ther B2 which is not true. Period.
              John k.... Music and Design NaO dsp Dipole Loudspeakers.

              Comment


              • #37
                Re: 6Db. crossovers????

                Originally posted by johnk... View Post
                You still have not addressed my main point. You claimed that the BE3 rings less than ther B2 which is not true. Period.
                i'll take your period with a grain of salt. I have downloaded several pc programs that promise to do circuits analysis and i'll probably buy a book or two for my e-reader. hopefully one of the programs can draw the plots for me. until then i am not sure I agree with your period.

                why do you limit it to Be3? does your claim extend to include Be4? be3 is the quick and simple that added about $0.19 to the manufacturing cost. It isn't the only possibility. it's possible that the faster rolloff contributed to lack of ringing but i doubt it. I'll have to pull out my papers and see if the ringing had a characteristic frequency. I'm pretty sure i measured that.
                if you have links to engineering or math documents then I would love to read them.

                http://www.aes.org/e-lib/browse.cfm?elib=11810

                Comment


                • #38
                  Re: 6Db. crossovers????

                  Originally posted by moron#99 View Post
                  Linkwitz is after my time. He isn't mentioned in any of my old books or papers. I'll have to look go to the librabry and look for a book.

                  I suspect what I am doing is a subset of his work in a more cookbook fashion. I am simply taking a polynomial and splitting it into two halves. Output = speaker * network. I know in advance that I want a bessel and therefore I can pick in advance a speaker alignment that results in the easiest possible network. two of the poles lines up by design and the "linkwitz filter" (?) ends up being as simple handful of passive components.

                  i built and tested three different versions before quitting audio for computers. it was not a fancy test facility. spectrum analyzer, pink noise, a mic, a square wave, and a scope in the middle of a big warehouse. I was unable to figure out a way to generate pure impulse with the equipment on hand other than a square wave with smallest possible duty cycle. I felt lucky to have that. It was a bad time for US audio. just about everybody but JBL and Altec was going belly up.
                  Aren't you making this a lot harder than it needs to be? Toss the cookbooks and the polynomials when it comes to crossover design, all that matters is the acoustic response with the driver and circuit when combined. Most decent software tools will let you select a target response, even if you love a Bessel function, then you import the measured driver response, and optimize the circuit till you curve-fit to the target. It's pretty much impossible to do this empircally. Talking about poles is nice for the classroom, but it's pretty useless when it comes to designing a crossover.
                  Click here for Jeff Bagby's Loudspeaker Design Software

                  Comment


                  • #39
                    Re: 6Db. crossovers????

                    Originally posted by moron#99 View Post
                    i'll take your period with a grain of salt. I have downloaded several pc programs that promise to do circuits analysis and i'll probably buy a book or two for my e-reader. hopefully one of the programs can draw the plots for me. until then i am not sure I agree with your period.

                    why do you limit it to Be3? does your claim extend to include Be4? be3 is the quick and simple that added about $0.19 to the manufacturing cost. It isn't the only possibility. it's possible that the faster rolloff contributed to lack of ringing but i doubt it. I'll have to pull out my papers and see if the ringing had a characteristic frequency. I'm pretty sure i measured that.
                    if you have links to engineering or math documents then I would love to read them.

                    http://www.aes.org/e-lib/browse.cfm?elib=11810
                    No standard third order rings less than a critically damped second order (LR2).
                    Click here for Jeff Bagby's Loudspeaker Design Software

                    Comment


                    • #40
                      Re: 6Db. crossovers????

                      Jeff, Linkwitz explains the theory with poles and zeros and then comes up with a solution and a real world example, nothing wrong with that. His 1980 paper is an excellent example of designing with active crossovers and he really covers all the bases.

                      Comment


                      • #41
                        Re: 6Db. crossovers????

                        Originally posted by Jeff B. View Post
                        Aren't you making this a lot harder than it needs to be?
                        That's explained by his reference to Altec still being in business, giving a time frame to his work.
                        www.billfitzmaurice.com
                        www.billfitzmaurice.info/forum

                        Comment


                        • #42
                          Re: 6Db. crossovers????

                          Originally posted by moron#99 View Post
                          i'll take your period with a grain of salt. I have downloaded several pc programs that promise to do circuits analysis and i'll probably buy a book or two for my e-reader. hopefully one of the programs can draw the plots for me. until then i am not sure I agree with your period. if you have links to engineering or math documents then I would love to read them.

                          http://www.aes.org/e-lib/browse.cfm?elib=11810
                          Unfortunately the paper you are referring to is 1) dealing with a Bessel crossover, not just a HP filter alone, and 2) Out of date and not really correct. Bessel crossovers do not sum flat under any conditions. The HP and LP filters can be over or underlaped to approximate flat response. The group delay of a Bessel LP filter is maximally flat, meaning the region of linear phase extends as far as possible toward the cut off point while remaining constant. This make the Bessel LP filter approximately linear phase. However, the same can not be said for the Bessel HP filter. The phase and GD of the HP Bessel filter is not all that much different that that of a HP Butterworth of Linkwitz filter of similar order. There have been a number of approximate linear phase speaker designed using a Bessel LP response coupled to various order HP response where, to match the GD of the LP section the tweeter is offset significantly. Spica speaker followed such a design process. However, now of these approaches addressed the nonlinear GD associated with the HP cut off of the woofer.

                          So we may differ on our interpretation of the impulse response and also based on how the cut off frequency of the Be3 is defined. But that alone is n ot the issue.
                          My interpretation of the impulse response of the Be3 and B2 HP is as follows. After the initial positive pulse there is a negative swing and then a positive over shoot and then continued oscillation as the impulse decays. In the case of the BE3 the overshoot, while happening faster that for the B2, is greater in magnitude that for the B2. I consider that worse. However, I also stand by my initial point that the ringing of the impulse has little to do with the quality of bass reproduction as any bass instrument will typically have a much higher Q response than any of these HP filters. So it really makes little difference whether we agree or disagree on whether the impulse of a Be3 is better or worse than that of a B2.

                          Another way to look at this is to examine the group delay of the B2 and Be3 HP. If the B2 and Be3 are set up to have the same -3dB point then they have very similar, nonlinear GD though around cut off and into the pass band, but the Be3 shows a slightly more rapid increase which would correspond to poorer transient response. On the other hand, if the Be3 is aligned based on phase so that the phase of the Be3 is 135 degrees at the same point he B2 is 90 degrees, (the BE3 will be down about 6.3dB at the frequency the B2 is down 3dB) then the Be3 will have considerably higher GD in the low frequency part of the pass band.
                          John k.... Music and Design NaO dsp Dipole Loudspeakers.

                          Comment


                          • #43
                            Re: 6Db. crossovers????

                            Originally posted by Pete Basel View Post
                            Jeff, Linkwitz explains the theory with poles and zeros and then comes up with a solution and a real world example, nothing wrong with that. His 1980 paper is an excellent example of designing with active crossovers and he really covers all the bases.
                            so why isn't anybody doing passive linkwitz speakers?

                            Comment


                            • #44
                              Re: 6Db. crossovers????

                              Originally posted by moron#99 View Post
                              so why isn't anybody doing passive linkwitz speakers?
                              Not sure what the definition of a "passive Linkwitz speaker" is, but there's no shortage of speakers using LR4 and LR2, both DIY and commercial.

                              EDIT: I just read the 10 posts I skipped. I now get that "Linkwitz" refered to LT circuits.

                              A passive LT speaker would have very low sensitivity. You'll need an 18" woofer with an fs around 15hz, qts around .35 and some room gain... to do it usefully.

                              He seems focused on extending the bass while I was focused on fixing up the impulse of a satelitte. .
                              They're one and the same.... and pretty much meaningless either way in real rooms.
                              :blues: Flat frequency response, a smooth sound power response free of resonance, careful driver-integration, and high dynamic range both upward and downward :blues:

                              Comment


                              • #45
                                Re: 6Db. crossovers????

                                Originally posted by moron#99 View Post
                                so why isn't anybody doing passive linkwitz speakers?
                                Gain is usually needed.

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