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Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

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  • Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*



    Maybe this should have been a blog entry? :rolleyes:

    Jeff B.
    Click here for Jeff Bagby's Loudspeaker Design Software

  • #2
    Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

    Thanks for posting this Jeff.

    Greg

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    • #3
      Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

      An alternative method for dealing with the offset issue is to add delay to the tweeter signal to compensate for the offset. This is easily implemented with digital active crossovers or by adding an all-pass in an active analog design. Phase tracking is preserved. It is still necessary to address the phase shift caused by the tweeter lf roll off . . . that can be done by adjusting the delay (at the expense of phase tracking), or by incorporating the tweeter roll off in the crossover slope with a bi-quad, or in some instances simply by using a lower order (electronic) slope. Delay is also sometimes used for lobe steering . . .

      In passive designs where the crossover is used not just for signal splitting but also for driver response corrections (which always introduce phase shifts of their own) . . . well . . . it's still an "art" . . .
      "It suggests that there is something that is happening in the real system that is not quite captured in the models."

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      • #4
        Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

        Originally posted by Deward Hastings View Post
        An alternative method for dealing with the offset issue is to add delay to the tweeter signal to compensate for the offset. This is easily implemented with digital active crossovers or by adding an all-pass in an active analog design. Phase tracking is preserved. It is still necessary to address the phase shift caused by the tweeter lf roll off . . . that can be done by adjusting the delay (at the expense of phase tracking), or by incorporating the tweeter roll off in the crossover slope with a bi-quad, or in some instances simply by using a lower order (electronic) slope. Delay is also sometimes used for lobe steering . . .

        In passive designs where the crossover is used not just for signal splitting but also for driver response corrections (which always introduce phase shifts of their own) . . . well . . . it's still an "art" . . .
        Of course with active circuits you can add delay and compensate for the offset. This is true.

        Now remember, passive elements are all minimum phase. Any circutry used to flatten the frequency response will also flatten the phase response and move it in the direction of less phase error as well.
        Click here for Jeff Bagby's Loudspeaker Design Software

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        • #5
          Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

          Thanks Jeff, I copy and pasted into word for future reference.
          "I have not failed. I've just found 10,000 ways that won't work." Thomas A. Edison

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          • #6
            Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

            Originally posted by Jeff B. View Post
            Now remember, passive elements are all minimum phase. Any circutry used to flatten the frequency response will also flatten the phase response and move it in the direction of less phase error as well.
            That's not always the case in practice, though. Cone breakup, the most common inducement to apply notch filters, hardly shows up on a phase curve at all, but a notch filter used to suppress it most certainly will. Other examples are response correction to compensate for driver beaming, and baffle step correction (which is rarely applied globally as it should be, but is commonly included instead in the low-pass filter).
            "It suggests that there is something that is happening in the real system that is not quite captured in the models."

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            • #7
              Thanks Jeff!

              That is a (relatively) concise overview and much appreciated. I feel that many times people with strong opinions who are largely in agreement are done a disservice by the lack of communication inherent in this nuance free one directional electronic exchange we generously refer to as communication ;) . Many conflicts would resolve themselves in the presence of both parties, good music, and a respectful klink of a couple of beverages.
              When you run make sure you run,
              to something not away from, cause lies don't need an aeroplane to chase you anywhere.

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              • #8
                Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                Great write-up, Jeff. I say Blog-it, Blog-it, Blog-it ... and add your other articles if possible. The blog feature is pretty neat and I hope to see people using it.

                Seems that the additional difference between the two methods is that the target is no longer LR4 @ 2kHz. The first method maintains the target and the second does not. I would not consider that the end of the world, but when I design a crossover I am trying to hit a target.

                - Brad
                Brad
                piano black sealing mdf irregular recesses grill technique

                Comment


                • #9
                  Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                  Originally posted by Deward Hastings View Post
                  That's not always the case in practice, though. Cone breakup, the most common inducement to apply notch filters, hardly shows up on a phase curve at all, but a notch filter used to suppress it most certainly will. Other examples are response correction to compensate for driver beaming, and baffle step correction (which is rarely applied globally as it should be, but is commonly included instead in the low-pass filter).
                  Hi Deward,

                  It is always the case.

                  It must always be the case.

                  The reason natural (mechanical and passive electrical) systems have a minimum phase relationship with their magnitude function is that events passing through the system would show up before they actually occur (acausal).

                  For instance...

                  If you take system with a peak in it's transfer function and then overwrite it's phase response so that it's flat then it's impulse response will ring before and after the impulse.

                  Transfer function (frequency/phase response) is everything no matter what has effected it.

                  No separate considerations for tweeter rolloff, diffraction loss or anything else.

                  Comment


                  • #10
                    Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                    Originally posted by AJ View Post
                    Thanks Jeff, I copy and pasted into word for future reference.
                    Dually-noted!
                    Wolf
                    "Wolf, you shall now be known as "King of the Zip ties." -Pete00t
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                    • #11
                      Practical factors considered

                      Jeff showed, with excellent clarity, that a phase mismatch in LR4 2-way designs due to a driver offset on a flat baffle can be compensated by relaxing either the woofer or the tweeter's rolloff. Thanks, Jeff, for taking the time to write a good summary. What I'm going to add in the following is that in practice with real drivers and crossovers, we often end up using sort of an in-between approach of the above two methods. That is, it is very likely to "relax" both drivers' rolloffs to achieve flat summation or symmetric lobing in an LR4 design with a driver offset.

                      I'll take an actual design and simulate some different crossovers to show how a desinger can achieve a desired driver summation with practical factors considered. The example is Zaph's SR71. This design uses the Seas ER18RNX 7" and 27TDFC 1" drivers. If we use theoretical, textbook LR4 rolloffs with a crossover point of 1.75 kHz, we will have a response with a vertical polar response tilted downward due to the driver offset. On-axis summation does not have a full 6 dB gain at the crossover point as shown below:



                      In this simulation, I used a 30 mm driver offset for the 7" midwoofer. As expected, a phase mismatch occurred. Now, to compensate the mismatch, only the woofer's rolloff is relaxed:



                      As you can see, the phase mismatch has been compensated very well. But there are two practical problems with this approach:

                      1) Some people may want to suppress the cone breakup node at 4.3 kHz a little more.
                      2) The 4th order acoustic HP rolloff requires a 3rd order electrical filter. An additional capacitor may not matter, but if we really don't need it, then why have it? And some people want to design as simple a crossover as possible.

                      If we relax both drivers' rolloff---a little steeper rolloff on the woofer than the above and a slightly relaxed rolloff on the tweeter---, we obtain the following response:



                      As you can see, the phase alignment is excellent around the crossover frequency. The breakup node is attenuated a little more than the case of only the woofer's rolloff being relaxed. And this crossover requires only 2nd order electrical filters for both drivers.

                      Many existing designs' crossovers belong to this category. For example, Jeff's Dreydel 2-way uses a 3rd order electrical filter for the RS150 to give a sufficient attenuation to breakup nodes. As a result, the midwoofer's acoustic rolloff is not relaxed enough to fully compensate the phase mismatch. But he used a 2nd order filter on the tweeter, which results in a slightly relaxed tweeter rolloff. By doing this, he achieved good phase alignment at the intended listening axis.

                      In sum, to obtain a good LR4 phase alignment for drivers mounted on a flat baffle, we can relax either the woofer or the tweeter's rolloff rate. Relaxing only the woofer's rolloff gives a better compensation than relaxing only the tweeter's rolloff. But for practical reasons, we often end up relaxing the tweeter's rolloff slightly as well. The reasons are:

                      1) By doing this, we can use a bit steeper rolloff on the woofer's response and still have good phase alingment. This is useful to attenuate the woofer's breakup nodes.

                      2) Even a slightly less steep HP rolloff than a true 4th order slope can provide sufficient protection for today's well-designed tweeters.


                      In this sense, the "asymmetricity" may not be viewed as the key element of this method. It is "relaxation" that makes this method work. How about coining a new term "relaxed LR4?" ;)

                      -jAy

                      Notes

                      1. In my above sims, irregular ripples at 1.5 kHz to 4 kHz are mainly due to the diffraction effect on the tweeter's response. "Relaxation" of the rolloffs is not the major cause of them.

                      2. Although the relaxation occurs out of the crossover region, it has an effect upon the summation in the crossover region due to a phase shift caused by it. If you apply this "relaxing" technique to LR 4th order designs, its effect out of the narrow crossover region is not that significant, because individual drivers' SPL in regions where the actual relaxation occurs is already too low to affect the system SPL to a significant degree.

                      3. In theory, you can also apply this technique to LR type crossovers of higher orders. For example, you can relax the rolloffs of Linkwitz-Riley 6th or 8th order filters to compensate a phase mismatch due to a driver offeset. One may think of this as a different technique since steeper rolloffs than a 4th order slope are used. But it is essentially the same thing. The only difference is the original rolloff rate before the relaxation applies. Technically, this should be viewed as "relaxed" LR6 or LR8 (not some different kind of LR4), because the resulting, total amount of phase mismatch at the xover point is 540 degrees (in the case of LR6; requires reversed tweeter polarity) or 720 degrees (in the case of LR8).
                      Last edited by jkim; 06-10-2008, 10:22 PM. Reason: Notes added and edited

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                      • #12
                        Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                        It's a nice theory that explains everything.

                        I'm looking for the practical application of it in a filter that address the cone breakup of, say, a RS150, and brings it's frequency response to flat through the breakup region (and its phase curve too). At the moment I'm stuck with notch filters that suppress the driving signal at the breakup frequency and that mess up phase relationships in the rest of the crossover . . . the ones jeff was talking about above).

                        Something odd seems to happen with bsc as well . . . build it into a crossover, and then push the speaker back against the wall. Does phase at the driver change? What can I do, filter wise, to make it sound the same whether the speaker is out in the room or against the wall without changing frequency response or phase (in the crossover)?
                        "It suggests that there is something that is happening in the real system that is not quite captured in the models."

                        Comment


                        • #13
                          Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                          Originally posted by bmaupin View Post
                          Seems that the additional difference between the two methods is that the target is no longer LR4 @ 2kHz. The first method maintains the target and the second does not. I would not consider that the end of the world, but when I design a crossover I am trying to hit a target.

                          - Brad
                          Hi Brad,

                          The slightly lowered Fc in the sim of the second method is simply an artifact of this particular sim. If we want to, by adjusting the starting point of each rolloff, we can move it to the target Fc and still have the same effect.

                          -jAy

                          Comment


                          • #14
                            Re: Practical factors considered

                            Now, check out an example whose target response is 2100Hz LR4, with a 20mm offset using response plots provided by Jeff B for the RS150 and RS28.

                            These response plots follow the target LR4 responses quite closely through the XO region. They don't look much relaxed to me, yet we can all see the excellent on axis response as well as the tight phase alignment reflected in the 20dB reverse null.
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                            • #15
                              Re: Offsets, Asymmetrical Slopes, and Mysticism - revisited *PICS*

                              Originally posted by Deward Hastings View Post
                              It's a nice theory that explains everything.

                              I'm looking for the practical application of it in a filter that address the cone breakup of, say, a RS150, and brings it's frequency response to flat through the breakup region (and its phase curve too). At the moment I'm stuck with notch filters that suppress the driving signal at the breakup frequency and that mess up phase relationships in the rest of the crossover . . . the ones jeff was talking about above).

                              Something odd seems to happen with bsc as well . . . build it into a crossover, and then push the speaker back against the wall. Does phase at the driver change? What can I do, filter wise, to make it sound the same whether the speaker is out in the room or against the wall without changing frequency response or phase (in the crossover)?
                              There's only one other thing you can do and that is to treat the room. For placement against the wall, you'd need quite a bit of absorbing material to take care of boundary reinforcement. Even then, if the speaker has good bass extension, only ridiculous amounts of treatment would help.

                              If the response at the listening position is to remain the same, some form of EQ is required as the speaker is moved from a position radiating into 4pi space and towards 2pi space. If response changes, so does the phase since phase and amplitude are directly related.

                              And if you add damping to your notch filters by addition of a resistor, you can smooth out the breakup to make it more closely fit a smooth target response. That should take care of the phase problems you're citing.
                              R = h/(2*pi*m*c) and don't you forget it! || Periodic Table as redrawn by Marshall Freerks and Ignatius Schumacher || King Crimson Radio

                              Byzantium Project & Build Thread || MiniByzy Build Thread || 3 x Peerless 850439 HDS 3-way || 8" 2-way - RS28A/B&C8BG51


                              95% of Climate Models Agree: The Observations Must be Wrong
                              "Gravitational systems are the ashes of prior electrical systems.". - Hannes Alfven, Nobel Laureate, Plasma physicist.

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