Most separate subwoofers use an active filter and a dedicated amplifier precisely because it is a simpler way to solve problems that arise from matching a midwoofer/subwoofer. With a passive crossover you need large inductors and capacitors, and are also dealing with the impedance peak at resonance of the midwoofer. All of these factors make it difficult to implement a passive design effectively. There were subwoofers designed with passive crossovers, but it was very tricky to get a good match to an existing speaker design.
A ported design creates a double peak in the impedance curve, which creates an additional problem with a passive crossover design. The single peak of a closed box design is easier to deal with, though not a trivial problem to solve by itself.
The "significant" excursion below resonance is really no different than the excursion of any 2nd-order filter of a particular Q. However, when a high pass crossover is combined with the natural rolloff below resonance you end up with a higher filter slope, which does reduce excursion quickly below Fbox (resonant freq of woofer in the box). It really isn't a big deal unless you are approaching the linear excursion limit of the driver in question. A large capacitor combined with the mid-woofer rolloff will provide protection below Fs. The real problem occurs when the desired crossover point is just above resonance, where the impedance peak is interfering with the rolloff of the filter.
A ported design creates a double peak in the impedance curve, which creates an additional problem with a passive crossover design. The single peak of a closed box design is easier to deal with, though not a trivial problem to solve by itself.
The "significant" excursion below resonance is really no different than the excursion of any 2nd-order filter of a particular Q. However, when a high pass crossover is combined with the natural rolloff below resonance you end up with a higher filter slope, which does reduce excursion quickly below Fbox (resonant freq of woofer in the box). It really isn't a big deal unless you are approaching the linear excursion limit of the driver in question. A large capacitor combined with the mid-woofer rolloff will provide protection below Fs. The real problem occurs when the desired crossover point is just above resonance, where the impedance peak is interfering with the rolloff of the filter.
Yes it is different because, as you point out "any 2nd order filter" is superimposed on the response of the drive/box resulting in a higher order roll off. I have seen few if any quality speakers which rely on the midranges natural roll off. They always employ some additional filter, passive or active, to increase the roll off above 2nd order and to reduce excursion below cut off. Any design that employs a 2nd order acoustic HP, where ever the x-o point, will have the problem. Any of this is better done active.
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What you are really arguing is that a 2nd order 12dB/octave rolloff slope is inadequate. I think it depends on the circumstances and the design choices. That does not mean one is preferable to another in every case.
A 2nd-order slope, whether implemented by active electronics, passive components, or box design, does not change the relationship between excursion and SPL at a particular frequency.
What higher crossover slopes accomplish is increased limitation of out-of passband power, which also affects excursion below the crossover point. Adding a capacitor (in series) to the natural or box-limited rolloff of a speaker changes the slope to 3rd-order (or quasi-3rd-order). In most circumstances this is necessary, particularly so when you have a small driver with limited excursion capability (or limited power handling), which describes the biggest reason crossovers are necessary. A 2nd-order filter changes the rolloff to 4th-order below resonance.
But how much do you really lose when using lower crossover slopes? Comparing Butterworth (Q=.707, maximally flat passband) filters, a perfect 4th-order Butterworth high pass will have maximum excursion at the crossover frequency, and decreasing excursion below. A 3rd-order Butterworth will have maximum excursion at approximately 10% below the crossover frequency, and that will cost approximately 1 dB of output capability. What I mean by this is: for a given excursion limit you need to allow an extra 1dB to account for "excess excursion" below your crossover point, and if you really want that 1dB of output you need to raise the crossover frequency by around 10%. For a 2nd-order Butterworth you really cannot specify a single frequency where maximum excursion is reached. That is because the rolloff slope now matches the increasing excursion as frequency decreases, and the two lines become one. But you can know how many dB you lose to that excess excursion, and that is 3 dB. So this entire discussion is over 3 dB of output and any increased distortion that would bring. Note: these relationships will change with different filter shapes. With Bessel or Linkwitz-Riley crossovers the general idea is the same, the details are different.
Of course there are other considerations. You may need to limit the power to a midrange, and a steeper slope will help with that. And you must consider the load on the amplifier. An acoustic rolloff does nothing to limit the current into that driver below resonance, and the amp is supplying that current. Effectively you are lowering the impedance and requiring the amp to deliver excess current that will not be converted into sound. At a minimum you would need a capacitor in series with the mid-bass to avoid this.
Lastly, when I suggested investigating the possibility of using the natural rolloff of the H602 in its sub-enclosure I did not intend that it would be used without a crossover. But, instead, that the rolloff be included in the crossover design. I was actually more concerned about the sagging response in the free-air graph on the datasheet, and realized that the response should be flattened by a properly sized sub-enclosure. This would change the rolloff shape and raise the resonance nearer to the desired crossover frequency. Too close for comfort, and interaction between the driver/enclosure rolloff and the crossover itself is unavoidable. I fully realize that the impedance peak at resonance is problematic with a passive crossover, which is a good argument for a dedicated subwoofer amp and electronic crossover. There are many things to consider in a design, and it is more convenient to discuss one issue at a time. But all aspects of a design must eventually come together.
A 2nd-order slope, whether implemented by active electronics, passive components, or box design, does not change the relationship between excursion and SPL at a particular frequency.
What higher crossover slopes accomplish is increased limitation of out-of passband power, which also affects excursion below the crossover point. Adding a capacitor (in series) to the natural or box-limited rolloff of a speaker changes the slope to 3rd-order (or quasi-3rd-order). In most circumstances this is necessary, particularly so when you have a small driver with limited excursion capability (or limited power handling), which describes the biggest reason crossovers are necessary. A 2nd-order filter changes the rolloff to 4th-order below resonance.
But how much do you really lose when using lower crossover slopes? Comparing Butterworth (Q=.707, maximally flat passband) filters, a perfect 4th-order Butterworth high pass will have maximum excursion at the crossover frequency, and decreasing excursion below. A 3rd-order Butterworth will have maximum excursion at approximately 10% below the crossover frequency, and that will cost approximately 1 dB of output capability. What I mean by this is: for a given excursion limit you need to allow an extra 1dB to account for "excess excursion" below your crossover point, and if you really want that 1dB of output you need to raise the crossover frequency by around 10%. For a 2nd-order Butterworth you really cannot specify a single frequency where maximum excursion is reached. That is because the rolloff slope now matches the increasing excursion as frequency decreases, and the two lines become one. But you can know how many dB you lose to that excess excursion, and that is 3 dB. So this entire discussion is over 3 dB of output and any increased distortion that would bring. Note: these relationships will change with different filter shapes. With Bessel or Linkwitz-Riley crossovers the general idea is the same, the details are different.
Of course there are other considerations. You may need to limit the power to a midrange, and a steeper slope will help with that. And you must consider the load on the amplifier. An acoustic rolloff does nothing to limit the current into that driver below resonance, and the amp is supplying that current. Effectively you are lowering the impedance and requiring the amp to deliver excess current that will not be converted into sound. At a minimum you would need a capacitor in series with the mid-bass to avoid this.
Lastly, when I suggested investigating the possibility of using the natural rolloff of the H602 in its sub-enclosure I did not intend that it would be used without a crossover. But, instead, that the rolloff be included in the crossover design. I was actually more concerned about the sagging response in the free-air graph on the datasheet, and realized that the response should be flattened by a properly sized sub-enclosure. This would change the rolloff shape and raise the resonance nearer to the desired crossover frequency. Too close for comfort, and interaction between the driver/enclosure rolloff and the crossover itself is unavoidable. I fully realize that the impedance peak at resonance is problematic with a passive crossover, which is a good argument for a dedicated subwoofer amp and electronic crossover. There are many things to consider in a design, and it is more convenient to discuss one issue at a time. But all aspects of a design must eventually come together.
