A trick for creating a higher-order slope

How about the phase shift?

If the low-pass of the woofers has already been achieved fourth-order by the active crossover, and the high-pass of the midrange is established by the combination of 2nd-order passive and 2nd-order active, at 540Hz, to formed a fourth-order slope, will there be a residue 90 degrees phase shift resulting from the use of passive crossover?
 
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Ideally, you will get a phase shift that varies from +180 degrees to 0 degrees over frequency, +90 degrees at the crossover frequency, from the passive filter, and the same from the active one. The total will vary from +360 degrees to 0, +180 degrees at the crossover frequency.

Your low-pass will go from 0 to -360 degrees, -180 degrees at the crossover frequency.

+180 and -180 degrees means they are in phase.
 
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Ideally, you will get a phase shift that varies from +180 degrees to 0 degrees over frequency, +90 degrees at the crossover frequency, from the passive filter, and the same from the active one. The total will vary from +360 degrees to 0, +180 degrees at the crossover frequency.

Your low-pass will go from 0 to -360 degrees, -180 degrees at the crossover frequency.

+180 and -180 degrees means they are in phase.
That’s different from my understanding. I always thought that the active system won’t cause any phase shift except the amplitude attenuation. Hence, the 4th-order low-pass of woofers do nothing with phase shift. Also true with the active 2nd-order high-pass of midrange. But the passive 2nd-order high-pass of midrange has phase shift by 90 degrees.
 
What kind of active crossover filter are we writing about? A linear-phase FIR digital one, an old-fashioned minimum-phase analogue filter, a minimum-phase IIR digital crossover filter? I have implicitly assumed it's a minimum-phase analogue filter, but maybe that's because I'm old fashioned.
 
Looking at the manual, I get the impression it is indeed an analogue minimum-phase crossover filter. The phase response will then be essentially the same as that of a passive filter of the same order, cut-off frequency and quality factor, so what I wrote in post #22 should hold.
 
I use this method all the time on the low pass of a woofer to get a steep (close to 4th order) slope using only a 2nd order electrical filter.
Thanks for the confirmation on this concept, I am doing this with my own active-crossover system.

I use a 10" Focal woofer that -when placed in a sealed 0.9cuFt box, just happens to have a 70Hz knee and a Q of 0.7. I combine that with a 12db electronic high-pass, also at 70Hz. And then the subwoofer has a 70Hz 24/db slope to match!
 
So, in sum, the safest method to make the acoustic response of the midrange to be a high-pass with 540Hz cut-off and 24dB/octave slope is to set the active crossover to operate in 12dB/octave mode, at 540Hz. Is this correct?

However, what will the sound be if I use 24dB/octave instead of the 12dB/octave? The result would be that the midrange will have 36dB/octave or sixth order at 540Hz, wouldn't it?

How about the sound of sixth-order alignment?
 
So, in sum, the safest method to make the acoustic response of the midrange to be a high-pass with 540Hz cut-off and 24dB/octave slope is to set the active crossover to operate in 12dB/octave mode, at 540Hz. Is this correct?
Yes.

There is more than just the rate of rolloff. What if the current crossover is -6dB at the crossover frequency and you use another LR2 with -6dB. Then it will be down 12dB at the crossover frequency.
 
There is also a special kind of digital filtering that can unnaturally force phase to remain as it was.
Actually, no, because causality would be violated if that were true. There must be a delay between the input and the output, since the output happens because of the input. In the best case, this delay is constant causing the resulting phase to be linear (w.r.t. freq), but never the same as it was (zero).
 
I'm sorry to ask the same question again. From post #22, it's clearly explained, I have little knowledge about phase shift, though.

The low-pass signal for the woofer is filtered by a fourth-order active crossover, and the high-pass signal for the midrange is filtered by a second-order passive crossover integrating with a second-order active crossover.

To my understanding, the active filter won't cause any phase shift because it has the ability to attenuate the small signal and will follow the slope rate. But the passive filter will cause the phase shift because it utilizes capacitive and inductive components to shape the amplified audio signal going to the speaker. Is this correct?

Therefore, the combination of the low-pass filter for the woofer and the high-pass filter for the midrange will be composed of two active filters and one passive filter. As a result, the two active filters won't cause phase shift, or maybe did but cancelled each other, and a remaining passive filter will leave the phase shift of 90 degrees alone. Do I understand correctly?

In addition, could it be considered the same situation with the two-way speaker system that uses a full-range woofer and employs a second-order high-pass filter for the tweeter?
 
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To my understanding, the active filter won't cause any phase shift because it has the ability to attenuate the small signal and will follow the slope rate. But the passive filter will cause the phase shift because it utilizes capacitive and inductive components to shape the amplified audio signal going to the speaker. Is this correct?
No. The phase is defined by the natural properties of the rolloff, and this holds even after digital filtering. Don't be distracted by the behaviour of reactive components, they are simply of the same nature.
 
I'm sorry to ask the same question again. From post #22, it's clearly explained, I have little knowledge about phase shift, though.

The low-pass signal for the woofer is filtered by a fourth-order active crossover, and the high-pass signal for the midrange is filtered by a second-order passive crossover integrating with a second-order active crossover.

To my understanding, the active filter won't cause any phase shift because it has the ability to attenuate the small signal and will follow the slope rate. But the passive filter will cause the phase shift because it utilizes capacitive and inductive components to shape the amplified audio signal going to the speaker. Is this correct?

No. Using capacitors, resistors and amplifiers, the active filter solves the same differential equation as the passive filter does with capacitors, resistors and inductors, giving the same phase shift.
In addition, could it be considered the same situation with the two-way speaker system that uses a full-range woofer and employs a second-order high-pass filter for the tweeter?

I'm not sure what you mean here.

In general, a mechanical roll-off can be described by the same type of differential equation as your passive and active crossover filters if the mechanical system is lumped, that is, can be treated as a system of concentrated masses, springs and dampers. The phase shift is then the same as that of an electrical filter with the same order, cut-off frequency and quality factor.

I know what I just wrote applies to the low-frequency roll-off of most loudspeakers, but I don't know about the high-frequency roll-off.

In practice you also have to look out for path length differences between the loudspeakers and your ears. That is a distributed (opposite of lumped) effect giving a practically constant delay, which results in extra phase shifts. For example, when the acoustic centre of the woofer is 10 cm further from your ears than the acoustic centre of the tweeter, sound travels some 300 us longer from the woofer to your ears than from the tweeter to your ears. 300 us gives 180 degrees of phase shift at 1.6666... kHz.
 
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They are equipped with a 2" midrange dome, and their passive high-pass filter for the midrange is composed of 32 uF and 2.6 mH. From the online calculator, the result is that the crossover is set at approximately 540 Hz with a 12 dB/octave slope.
In case no one has mentioned it yet:

I would check that in any case metrologically: such online calculators usually assume that the impedance is constant over the frequency. But this is usually not the case, not even with a midrange dome: to make matters worse, it should also have its resonant frequency in the vicinity.

Many greetings,
Michael
 
Therefore, the combination of the low-pass filter for the woofer and the high-pass filter for the midrange will be composed of two active filters and one passive filter. As a result, the two active filters won't cause phase shift, or maybe did but cancelled each other, and a remaining passive filter will leave the phase shift of 90 degrees alone. Do I understand correctly?
How about this statement? Is there anyone who can confirm, please?
 
Dear presscot,

Please note that for all practical intents and purposes, there is no difference between active and passive filters. An active filter is just another way of synthesising the same transfer function exhibited by a passive filter.

Douglas Self has a beautiful reference, with details of all kinds of analogue filters, gain/phase/delays etc. below. You may also use software such as WinISD to visualise the various filter characteristics according to order, type etc.

The Design of Active Crossovers
 
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