Dear Golix,
You are right in several ways. First-order filters shift the phase of each driver by 45 degrees, one driver's output is "leading", the other's is "lagging". Thus, the Phase Difference between them is 90 degrees, as I think you implied. But your concerns about the impossibility of achieving "phase coherency" for "odd-order" crossovers are not warranted:
For a second order filter, the phase shift is 90 degrees per driver at the crossover point. This is where your 180 degrees comes from- as the Phase Difference between them, at the crossover point. That Phase-Difference analysis extends, with your numbers, for the third-, and fourth-, and higher-order filters, at their crossover point.
Higher-order circuits, from 2nd on up, cannot be made time-coherent, because that Phase Difference each one exhibits at the crossover point does not remain a Constant Phase Difference when the tones move away from the crossover point. In other words, the drivers' Relative Phase Difference is always changing- which can be heard in many ways:
- As an image always shifting (depending on the note).
- Complex timbres which are not realistic.
- Dynamic attacks that are slurred.
- Truncation of the depth of the image in that crossover region.
- An audible "disconnect" in the depth of the image heard from the tweeter, compared to depth of the image revealed by the woofer. When an instrument demands some output from each of those two drivers, the same instrument apparently exists in two different rooms.
- There is "height" in many recordings.
- The speakers "don't measure like they sound."
Listen to a tambourine on a high-order speaker (an instrument that requires output from woofer AND tweeter), then listen to it on a decent pair of headphones, which are most always time coherent across that tambourine's tone range. You'll hear most all of the effects listed above from the speakers. Then compare using applause, acoustic guitar, piano, voice, using any wideband signal with transient complexity.
The audible effects of a constantly-changing phase relationship depend entirely on your choice of music- on what frequency range your music occupies, and also on the "frequency content" of each transient.
Different listeners use different music, some that easily reveal phase shift around the crossover point. Most crossovers to tweeters occur around 2 to 3kHz. A constantly-changing phase relationship between the two drivers above and below that crossover frequency has specific audible consequences we have all heard. In my experience, it is the leading cause for someone to say a speaker is "too analytical" or "too revealing", "too forward", or even "too exciting". One often remarks that a recording is "too harsh, too hard to listen to." It is why the preferred audiophile recordings are rather bland.
If the speaker designer physically steps that out-of-synch tweeter back from the woofer, and/or "pulls" the crossover point apart between the two drivers, you often hear "laid back", often with "a little less energy around the crossover point."
So, why use a first-order filter?
That Phase Difference remains Constant for a first-order filter: The output from the two halves of a first-order filter are always 90 degrees apart, on every frequency, not just at their crossover frequency. So their Relative Change in Phase Difference, at every frequency, is zero.
With a first-order circuit, the image does not wander on different notes, transients are preserved right down to knowing when the tip of the tongue left the roof of the mouth, and existing distortions in the recording or in your gear are not re-distorted, by being smeared out in time.
So, after passing through a first-order circuit, when the high- and low-passed signals are recombined, then the original, transient perfect, signal is recreated. Of course for a speaker, those high- and low-passed signals can emerge from drivers that have their own severe, mechanically-caused phase shifts. Perhaps the high and low sounds start off at unequal distances from your ears, or arrive at different times from "duplicate" drivers (like multiple tweeters). They could be time-warped from improperly-designed Zobel networks in the crossover circuit. Then there is a good chance that the high-passed signals will be "hazed-over" by cabinet reflections.
Fortunately, all of these difficulties can be minimized.
I hope this clarifies things. Thank you for your participation in an interesting thread.
Best regards,
Roy Johnson
Founder and Designer
Green Mountain Audio
You are right in several ways. First-order filters shift the phase of each driver by 45 degrees, one driver's output is "leading", the other's is "lagging". Thus, the Phase Difference between them is 90 degrees, as I think you implied. But your concerns about the impossibility of achieving "phase coherency" for "odd-order" crossovers are not warranted:
For a second order filter, the phase shift is 90 degrees per driver at the crossover point. This is where your 180 degrees comes from- as the Phase Difference between them, at the crossover point. That Phase-Difference analysis extends, with your numbers, for the third-, and fourth-, and higher-order filters, at their crossover point.
Higher-order circuits, from 2nd on up, cannot be made time-coherent, because that Phase Difference each one exhibits at the crossover point does not remain a Constant Phase Difference when the tones move away from the crossover point. In other words, the drivers' Relative Phase Difference is always changing- which can be heard in many ways:
- As an image always shifting (depending on the note).
- Complex timbres which are not realistic.
- Dynamic attacks that are slurred.
- Truncation of the depth of the image in that crossover region.
- An audible "disconnect" in the depth of the image heard from the tweeter, compared to depth of the image revealed by the woofer. When an instrument demands some output from each of those two drivers, the same instrument apparently exists in two different rooms.
- There is "height" in many recordings.
- The speakers "don't measure like they sound."
Listen to a tambourine on a high-order speaker (an instrument that requires output from woofer AND tweeter), then listen to it on a decent pair of headphones, which are most always time coherent across that tambourine's tone range. You'll hear most all of the effects listed above from the speakers. Then compare using applause, acoustic guitar, piano, voice, using any wideband signal with transient complexity.
The audible effects of a constantly-changing phase relationship depend entirely on your choice of music- on what frequency range your music occupies, and also on the "frequency content" of each transient.
Different listeners use different music, some that easily reveal phase shift around the crossover point. Most crossovers to tweeters occur around 2 to 3kHz. A constantly-changing phase relationship between the two drivers above and below that crossover frequency has specific audible consequences we have all heard. In my experience, it is the leading cause for someone to say a speaker is "too analytical" or "too revealing", "too forward", or even "too exciting". One often remarks that a recording is "too harsh, too hard to listen to." It is why the preferred audiophile recordings are rather bland.
If the speaker designer physically steps that out-of-synch tweeter back from the woofer, and/or "pulls" the crossover point apart between the two drivers, you often hear "laid back", often with "a little less energy around the crossover point."
So, why use a first-order filter?
That Phase Difference remains Constant for a first-order filter: The output from the two halves of a first-order filter are always 90 degrees apart, on every frequency, not just at their crossover frequency. So their Relative Change in Phase Difference, at every frequency, is zero.
With a first-order circuit, the image does not wander on different notes, transients are preserved right down to knowing when the tip of the tongue left the roof of the mouth, and existing distortions in the recording or in your gear are not re-distorted, by being smeared out in time.
So, after passing through a first-order circuit, when the high- and low-passed signals are recombined, then the original, transient perfect, signal is recreated. Of course for a speaker, those high- and low-passed signals can emerge from drivers that have their own severe, mechanically-caused phase shifts. Perhaps the high and low sounds start off at unequal distances from your ears, or arrive at different times from "duplicate" drivers (like multiple tweeters). They could be time-warped from improperly-designed Zobel networks in the crossover circuit. Then there is a good chance that the high-passed signals will be "hazed-over" by cabinet reflections.
Fortunately, all of these difficulties can be minimized.
I hope this clarifies things. Thank you for your participation in an interesting thread.
Best regards,
Roy Johnson
Founder and Designer
Green Mountain Audio