First Order Crossovers: Pros and Cons

I have heard that, for example, because of the use of this crossover configuration on the Vandersteen 5 one has to sit at least 10 feet away from the speakers in order for the drivers to properly mesh.

Any multi-way, non-coaxial speaker needs a minimum distance to be heard as intended.  The differences in arrival times as well as the angle between the drivers themselves is reduced with distance.  Imagine for instance if you are 1' from a 2-way speaker.  You can probably hear the tweeter and woofer separately.  I am not sure why Vandersteen recommends what they do, but I could see this with a variety of filter designs.

The other thing for people to keep in mind with drivers and crossovers is that the slope and angle is a function of the driver behavior AND the crossover components. This is true whether you use an active or passive crossover.

Best,

E

Absolutely wonderful read! Glad this thread was bumped recently back from 2005 or I would never have found it. I am an electrical engineer myself with significant signal processing background, and I truly appreciate the clarity of Roy’s and Karls explanations here. They are absolutely correct. At the same time, it is easy to see how without formal study of electrical signal mathematics it might be difficult to follow or even counterintuitive. Nowhere is this as obvious as the discussions relating to Phase coherency vs Time coherency (i.e. simultaneity). Time coherency is clearly the stricter condition as Roy points out. I also really liked Karls explanation of the sum of the high and low frequency drivers output after first order crossover as the sum of two phasors separated by 90 degrees at all frequencies. I think I would have further reinforced the fact that it is *perfectly fine* to add these "out of phase" signals because the result is always a constant phase at the average of the two individual phases, which is actually ideal. Without some background in signal processing it might be easy to think these two drivers were fighting each other and causing distortion. Karls post really helped clear this up.

Finally, it was good to see it pointed out correctly that the spatial lobing problem is a multiple emitter issue, and not a crossover issue. Steep crossovers merely narrow the region over which multiple emitters "exist" for that frequency. Thanks for the great read.

I hope there is more discussion on this. I have a pair of speakers with a first order crossover now myself (Dynaudio Special 40), and they really do have a very special sound. Yes, I hear the lobing, but yes, I also hear the outstanding clarity which I assume is the phase and/or time coherency of the drivers in the sweet spot. Still trying to decide what I think of them overall, but so far very impressed. Btw, there are a lot of other LC components on the crossover boards (presumably used for impedance correction of the drivers?). Would like to learn more.

Transducers are not flat though there operating range they roll off the 1st order utilizes the reduced levels and since it overlaps do to its slight -6db per octave roll-off you can fill in these dips in response by allowing other driver to gently roll off overlapping and filling in. A 1st order is not for every loudspeaker type and I would say 1st orders require more costly drivers without peaks and severe breakup modes as well as smooth gentle roll-off. I find horns can take advantage of 1st orders since the horn itself has a fairly severe drop off at its operating range you can use a 1st order without worrying about to much overlap. A 1st order can reduce power handling and peak SPL but its advantages in-phase and lower parts count can have sonic benefits. 

@murphythecat That is exactly what my Coincidents due with the midrange and tweeter.  Midrange is connected directly to amp and the tweeter just has a single 4.7uF cap in front of it.  But then they've got an additional two 12" woofers after an inductor on each channel... I'll be using Nelson's crossover to skip the inductor and play a bit with the crossover frequency (they don't fall away until 2000hz and I'm getting some resonance up there with my current sub amps).

seas a26 is a great solution
1st order tweeter, woofer run as a fullrange with natural roll off so no filter in front of it.

simplicity as its best

In honor of the impending release of a diy version of the Nelson Pass designed First Watt active crossover, I thought I’d bump this amazingly informative thread on crossover design... looking forward to building the FW crossover and using it to facilitate bi-amping of my Coincident PREs.

https://www.diyaudio.com/forums/pass-labs/165756-pass-labs-b4-crossover-questions-58.html

I see... new to the crossover arguements. Wasn't sure what point the polarity was referring to.

Biomimetic...The polarity of the driver wiring is determined by how the speaker system is connected internally. If it has biwire terminals you could mess with this by reversing the cable at one terminal.

Ok, not to be over the top, but if speakers are time coherent and each cone, if I understand correctly, is 180 degrees out of phase from the other, wouldn't a perfect set-up only work with bi-wiring, where you can flip one of the sets of wires for the cone you want to put back into the same phase? Or am I wrong?

[email protected] the component values, for a particular frequency, differ from a first order filter because the cascaded filters are working from and into different impedances. But they are still two series filters. In the case of an electronic crossover, fourth order L/R for example, each of the four filter sections includes a buffer amp, so that each stage is similarly driven and loaded, and in this case the component values are the same.

Hi Eldartford.
Thank you for your comments. Just a quick note, however. A second-order filter is not two first-order crossovers in series, nor "cascaded". The parts in a second-order filter, the capacitors and inductors, are of different values than those used in a first-order circuit.

Best regards,
Roy Johnson
Founder and Designer
Green Mountain Audio

Skrivis...If, as you say "a 1st-order x-over sums to a piece of wire" it must follow that a second order crossover, which amounts to two first order filters in series, is the sum of two pieces of wire.

But I agree that digital crossovers can do wonderful things.

A 2nd-order x-over with the tweeter's leads reversed gives you an in-phase output if you're considering _absolute_ phase (polarity). The 4th-order x-over is similar.

However, you're still seeing a phase shift. If you look at the electrical input and output with something other than a simple sine wave, it becomes obvious that the output is different from the input.

The classic statement I keep repeating is "a 1st-order x-over sums to a piece of wire." This is not true of other standard x-overs.

It's possible to add a delay in an active x-over to put things closer to normal, and this is even easier when the x-over is digital.

Technologies like DEQX hold a lot of promise. It's like having your cake and eating it too. :)

Dodgealum...There is no magic! No matter who designs the crossover each section, which is worth 6 dB, causes a 90 degree phase difference between Hi and Lo. Both Hi and Lo phase vary with frequency, but the difference remains 90 degrees. Of course, as you go away from the filter break frequency (crossover frequency) the amplitude of the Hi and Lo signals diminish so that phase is not a big issue.

So, a 12dB crossover has a phase difference of 180 degrees, and if you hook the tweeter up with reversed phase the audio output will be back in phase. With the 24dB crossover that you mention the phase difference is 360 degrees, which is the same as zero, so the drivers, both connected with normal polarity, will be back in phase.

So why do people like 6dB crossovers? The audio output of the drivers may be phase shifted from the electrical signal, and, at a selected frequency, can also be adjusted by positioning of the tweeter with respect to the woofer. So, with tweeks, a 6dB crossover can avoid the 90 degree phase shift, at least at the crossover frequency which is where it matters most. FWIW, 6dB crossovers also require the minimum of crossover components.

A passive 24dB crossover is a tough nut to crack, and therefore rare, but is easily implemented in electronic crossovers, where it is very common.

Not sure if anyone is still paying attention here but I was just reading a review of the PMC OB1 loudspeaker in which the reviewer states that the crossover is wonderfully designed and produced a plot of phase coherence that is the best he has ever seen. According to the review, the crossover maintains the drivers in perfect phase with each other except for a small abberation at one point in the frequency spectrum. Given all that has been stated above by the first order crowd, how can this be given the use of 24db fourth order slopes? I'm sure I'm missing something here as this discussion lost me a long time ago. I'm just wondering how a steep slope design like the one in the OB1 can produce such perfect phase relationships as measured in the review.

I don't think I've ever seen a perfect driver, let alone a perfect full-range driver.

Given the limitations of current materials, I think that it's possible to do less damage by using multiple drivers, even though you need x-overs.

The end result seems to be better than what you get with single-driver speakers. Even the most savvy (IMO) of the single-driver designers (Ted Jordan) doesn't really recommend single-drivers. He recommends line arrays of mid-tweeters, along with subwoofers.

Perhaps the single driver IS the perfect solution. They just don't want people to know. Satisfied people don't need to upgrade every few months.

What happened to the "edit my post" feature so I don't have to post twice.

Perhaps the single drive IS the perfect solution. They just don't want people to know. Satisfied people don't need to upgrade evry few months.

To many Doppelspaten's while trying to figure out the Doppler Effect! ;-)

Srajan doesn't quite grasp the concept either. :-)

Skrivis - Srajan Ebaen has recently written about the "Doppler Effect" in his quasi review of the Zu Cable Druid speaker. The following is an excerpt in which he mentions the Doppler Effect.

"Conceptually, single-driver loudspeakers (this one's technically a 1.5-way) are phase and time coherent though the Doppler effect could be cited when you consider how the high-frequency whizzer cone rides atop the woofer. The day-to-day observable Doppler effect occurs with police or fire sirens. They sound higher pitched as they approach (wavelengths shorten), then successively lower as they pass us and recede into the distance. Theoretically, each time the Druids' woofers move forward, they modulate the tweeter response. Once you do the math and consider the average stroke of this 10" driver -- to calculate possible tweeter response deviations in terms of how woofer distance traveled equates to wave length -- it seems more of a conceptual than audible problem. Still, it's only fair to mention in this context and avoid painting a picture of theoretical perfection. Clearly, if the single-driver ideal were the one perfect solution, nobody would bother with multi-driver designs. The market place rather demolishes any such notions in one brief instance. As usual, it's about priorities. What type of compromises are acceptable to facilitate certain concrete gains that matter more to you than that which is sacrificed?"

Here is the link: http://www.6moons.com/audioreviews/zu/druid.html

Driver aligment isn;t easy to do well (wavelengths are so short up there). A Supravox 215 fron mounted on the baffle and a tweet back mounted with a makeshift waveguide, blended quite well at ~8-9kHz. All open baffle.
bastanissells an open baffle kit called "prometheus airforce" that's reputedly very good (someone does sell import it in the US).
Do check the Tangbang's excursion capabilities -- I think you'd need to cross the Tang to a woof quite high up to avoid hitting xmax too soon. Also run a quick test to see if a small contour wouldn't be indicated (quite a few people at diyaudio have worked with the Tang).

As to the Hammer, I haven't heard it but given the many accolades (esp with a fostex supertweet) it may be an option. Good discussion at melhuish's site (super 12.
Cheers

Diaural v. Acoustic-Reality what is the differance? and how do they differ from other series crossovers?

Greg, I like the concept. The equation I use is 1,100/ freq = wavelength (ft). So a 2" driver would start to beam at 8K. How do you align the drivers? If you use a 1" tweeter I would think you get a flare if you drop it in at under 13K.
My concept is to use a 4" Tang-Band or new WR125S from Creative Sounds. Both roll off over 10K so you use the natural rolloff of the driver and add a tweeter with a capacitor to cut frequency below 10K. I'm sure my inexperience is showing here but this is what I'd like to do. Minimal x-over and F-R to 20k. Beaming would be a minor issue.
On your 8K concept there is Hammer Dynamics 12" but I think the main driver has a whizzer which I am against using. Here are Other single drivers
Have fun. Let me know what you think.

Cdc: forget the perfect piston. It'd be nice to have -- but let's just dream for now:)
An 8" driver has the advantage of being able to cope with mid & low-mid frequencies w/out extreme excursion. A smaller driver would be straining. OTOH, it WILL beam, as you hint, higher up. That'll narrow the sweet spot but, on the brighter side, IF the dispersion changes in a reasonably controlled manner, you reduce reflections... (at least that's s/thing). If the full-range can take it elegantly, I would try cutting in the tweet, 1st order, higher around 8kHz.
It's a pain to align the drivers -- but once it's done, it sounds good.
Cheers

Thanks Skrivis and Gregm. I have tried twice to respond but both times, 15 minutes into my response my computer crashes from doing Ebay auction at the same time. So I give up.

Gregm> "Why not use a wide-range drivers -- i.e. a 8" + supertweet, then a hefty subwoof"

Well, an 8" driver is generally going to be getting pretty far away from a pure piston at treble frequencies.

Perhaps a smaller mid-woofer crossed at 3-4K to a tweeter, and then a woofer or sub below it, crossed at maybe 100 Hz?

Cdc-- I only dimly remember the Jordan circuit, but it looked like a contour rather than BSC (it was across the driver -- but don't hold me on this!).

Skrivis:
Re: first order+ drivers. Why not use a wide-range drivers -- i.e. a 8" + supertweet, then a hefty subwoof. You'd have to biamp (at least) but, as you note, there's no free lunch!

Well, a single "perfect" driver would be large in diameter so as to achieve good coupling with the air load so that it could reproduce low frequencies well. Unfortunately, that leads to problems with directivity and also possibly smearing of the high frequencies from widely spaced sources of the same signal. (Think panel speakers.)

So we'll go with a smaller driver and increase excursion. Then we start seeing problems with IM.

Since real drivers aren't perfectly stiff, they don't maintain pistonic motion at all frequencies. (Real drivers also have mass, and that changes things too.)

So, a cone driver will "want" to become a smaller cone at higher frequencies, and we start seeing breakup modes. This can be damped to some extent by the surround.

Ted Jordan explicitly allows for this behavior. He claims to control it in his drivers. But he's still using metal cones, and there's going to be a nasty breakup mode. the only question is how well controlled it is.

I suspect that some "full-range" drivers actually use these breakup modes to increase output at high frequencies and provide some impression of treble. Not what you'd call accuracy. :-)

So what's wrong with a multi-way system with drivers that are more likely to be able to display pistonic motion throughout their passband? Crossovers and the physical spacing of the drivers. This causes some problems and makes it harder to provide an accurate "re-assembly" of the waveform at your ear.

1st-order crossovers screw things up less than steeper slope crossovers, but place higher demands upon the drivers. (But still not as high as the demands upon full-range drivers.)

Physical placement is harder to cope with, but you can control some of it, particularly since we're only listening from one point at a time.

It's almost a Catch 22. Real full-range drivers have major problems. To solve those problems we use multiple drivers, which introduces other problems. I submit that the problems with multiple drivers can be solved more easily and more fully than those with full-range drivers, given the current state of technology.

(One possible solution is to use full-range drivers at very low power levels. This works with headphones, but not so well for normal speaker systems.)

There's just no free lunch. :-)

Gregm, that's interesting about the Jordans. Is this a baffle step compensation if they are not put up against the wall?
In my limited experience with single driver speakers, the biggest shortcoming IMHO, and this is highly listener dependent; is lack of detail especially in the higher frequencies. They are there but at a very low volume level. Maybe the driver jsut can't move this fast to reproduce at full volume level.
The Fostex F200A is an 8" driver which measures maybe -2dB at 20Khz. Wish I could give that a listen.

Cdc -- there may be numerous advantages to multi-driver spkrs but spl is not necessarily one of them (think of those 22.000 gauss Lowthers with a front horn).

I love wide-range drivers. Single wide-range drivers are actually rare; remember the whizzers on most such drive units. Limited frequency range, beaming, dispersion, IM, (response peaks & valleys)... are some of the most annoying (to me) problems. {BTW, you DO use a circuit on the Jordan & it actually sounds good}.

BUT, a single wide-range unit has immediacy, reasonable response in a critical region (200-4kHz, most will do 8kHz for you, some will actually hit F6 @ 20kHz withOUT a whizzer!!), phase & the like are out... it's marvellous. Extension can be had using a supertweet (not easy to match) and, better still, using a stereo subwoof.
Tough to beat.

Ultimately though, these are EXPENSIVE spkrs. Driver cost alone for a high level full-range biamped design can easily top $6k (that's $35-50k in commercial equivalent).

So what makes a time and phase coherent 1st order speaker better than a single driver design like Jordan JX92s or Fostex F200A? Jordan has NO crossover, no components in the signal path to create distortion, no driver blending problems, etc. etc.
Seems the more people talk about their 1st order T & P designs the more I like the single driver approach. Are the only benefits broader frequency range and louder volumes?

Some series xover related pages: Graddon, Murray H, K Lehma, Jon Risch.

Of course, any ref list on xovers would be incomplete without the frd consortium.

Cheers

Rod puts a lot of thought into the articles he writes. :-)

I feel series crossovers are better than Rod makes them out to be, but they're not the greatest thing to ever happen to speakers - as some people claim. :-)

Bud had an article that he was making available that contained a summary of his knowledge on series crossovers. However, I was told that this (and other) articles are no longer available. Perhaps someone will make it available on the web so I can read it.

Where I disagreed with Bud (and the current Fried Products) is the claim: "Properly implemented series networks provide superior driver coherence, increased dynamic range and introduce a Doppler effect similar to live music that increases the sense of realism."

"Doppler effect?" Sounds like pseudo-science to me, and it also would qualify as distortion if it exists.

Perhaps it simply strikes me as odd because DiAural were making some unfounded claims about "Doppler" effects, but they were using series crossovers to reduce them. :-)

Nevertheless, I'd like to see some proof for this "Doppler effect" and how it "increases the sense of realism."

Skrivis, I must applaud you on the link you provided!

Also, along with the series crossover being "self correcting" in terms of driver variation, it exhibits the same characteristics for variances in the crossover components. For example, as we know, using a 5% capacitor in the network can result in a fair bit of variation from speaker to speaker. While painstaking matching of all components is a solution, the cost effects (time, testing, and parts) cannot be dismissed. The series network yields some very positive advantages here.

However, as the article points out, in the end, there is no free lunch. But, we have always known that and come to this conclusion for a lot of things. Otherwise, there wouldn't need to be much variation in crossover design.

Ooops, no "edit" function anymore. Well, the BIG Heil is dipole, of course, the other one has a back chamber...

As per Skrivis, my own (unsollicited) opinion would be slightly in favour of a series -- IF you can easily get the drivers' electrical parametres VERY close (or near identical). Again, I'm just a hobbyist -- not a professional.

As to the Heil, 3kHz seems quite high -- which model are you using? As I know nothing about the Peerless, I really can't offer an opinion as to that particular match.
However, the Heil is dipole, so are you considering a 3-way with an open baffle mid -- or are you going closed cab after the Heil? If so, getting your system radiation pattern acceptable 3kHz downward could be a bit tricky!

ASAIK, the guy who makes "Heil" speakers crosses his AMT's about two octaves lower onto an upward firing peerless (quite a big unit if I remember correctly...). Frankly speaking the result is excellent down to the peerless: then things get a bit messy BUT that's just my opinion.
Cheers
Cheers

There's some disagreement on the benefits of series vs. parallel. I feel series is superior, but I'm not the last word on things. :-)

You can find a fair bit of info on the net about series and parallel crossovers. Rod Elliott has some good info, for example. http://sound.westhost.com/parallel-series.htm

I don't see that you can say that either the W/M or M/T interface is more important. Both will affect the operation of the mid driver, and that's where your ears are most sensitive.

I don't know enough about the Heil to render an opinion, sorry.

Karl,Roy&Skrivis:SERIES v PARALLEL 1st Order XO, What are the pos&cons of each in a two way and three way system also in a three way what is more important the T&M or the M&W interface?Would a HEIL be suitable for a 1st order tweeter if OX at about 3k with the new PEERLESS 134 HDS NOMEX paper cone? And A BIG THANK YOU GUYS for a great thread.

Thanks,
Ben

I gave the source as an explanation of vector addition. Then since the thread is about 1st-order crossovers, I included a quote that shows the superiority of 1st-order crossovers. There can be no argument with that. "It yields a piece of wire."

You might argue that some drivers won't tolerate 1st-order crossovers. Ok, that's valid. You can then either look for "better" drivers, or you can compromise with a higher-order crossover.

Lobing? If you're looking for certain types of directivity or power response, then that could be a valid concern. I would certainly look with favor upon a high-order L-R crossover for sound reinforcement use, and this is one of the reasons.

There is much concern with flat frequency and power response. I'm a bit skeptical about their importance. (I feel there are other more important problems. Besides that, to paraphrase Pat McGinty, "Once you solve the transient response, power and frequency response fall right into line."

A number of people have suggested ways to test whether phase coherence is audible, and there are indeed studies with conflicting results.

Rane's suggestion of passing a signal through a 4th-order L-R crossover and then summing the output makes sense. (Linkwitz suggests a similar thing.)

But, in order for the test to be valid, we need to play the summed signal via a transducer with no phase distortions of its own.

A panel speaker would seem to be out, since it has widely spaced sources of the same frequency. In the near field, it smears transients.

Speakers with high-order crossovers are out because they're doing the very thing we're trying to test for and there would be no possibility of a control in the experiment.

Speakers approximating a point source, with 1st-order crossovers might be suitable, but I feel the best bet is headphones. It completely removes any phase distortion due to the room as well.

I do plan on performing this test at some point, but at present I can only say that I find the sound of speakers designed to be time and phase correct to be more realistic than those that are not correct.

Looking at this logically, we can say that a speaker that can pass a transient is better than one that can't. We expect the same from other components in the chain.

The compromises needed to build a speaker that will pass transients is where argument arises. That, or the compromise of building a speaker that won't pass transients. :-)

As for "Infinite Slope," I question whether it is beneficial. What is the phase and time behavior like? Don't sharp filters like these ring? Do most drivers actually need such steep slopes? What kind of load does it present to the amplifier?

The NHT Xd would seem to offer more of an "Infinite Slope" than JosephAudio does. :-)

If one is going to go with steep slopes, then the approach taken by DEQX seems attractive. It corrects some of the problems.

As for the intent of the Rane article, for their purposes the high-order L-R alignment is ideal. They sell such crossovers, so their intent was to sell more of them. However, they certainly cannot say "It yields a piece of wire" about their crossovers.

I did not quote out of context, because I did not change the meaning of what I quoted by quoting only it. As for the author's intent, I don't actually care a fig for his intent. The quote I made stands alone.

The rest of the article deals with: "Are 1st-order crossovers more accurate?" "Yes, but..." The author's intent lies within the "Yes, but..."

Would I choose Rane crossovers for sound reinforcement use? You betcha. I wish I had had them. They offer a superior product for that use.

I was only quoting from the same source that was cited, since the earlier quote gave an impression that was different than the articles author intended.

Musical realism is the goal of every high end audio designer.

While visiting our local library last week, I heard some symphonic music and immediately thought "that sounds right!"
So I went to see what could sound like an orchestra in a library, and found....a live orchestra practicing in a library!

Each and every design approach has its advantages and its trade-offs. Getting a realistic sound from a system is a complex topic, and a sucessful design is the result of many decisions. The crossover slope is not the sole determining factor in the sound of the speakers. Examining the crossover slope in isolation is impossible outside the digital realm -
you are always introducing variables as the drivers interact and new radiation patterns are established.

I sympathize with the minority given voice on the forums. After all, I am the only manufacturer with Infinite Slope crossovers! I think its important to look at the acoustical wave interference and lobing patterns of the speaker - but since most other companies have no solution to these problems it is seldom talked about except on these forums.

Jeff

Is it audible ? I think the best answer is for everyone to demo for themselves and answer for themselves.

It always amuses me when someone makes the claim "It's not audible. Well, not audible to most people most of the time, anyway. Or at least not audible to some people some of the time....."

This is fundamentally no different than the claims that "all amplifiers sound the same" or "lamp cord is perfectly good for speaker wire." Anyone with good ears can only shake his head at such statements. Maybe they hold true in the world of budget-fi, because at some point those differences get swamped by the colorations of the rest of the system. But in a good system, with good music, the differences are plain as day, and time/phase coherence is no exception.

Now, it is not much of a surprise that Rane (and others) would downplay the audibility of time-and-phase coherence, given that they are in the business of selling high-slope crossovers. And in the pro audio world, this is indeed likely the best overall compromise, given that power bandwidth is a serious consideration. I mean that with total sincerity-- if I were designing a pro system with active crossovers, 4th or 8th order L-R would be my first choice, no question. But that doesn't necessarily make it the best for ultra-high-end home audio playback, where other priorities (fidelity to the musical signal in both time and amplitude, for example) take on much higher importance.

The most telling truth is that once someone has lived with a really good time/phase coherent system for some time, he finds it impossible to ever "go back". The lack of coherence in high-order systems, while potentially ignorable if one has never tried anything else, is nonetheless a major step backwards once one has heard the possibilities of an electrostat or a good first-order design. And since the vast majority of systems on the market are still non-coherent, it is quite possible that the majority of audiophiles have never actually lived long-term with a time/phase coherent system, and simply don't know what they're missing.

Luckily, forums such as these allow the minority not only to make our voices heard, but more importantly, to plant seeds of inquiry in the minds of those who may have simply never thought about such subjects before. For to me, there's nothing more satisfying than seeing that light bulb go off, and hearing someone say, "Wow, it sounds like real music!"

Best,
Karl

An even more telling part of the article regarding the group delay of a 8th order L-R crossover.
"Is It Audible?

The conservative answer says it is not audible to the overwhelming majority of audio professionals. Under laboratory conditions, some people hear a difference on non-musical tones (clicks and square waves).

The practical answer says it is not audible to anyone for real sound systems reproducing real audio signals."

Skrivis, great link. As always, a graph is worth a thousand words.

Just to add to the info on vector diagrams, there's a very good explanation of what's going on at the Rane site, particularly in http://www.rane.com/note119.html

The most telling part of that is "The 1st-order case is ideal when summed. It yields a piece of wire. Since the responses are the exact mirror images of each other, they cancel when summed, thus behaving as if neither was there in the first place. Unfortunately, all optimized higher order versions yield flat voltage/power response, group delay or phase shift, but not all at once. Hence, the existence of different alignments and resultant compromises."

Let me explain my porting question on GMA's C-3's relative to time and phase coherence. I have no idea if there is an audible issue with the C-3's design and based on Roy's published specifications there is nothing to suggest what I'm about ask actually takes place, nevertheless I thought I'd throw it out there to elicit a response regarding the porting theory behind this design.

In GMA's C-3 the bass port is firing in an upward direction, directly below and slightly behind both the midrange and tweeter, with a clearance of perhaps 4-5 inches. I'm wondering if conceptually there could be some type of Doppler effect taking place with the placement of the port relative to the midrange and tweeter that could slightly alter the phasing or timing of these drivers? Although there is no high-frequency whizzer cone riding on top the woofer; as in the Tannoy, in theory as the woofer moves backward and air is pushed out of the port, is it possible that this change in air pressure could somehow modulate the midrange and tweeter response by disturbing their wave lengths? Alternatively, when the woofer pushes forward, does the port suck in enough air to also disturb the wave length of the midrange driver and tweeter, thereby throwing off time and phase coherency?

"At the crossover point, for example, one driver is at .707, +45, and the other is at .707, -45, as I stated previously. Due to the fact that this is vector addition, they sum to unity at zero phase. And they do this not only at the crossover frequency, but at every single point from DC to infinity. The first-order is the only crossover that does this."

Karls, thanks for that explanation ... now I completely understand why the first order crossover can work in amplitude and phase terms through the region where both drivers are contributing to the sound. The power output of both driver is 3dB down at this point (amplitude is reduced by 1/(square root of 2), and they are 90 degrees out of phase, but the vector addition of these two waves results in a sine wave that is in phase and 0dB down in amplitude.

>But anyway, what I understand as phase coherent means that the entire output is in phase ideally independent of listening position. The only speakers capable of this are full-range, single driver designs.

Since that last sentence is not true in all cases, nor in the majority of cases if we want to talk about phase and time alignment, which we do want to in this thread, primarily. There are other threads to talk just about phase coherent speakers which are not time coherent.

Note that I am agnostic on whether first order crossovers and stepped baffles are always the best selection of tradeoffs or not. I've mentioned near field listening situations as one situation to consider.