First order/Time Phase-Coherent speakers discussions


"The game is done! I’ve won! I’ve won!"


I would like to use this thread to talk about this subject which I find rather fascinating and somewhat difficult to get my hands on. I went through a course in electromagnetism in college and I have to say this is even more confusing and you won’t find the answer in calculus, physics, Einstein relativity be damned it’s not in there either and definitely not in quantum physics. Listening to the "experts" from Vandersteens and Stereophile but ultimately it all came down to a missing link sort of argument ... something like this:
"Since if a speaker can produce a step response correctly, therefore it is time-phase coherent, and therefore it must be "good".

It’s like saying humans come from chimps since they share 90% genetic content with us, but we can’t find any missing links or evidence. FYI, we share a lot of gene with the corn plants as well. Another argument I’ve heard from John Atkinson that lacks any supporting evidence and he said that if everything else being equal, time-phase coherence tends to produce a more coherent and superior soundstage, but to the best of my knowledge, nobody has been able to produce some semblance of evidence since there is no way to compare apples to apples. Speaker "A" may have better soundstage simply because it’s a BETTER design, and the claim "time-phase coherent" is just a red herring. There’s no way one can say the "goodness" from "time-phase coherence" because you can’t compare apples to apples. Ultimately it’s a subjective quantification.

I’ve been doing some simulation and I will post some of my findings with graphs, plots, actual simulation runs so that we are discussing on subjective personal opinions. Some of my findings actually shows that intentionally making time-phase may result in inferior phase problem and NOT better! (will be discussed more in detail).

Having said all that, I am actually in favor of first order/time-phase coherent if POSSIBLE. I am not in favor of time-phase coherence just for the sake of it. It’s just that there are a lot of mis-information out there that hopefully this will clear those out. Well hopefully ...

Here my preliminary outline:

1. My "subjective" impression of what is "musicality" and how it’s related to first order filters.
2. Interpretation of step-response. I’ve read a lot of online writing with regard to the interpretations but I think a lot of them are wrong. A proper interpretation is presented with graphs and simulations.
3. A simulation of an 1st order and higher order filters with ideal drivers and why time-phase coherence is only possible with 1st order filter. This part will use ideal drivers. The next part will use real world drivers.
4. A simulation with actual drivers and how to design a 1st order/time phase coherent speaker. Discuss pros and cons. And why time-phase coherence may actually have phase issues.
5. Discuss real world examples of time-phase coherence with Thiel’s and Vandersteens speakers (and why I suspect they may not ultimately be time-phase coherent in the strictest sense).
6. I’ll think of something real to say here ... :-)
andy2
[lurk disengaged} @andy2 ....I won't disagree with you as to the 12:51 pm 11/3 post; all of which is generally acceptable.  As for your personal hearing range, lucky you. *S*

As for how you can discern that I'm drunk or under some sort of influence over and through this medium that we're engaged in....*hmm*
That will take a certain amount of explanation on your part to the viewers of this forum as to how you've arrived at that observation.
I'll leave that issue for you to explain to the viewers here.

Personally, I've been called worse.  How far you care to sink is your call.
EDIT: Woah! I typed this earlier and did not post. The got home and hit "post" and see that it's waaay outdated. This was in response to a definiteion of T/Φ coherence.

Let me preface this by saying that I am not an audio engineer, so I don't know how meaningful anything I say can actually be. What I AM is a fully trained physical chemist, specializing in quantum mechanics and neutron crystallography. I have a tremendous amount of training in wave mechanics and the theoretical mathematics behind it.

If we are concerned with the time/frequency domain, we must first agree on a mathematical definition of how to represent a sound wave propagating through atmospheric medium. Once we establish this, we can discuss things without any subjectivity. Of course, we will also need data to use with our expressions, and as we are dealing with wave functions, we will likely want a periodic eigenfunction of some sort, a la sine or cosine or perhaps e^(x), which gives a better representation, but is less well-defined when deriving or integrating with it.

This is my recommended starting point for a meaningful discussion absent the subjectivity or ambiguity that inevitably arises when talking Hi-Fi sound. It’s actually not as daunting as it sounds, and we could easily develop a simple system from first principles.

You have given a terrific definition above, now let’s quantify it! This is a fascinating thread. Thanks for this!
What I AM is a fully trained physical chemist, specializing in quantum mechanics and neutron crystallography. I have a tremendous amount of training in wave mechanics and the theoretical mathematics behind it.
I am pretty sure that you're pretty intelligent and capable but this time-phase coherent thing is a lot more complicated than quantum physics and I am not kidding.  

If we are concerned with the time/frequency domain, we must first agree on a mathematical definition of how to represent a sound wave propagating through atmospheric medium.
The problem is not about the mathematics.  As a matter of fact, the mathematics are rather simple.  

Once we establish this, we can discuss things without any subjectivity.
I agree in general but the problem is how to identify which part is objective and which part will always be subjective and you just have to deal with it.  For example, it's difficult to say which is better sounding since it's also dependent personal tastes.  No mathematical modeling can sort that out.

Of course, we will also need data to use with our expressions, and as we are dealing with wave functions, we will likely want a periodic eigenfunction of some sort, a la sine or cosine or perhaps e^(x), which gives a better representation, but is less well-defined when deriving or integrating with it.

Again, the problem is not the mathematics on the objectivity side of thing.  In term of measurements, simulations and so on, all these are fairly well established.  The problem is that our hearing is very complicated and no amount of mathematics can figure it out.  I don't mean to obfuscate the issue.  It's really true that nobody has been able to model our "hearing".  Not even close.

It's actually not as daunting as it sounds, and we could easily develop a simple system from first principles.
Already you have under-estimated the complexity of our hearing.  "A simple system" will not do it! 

let's quantify it!
Amen .....

While I can't say which is better, whether time-phase coherent matters or not, I can give a clear definition of what is time-phase coherent is.  Soon I hope!



Personally, I've been called worse. How far you care to sink is your call.
It depends on the level of weirdness of your posts.  If there are more than three run-on sentences and more than three random thoughts randomly put together into a sentence, then that would be qualified as being "drunk posting".

I can see there is no point in going any further. 

Nobody in their right mind would attempt to fully model a physical system when a perfectly good approximation will get you 98+% of the way there with a fraction of the work. Simple harmonic oscillator and rigid rotor are perfect examples of this. Yes, the electron probability density function is infinitely more complicated than our simple model, yer we are still able to predict with stunning accuracy observable properties using these simple models. This extends to many, many practical examples.

Granted, with access to a supercomputer, it can be fun to attempt to add as many perturbations as one can, but that's an entirely different exercise.

I leave you to it, as you are obviously very capable.
I am with you midnight_rider. You can't proclaim one hypothesis to start the post that defines a holy grail, then claim that something else is too complex and variable to model .... which means no holy grail.
Sorry, @andy2 .  My excuse is that I 'was born this way'.  If you haven't run into a 'personality type' of my sort, that's not my problem.

If you'd care to note the time this post has been made, it's a bit early for even my lifestyle to get fried enough to 'drunk post' this early in the day.

As is said, "It takes a lot of souls to fill a freeway."  And, having been born in SoCal (Long Beach) some 68 years ago, I might be able to legitimately claim the effects of smog causing mental dismangement....

But I won't.

As for the way I express myself; if you'd prefer monosyllabic retorts....not very likely from this mortal. 'Short & terse' isn't really my style, here or IRL.

Besides, this is really 'off-topic', you Are the 'OP', so...get back to it.
No apology sought or required.
Have a good week. 
Did someone earlier call Jim Thiel a genius and then reference his 5 model crossover? Look at this crossover and tell me this isnt actually the work of a designer concerned with only one aspect ignoring all else. All I can say is that this crossover is an affront. 
Did someone earlier call Jim Thiel a genius and then reference his 5 model crossover? Look at this crossover and tell me this isnt actually the work of a designer concerned with only one aspect ignoring all else. All I can say is that this crossover is an affront.
Do you happen to have a link?  I am very very very curious to see how they did it.  I agree that Thiel may have concentrated on the "time-phase coherence" part too much but may have ignored other parts of speaker Desgin which are equally important.  Their xovers have been accused to being "too complicated" but I've never got to see the actual "xover".  
Before posting any real data, simulations, plots and what not ... let's put down some basic definitions of what is time-phase coherence.  

I can see three basic types - from easiest to most difficult.  Let's start with the easy first.

1. First order/No Time-Phase coherence: this speaker will use first electrical order, but there is no time-phase coherence.  It will not be able to produce a proper step response.  It's more or less conventional with the exception that it uses first order filters.

2. First order/Time-Phase Coherence, BUT NO "Time coincidence"
    (which will be explained in #3).
  This speaker will be able to produce a proper step response, BUT and an important BUT.  It may not be able to produce an excess phase of 0 degree from say 50Hz to 20KHz.  This means that the speaker, for example, may have a phase shift of 50 degree or more or could be a full 360 degree at 15KHz, but only 5 deg at 500Hz.  That is its excess phase will vary especially at higher frequencies as the tweeter approaching 20KHz.  John Atkinson would agree this speaker meets his definition of "Time-Phase Coherence" since it could produce a proper step response.  My guess is most speakers that were measured by John Atkinson would fall into this category.  I've seen some measurements done on Vandersteens speakers and I was like ... hmmm... I am not quite sure.   But the most stringent definition is reserved for #3.

3. First order/Time-Phase Coherence AND Time-coincident: this is the most difficult definition for any speaker to meet.  That is it has to be able to produce a proper step response like in #2, BUT it also has to be able to have a 0 degree of excess phase from DC - 20KHz.  In reality, no speaker will have absolutely 0 degree, but the variations should be very small.  I believe Thiel claims that their speakers excess phase shift is only a few degrees (less than ten).  To be honest, I am not sure many speakers in the entire history can meet this definition.

So to summarize, you have three distinct possibilities from easiest to hardest:
1. First order/No Time-Phase coherence
2. First order/Time-Phase coherence BUT NO "Time coincident"
3. First order/Time-Phase coherence AND "Time coincident"

As for terminology, I guess you can call anything you want, but as far as the measurements, those are the three categories. 

With real data, graphs, plots, simulations those three cases can be clearly demonstrated.  Just talking about it making things more confusing.  
You can Google and find photos of this crossover. When I look at this thing I dont know if I should laugh or cry. 
When I look at this thing I dont know if I should laugh or cry.
Ultimately it all ends up in "cry" like the "Crying Game".  But I give that it helps to laugh every now and then.
You can Google and find photos of this crossover
OK, just did.  Actually they don't look that bad.  It all depends.  


As Danny Richie (GR Research) explains in his series of excellent You Tube videos on the subject of loudspeaker design, cross-over design is a matter of getting the individual drivers to coalesce. He uses the waterfall plot as his number one design tool, as it reveals a LOT about what the drivers are doing, both in amplitude and phase, which are inter-related.

The phase responses of the drivers in a speaker is a major component in that speaker’s frequency response. The summed output of two drivers which are out-of-phase at any given frequency cancel, creating a null, and a resulting depression in the frequency response. Listening to Danny discuss a speaker which uses two widely-spaced tweeters to reproduce the same frequency is pretty amusing. ;-)

Yes getting to get the drivers to coalesce using the simplest and most efficient method possible which presupposes using the fewest crossover components. Amplitude and phase are very important but even the best crossovers just minimize the damage. It is impossible to solve amplitude and phase problems when a crossover is present in the design.

Unfortunately, a full-range driver has yet to be invented! Big ESL’s are close, though. The best we can do for now is use two or three drivers integrated with filters designed to make them behave as one.

Danny Richie has designed loudspeakers in which he used the NEO3, NEO8, and NEO10 drivers in an open baffle frame. All the NEO’s share the same sound characteristics (unlike the drivers in most multi-way dynamic speakers), with each driver covering a different range of frequencies (each driver’s dimensions determining it’s optimal frequency band). He then created filters that combine their individual outputs into a cohesive whole. He mated them with OB/Dipole subs for very full-range music reproduction.

Nelson Pass is a single-driver loudspeaker proponent---watch the You Tube videos made in his listening room to see his. By the way, Nelson has created active analog x/o filters for the OB loudspeaker designs of his good friend Siegfried Linkwitz (R.I.P.), a true master of loudspeaker design. Nelson’s analog x/o’s are used in place of Linkwitz’s stock digital ones.

Dont get me wrong I am not a huge fan of single driver speakers, but the lack of crossovers in some speakers is a significant factor in making them viable for some. Also of note is manufacturers which operate certain drivers full range in 2 and 3 way dynamic designs. 
@bdp24 probably not effective to put real designers with patents and viable products up against theoretical “ hmmmm” musings... back to the music for me with a great speaker ( since 1977 ) that measures well 2

Satchmo at 45 RPM... sublime


The hardest parts are the beginning and the end. I probably got the beginning all wrapped up, but the end ...

For want of small
I lost self control
For want of beauty
I loss almost everything

Though small comes big
But I’ve been small
And I’ve tasted small
Now I want big

How will it end
Fire or Ice
I’m no Robert Frost
So I want both
Experience the insane imaging of a Vandersteen Model 7 and you will become a believer in time and phase coherence. 
Experience the insane imaging of a Vandersteen Model 7 and you will become a believer in time and phase coherence.

Although I am an proponent of time-phase coherence, I can't conclusively say that the reason the Vandersteen and the Thiel are so good because mainly because of time-phase coherence.  I guess I am not fully convinced until I know for sure.  From a theoretical stand point, time-phase coherence is better, but a speaker has so many variables that it's hard to pin down which is the most responsible for the "goodness".

I am sure a lot of people would be impressed by the various Wilson high-end models but they are not time-phase coherent.  

IMHO.
I think bdp is correct, no truly full range driver has been invented. However I have heard some lately that gave me pause and so completely eclipsed what was available even a few years ago.
Forgot to add that I have really liked some of the Vandersteen speakers I have heard over the years. To this day I think they make superb lower cost speakers. Hated the older Thiels to a large degree because of the tweeter he used. 
simonmoon: 

      Actually, we and other apes evolved from several ape-like critters, not only one.
     As far as phase coherence, having grown up with B&W from the beginning, I saw that their original test equipment demonstrated that what was measured by lasers reflecting from the drivers, when compared to the electrical signal,  became more coherent when the drivers were time aligned.  I measured my sub driver and aligned the center of voice coil magnets with my B&W 803 magnets.
     It does work, but phase alignment alone does not make a speaker out of a cow's ear.  Also, if you are getting a lot of wall reflection, your question is moot. 
     Thiel slanted their cabinet face for time coherence. Tilted Sound Anchor stands do the same thing.  It makes the sound from the drivers reach your ears in closer time phase.
     Think about this: The electrical signal reaches the deep-in-cabinet woofer magnet at the same time as the mid-sized mid-range and shallow tweeter. By aligning the magnet centers, the sound from the tweeters does not reach your ears before the mids, which is ahead of the woofers.
      Amazingly, some people use tilted stands with internally phase aligned positioning of the drivers, making the alignment bass ackwerd.
     Panel speakers do not suffer from alignment issues, for obvious reasons. 
a careful study of the ten or so first principles that go into Vandersteen speaker design will illuminate why time and phase are just the start. You could explore the just expired patent on the aerodynamic low reflection driver for starters, or perhaps the shared Low/ Vandersteen patent on DBS, which is applied to the internal filters  for the 5a or the pistonic CF/balsa core midrange which is a trade secret, or cabinet within a cabinet, or the co-cured Cf stealth cabinet, etc....the list is long, since 1977
@andy2 looks so far like you’ve come to this thread demanding some answers (you keep flailing away at the one practical-based q[what does it sound like?]). It’s one thing to want answers, everybody in this forum does, but it’s another to just plop down in a thread and bitc# and moan and blame everyone else for the fact that You don’t understand something, like we’re supposed to think you’re ’spatial’...you seem to think that Your ignorance is somehow Our fault.

You probly would’ve had more support if you had accepted responsibility for that from the start, but you evidently decided in advance that all of us are b@stards from the start for not telling you what it is you want to know.

I think at this point someone could give you the answer you’ve been looking for all along and you’d have too big of a chip on your shoulder and be too stupid to recognize it. Personally I have no interest in whether or not you ever do recognize it...and I don’t think anyone else here should either.

Yeah it’s Friday. And tomorrow’s Saturday and the next day is Sunday...I for one, don’t especially care how long it will take you, or how old you will turn out to be, before someone ’Finally’ leads you by the hand and delivers you (and the rest of us) from your own stupidity.

Have a nice weekend.
Yeah it’s Friday. And tomorrow’s Saturday and the next day is Sunday...I for one, don’t especially care how long it will take you, or how old you will turn out to be, before someone ’Finally’ leads you by the hand and delivers you (and the rest of us) from your own stupidity.

You can’t be so desperate, can you? Are you saying "stupidity" is what you’re waiting to save you? If that’s the case, can you jump off a building somewhere lols? If "stupidity" is what you’re waiting for, well just go and say "Hi" to whoever closest to you.  That should give you a quick "stupidity" fix.  

I got more poetry for you. More "stupidity" for you every week. Chew on that brother.
@ivan_nosnibor ...there's a lot of it going around of late. :(

@andy2 ....here, from 20:30 on...try to get the picture.  I'm not drunk....just...

Oh, 'ell....it's Friday. Try to have a nice weekend, huh?

https://www.youtube.com/watch?v=RQeOm3CuUFY
"You can’t be so desperate, can you? Are you saying "stupidity" is what you’re waiting to save you?"


Uhh...No. That refers to your wanting to berate or challenge anyone who is not answering your questions, particularly the unanswerable (what does it sound like), to suit your impatience, and then getting irate at the answer when it comes. You’re acting a bit like a drowning man who’s spitting at anyone who tries to throw you a life preserver. That’s pretty stupid, even for a forum.

But, if you’re saying that’s not stupid for you, then I’ll take your word for it...I guess.
So desperate!  I figured since you're probably a high school drop-off, I'll start with "stupidity" first lols.  Then maybe go somewhere from there.  After that I'll work with you to make you feel less pathetic.  I feel ashamed for you, I really do.  
He started it. I think he intentionally tried to piss me off so I’d give him some bread :-) Hey self defense and gun ownership are still alive and well.
Well, I suppose I'm tired already of the ramblings of an 'educated' man who can't think his way back down to earth long enough to answer his own question...ya got me there I guess. 

My hat's off to you, if you can fly as high on yourself as you claim to and still not know how to fix your problem.

I'd say your first blow up in your thread 'started' it, you just snowballed from there.
...and I'm now quite happy to be on the other side of the country... *G*

Anyway...calm down, stay on topic....

I came back 'cuz you started a topic that got my interest, and that of others.  I/we don't mean to make you feel attacked, far from it.  Phase issues, which you yourself stated earlier are complicated.  

Resorting to 'quantum states' ain't gonna help us typical audioholics, no.
I'll return to my last aside that active xovers may cure the bulk of the issues.  Give the drivers what they Need 'upfront', so to speak.

Yes, it requires bi-, tri-, or whatever amping quantities required...
....but it sure works in my space....

Just saying....

Don't shoot. ...please?
Most of the better systems I've been around are such.  It makes sense to cope with the signal on a lower level before adding 'power'.  Better and more discrete control without having to cope with high drive levels.

The same holds for active eq; I can 'adjust' for my space, even with omnis.  I can 'ignore the room' so to speak, since I'm in the midst of it.

I know I'm ignoring most of the past posts...but I'd rather cut to the chase.
MHO.....and please, 'humble' is the word of the day....well, this evening here. *G*
5:40 in Anaheim...time for dinner, I guess....*S*

I'm patient....Bon appetit...;)

man who can’t think his way back down to earth long enough to answer his own question...ya got me there I guess.
aaahhh ... so I guess that’s your problem all along. Come clean and you’ll be forgiven brother.

Why go around the neighbor dog? Just come and knock on the front door. You look kind of stupid now, don’t you!

I know enough not to sprout around someone else nonsense.  
Ivan Ivan come out where ever you are lols.  Are you hiding in my closet lols.
The way you treated me I could expect, my problem was with the way you treated everyone else here.

Like about everyone else in this thread before me has figured out and gone (where are they now), you're long on making a splash and short on contributing anything useful. There were plenty useful comments here to make a good thread out of, but you were only interested in what you think you know, as others tried to tell you.

But, for everyone here and any exchange of ideas, you were too much of a headache and too much of a PITA...I'll leave it to you as to how that pairs up.

I think I'm out.
I think I'm out
Yeah, why don't you're out of this universe if you know what I mean.  Some how I doubt it.  I'll probably have to deal with your shenanigans sooner or later.  


Look, I'm not out to dog you to hell and back. I'm not asking you to change your style or anything...just try to be just a Little more respectful of everyone else's point of view...maybe even if you don't entirely agree...maybe offer a civil but rational response that might explain your objections in the terms they presented??…just a little more give and take maybe?? 

That's all I'm trying to say.
Timlub,
I appreciate you sharing your knowledge on this vexing aspect of audio.  I can't say I understood it all, but it greatly aided my background on the topic.  

Roy at Green Mountain Audio was a big proponent of time alignment of the drivers in this speakers.  He also advocated removing ones eye glasses when listening to speakers because of the "smear" ? that they  caused in aural perception.  I built a pair of Linkwitz LXmini's a few years ago, before they came out with the companion subs for them and they were pretty sublime, but rendered my expensive 2-channel amps unusable and had limited LF response.  

I remember in 1983 when bought a pair of Spice TC50's.  I was casually listening to them one night when my neck and attention snapped to the left of the room when some violins started playing on the track... the imaging was simply unbelievable, palpably realistic.  At the time I listened to music at pretty high SPL's and went through several woofers and tweeters before moving on to JSE Infinite Slope speakers from Jeff Joseph.  They imagined quite well too, but not like the Spica's.  The Spica's were like electrostatics with a very narrow sweet spot.  
Hello!
I'm inventor of well-known  (infamous?) Infinite-Slope crossover system currently marketed by Joseph Audio. My patent license agreement with them expired in 2005 and at that time I went into blessed retirement at age 67.  In 2017 I was pulled out of retirement by three audiophiles owning Joseph Audio with the question, can your invention be improved? I said no but they insisted and I gave up to shut them up and returned to my notebooks (thankfully saved and in local tech museum) to study network topology and see if I have any new ideas.
The major problem hinges on simultaneous realization of flat frequency response and uniformgroup delay in three-dimensional acoustic space of the listening room. Actually impossible but at least a good approximation is the best that we can do and I come close in with Joseph Audio's products as is well known.
Mathematically one  can achieve flat frequency response and linear phase (flat group delay) using a single very good 4" driver without crossover in a transmission-line box. This system will have nearly perfect performance over a limited frequency range and with limited  loudness capability. Next, a 2-way first-order crossover is theoretically perfect in the math, but when realized in a speaker system, it is "perfect" only in the so-called "sweet-spot"  where the sonic outputs of the drivers add correctly without acoustic wave interference.
In 2018 at age 80 I attacked the problem again. With study of my notes, I came upon an idea which may work: Combine the idea (1) of so-called "constant-resistant" network theory with my already realized "infinite-slope" theory (2) (based on high-selectivity filters in radio circuits).
I worked up a schematic-diagram of this new crossover idea using circuit-analysis models in a computer to start.  The results looked promising, and at some month's work developed a 2-way crossover model  in virtual cyberspace having both optimum frequency and delay responsesimultaneously!  Now it was time to build a physical crossover and try it in a prototype speaker system and found a quick-easy way to proceed:

I ordered the so-called "Solstice" loudspeaker kit from Parts Express , built kit, and installed my
2-way prototype crossover. At first I did not expect anything unusual, just another pretty-good sounding speaker system. I fired up my test equipment and made frequency, phase tests, and determined that system had good frequency response but surprisingly, flat group delay above the cabinet bass resonances!  A trip to the anechoic chamber at Binghamton University's Tech Center confirmed my measurements.  Now it is time to listen!

Played a CD of John Pizzarelli "Dear Mr. Cole" and the sound hit me so hard I burst into tears!Never have I heard sound like this from a loudspeaker box! The room disappeared and I heard the band!  Switching to my Pearls, I heard a good loudspeaker system. Now time to call my pesky audiophile friends, do listen with everyone astounded! We all hear something magic! I, almost with accident, had hit upon something unexpected!
We repeated test of my prototype in audio showrooms with three listeners against systems in the $30,000+ price range with same results, the little 2-way prototype was clear winner having obvious easily-heard sonic improvement. There was uniform spectral-energy sound throughout the entire listening space, with uniform sound without  "sweet-spot"  with all hearing music coming from a nearly perfect "orchestra" instead of a set of speaker boxes.

I had to develop (successfully) a 3-way crossover so invention could be installed in Joseph Pearls, with the same astonishing results. Stay  tuned everyone!
Patent on invention filed July 2019.

RIMO.
Hi Richard,
     I have read your review on Parts Express several times as I find this speaker that you drastically changed a true bargain in the audiophile world.  I look forward to hearing the results of your constant resistant technology combined with infinite baffle.  
Just curious,  will your constant resistant technology work with any parallel or series crossovers?  Please expand on this once you are comfortable with your patents.  I appreciate you chiming in, Tim