TriTrix crossover design: gaps in understanding

[juddwilcox]

Warm Holiday Greetings to all!
I built a pair of TriTrix speakers a few years ago and I have enjoyed them immensely. I offer many thanks to Mr. Campbell for his design and to all of you folks who encouraged me, by your excellent examples, to go through with that project!
For the past couple of weeks I have been studying/modeling the TriTrix crossover design, mostly as an academic exercise. My study has led me to two questions (which indicate large gaps in my understanding) that I'm hoping you can help with.

1. The textbook low-pass corner frequency (1/2*pi*sqrt(LC)) is 712 Hz while the high-pass corner frequency is 2050 Hz. For a first-order crossover I think I can understand a 1.5 octave (or even larger) crossover region. However, the second-order, 12dB/octave, high- and low-pass sections used in the TriTrix crossover design, especially when coupled with the natural roll-offs of the drivers, would seem to mate the drivers well beyond their respective -6dB points and so I would naiively expect a significant "hole" somewhere between 712 and 2050 Hz. The home-brew modeling workbook that I'm using bears this out. My ears, however, disagree: I can't detect any such hole when listening to frequency sweeps through the crossover region. Therefore, I doubt both my reasoning and my workbook - clearly I'm missing something major, here. Any ideas that could help further my understanding?
2. The home-brew modeling workbook that I'm using indicates that the tweeter and woofers, when connected to this crossover network, should be approximately 180 degrees out of phase through the crossover region yet the drivers are connected in-phase in this design. On page 79 of "Speaker Building 201," Mr. Alden cautions that, "If you use second-order 12dB/octave electrical crossovers, it would be wise to listen with your own ears to the system both with the tweeter polarity normal and then reversed...use the connection that your hearing says is correct..." I'm totally fine with his advice - and I have no doubt that this is the best choice for the TriTrix - but I am at a loss to understand it. Would any of you be able to point out any physical effects (that I am doubtless missing) that could cause the theoretical 180 degree phase relationship to disagree (so completely) with reality?

Many thanks from a vicarious hobbyist.

[kanemack]

Re: TriTrix crossover design: gaps in understanding

the tritrix crossover uses christmas magic. can't really help here, but i hope a little elf chimes in to help you out. merry christmas to all!

[Chris Roemer]

Re: TriTrix crossover design: gaps in understanding

If you're trying to analyze crossovers using "textbook" formulas, you're not going to really learn much. It is imperative that you use software that makes use a driver's unique freq. response AND impedance profiles. Granted, "simulated" impedance curves (even those generated by the more common "box" programs) COULD be useful (if actual Z data is not available), but (at a minimum) you should really try to "trace" (using "SPLtrace") these 2 plots off of manufacturer's data sheets.

On your 1st ?, are you using Alden's equations to determine these "corner frequencies"? Using data curves and XO "sim" software, I see the drivers "acoustically" crossing near 1400Hz, -5dB down (from their "summed" response), approx. 40* out of phase. This is all normal (IMO). Their DOES appear to be a slight "dip" in FR around 2.2kHz, but it's only -1.5dB down (from a nominal "system" sensitivity near 87dB), which is fairly insignificant (that's less deviation than the tweeter as used in this design, which on its own is about +/-2dB - and that ain't bad, either).

Phasing is a LOT more complicated. I THINK Ray talks about most aspects of it, but I believe it's scattered about in the text, and has to be searched for. A driver's actual phase is not a "flat line", anymore than its FR or impedance profiles are. That's why FRD and ZMA files have phase data incorporated in them. Also, if you had woofers and tweeters whose phase profiles WERE flat, you'd have to (ordinarily) place the woofer closer to the listener than the tweeter, just to get the phase "zero points" aligned (MY term here, meaning you'd have to physically offset the woofer, relative to the tweeter, otherwise - say you sent an "impulse" to both drivers at the same time, w/out a physical offset, the initial sound would reach your ears sooner from the tweeter than from the woofer, since the woofer's voice coil is farther away from you due to it's typical placement behind the rear of the cone-shaped woofer cone).

With NO filters in place, the woofer and tweeter would already start out about 70* out of phase (if mounted on a flat baffle). In THIS design, the 2nd order HP filter shifts the tweeter's phase about 110* farther out of phase (at the Fc, near 1.4kHz). It also shifts the woofers farther out by about 140*. So, starting 70* out, adding the HP filter now puts the drivers 180* oop (out of phase), so IN THIS INSTANCE (say you were running the woofers wide open), you'd want the tweeter connected reverse polarity. However, adding the LP network to the woofer pushes the drivers another 140* out (meaning 320* out, or 40* out in absolute terms). If you connect the tweeter reverse polarity, it'll end up about 140* oop.

Gotta go now.
Chris

[Jeff B.]

Re: TriTrix crossover design: gaps in understanding

Not discounting the possibility that Kanemack is correct, I think Chris' answer is a bit more technically savvy. Just a to add a couple comments before heading off to my Aunt's for Christmas dinner -

When you consider baffle step into a speaker's response and the fact that 4th order Linkwitz-Riley crossovers require the drivers to be 6 dB down at the crossover point, it is common for the midbass driver to cross at a point where the transfer function is -12dB (or more if there is any rise in the driver's upper end response) at the crossover point.

Likewise, tweeters, tend to get a lift in response near 2khz and below due to baffle diffraction effect. Consequently, they commonly need to be down several dB at the crossover based on the crossover transfer function too. This can all make it look like there should be a big gap in the response which isn't correct because we have to factor in the response of the drivers on the baffle into the equation.

In addition, if the woofer has a rising impedance due to voice coil inductance then this will work against the crossover's roll-off and will need to be factored in as well.

And finally, it is only the final acoustic crossover that matters, not the circuit used to get there. Due to driver roll-offs, two second order filters will usually result in a 4th order acoustic crossover when combined with the drivers. The phase will match that of a 4th order crossover, because the acoustic phase will follow the acoustic roll-offs. So, with second order filters and real drivers the connection will almost always need to be with the same polarity, not reverse polarity, because of the phase shift the drivers being included in the overall phase response.

Gotta run, it's almost dinner time.
Merry Christmas
Jeff

[johnastockman]

Re: TriTrix crossover design: gaps in understanding

As someone who came here 14 years ago asking "why, if the math/algebra always added up, the SQ was always crap?", and having tried many different kinds/brands of pre-made XOs, you must get away from any form of textbook algebra. It was difficult for me, as algebraic formulas came easy to me and I understood them. That's why I was so baffled as to why I could not get even a marginal result from them. Numbers do not lie when they're calculated correctly, so I came here asking "why". The main issue is you're using a fixed number for one that constantly varies. The variables must be accounted for when working up any XO. LR, Butterworth, and the others never got me anywhere close to listenable. The light went on above my head about using a fixed number for one that is variable. Of course that made complete sense. There's no need to understand algebra at all, as anyone can understand the problems with using a fixed parameter for one that is variable. Wow, no wonder I could never get a good result. I am certainly not a XO designer, yet, but I can understand the complete folly of the fixed number vs variable aspect in the "design" process. Any of the on-line calculators or pre-made XOs all use textbook formulas. I started with a slide rule, then I got a scientific calculator to try and get decent results. If you see any method that only asks for the nominal/average impedance as a fixed number and an arbitrary cross-frequency, stay away from it. I also tried to reverse-understand properly-designed XOs using textbook algebra. I started with the Speakerlab designs I had made for myself and many friends and family members, since they embarrassed the name-brand speakers they all used to have. The numbers never "added" up there either. The guys on the TT forum back then were kind and generous with their knowledge, and one gent corresponded with me via e-mail offering even more insight and instruction. That was my intro and I never looked back. I realized it was much more complicated and involved than I had thought, so I started building designs that had a properly worked up XO as my beginning learning process. Jeff Bagby has his excellent PCD that many here use. My computer illiteracy made that quite challenging for me, but I have found a different program, XO Sim, that has a shorter learning curve and is easier for my computer-challenged brain. It is not as comprehensive as Jeff's program, but by working with it, it's perfect training for getting more comfortable & familiar with the aspects so I am better prepared for PCD and its requirements and knowledge. Maybe Paul Carmody can shed a bit more light on some of the specifics at his site:

https://sites.google.com/site/undefinition/diy

If you haven't seen/read it already, at the right is "Resources". Read everything under that...it won't take but a few minutes and it'll help steer folks away from the algebra/textbook methods and why they can never work. Even for trying to understand why a particular XO design was derived and what it's actually doing regarding those aspects you were looking at. Good luck; it is a fun and interesting journey, the XO part of the speaker. Looking at an impedance plot and/or a frequency response plot, you'll see how those "numbers" vary across the drivers useable frequency range. And those are only two of the variable characteristics that must be taken into account when doing any XO design work. Don't hesitate to ask if something doesn't make sense...I had a bunch of those ?'s at first, so none are dumb or of the maybe-they-have-been-asked-before variety. If you want to learn PCD, help for that is also plentiful with tutorials and advice from actual users.


John A.

[juddwilcox]

Re: TriTrix crossover design: gaps in understanding

For what it's worth, I am using my own Excel workbook only to help me identify areas where my understanding falls short. For a concrete example, I am using the drivers and crossovers that are in the TriTrix.

The inputs to my workbook include:
1) capacitor and inductor values from the TriTrix crossover. I assume the that capacitors have perfect dielectric and that the inductors have zero DC impedance (I might add this later)
2) driver impedance as a function of frequency (extracted from Dayton Audio data sheets)
3) driver phase as function of frequency (extracted from Dayton Audio data sheets)
4) driver phase delta, due to the offset from the baffle, as a function of frequency (THANKS, Chris!)
5) driver efficiency as a function of frequency (backed into efficiency by using SPL data from the data sheets). By efficiency, I mean, eta_0=P_acoustical/P_electrical, as defined by Mr. Alden.

The functions of the workbook currently include:
1) calculate (complex) impedance of the network, drivers attached, as functions of frequency. These check out - the curves I get show correct f3's and (logarithmic) slopes for both high- and low-pass sections
2) calculate (complex) voltage and (real) electrical power in each of the components, as functions of frequency.
3) attempt to calculate the amplitude of acoustic pressure (?) for each driver. I am struggling with this at the moment - any decent references would be appreciated.

In the near future I hope to add the following outputs to the workbook:
4) calculate summed (interfering) acoustic power from the integrated speaker system. Heuristically, I know what this means but I'm having trouble articulating/calculating it. Again, any decent references would be appreciated.
5) calculate system SPL from the summed power

Jeff, I've experimented with PCD already. I thank you very much for your work on it and your willingness to share but I admit that it's a bit beyond me at this stage of my learning. I also totally get that the work I'm doing is already done in PCD and other tools which can easily use FRD/ZMA data. My goal is not to reproduce any part of your work, only, hopefully, to give myself a springboard from which I can begin to understand and effectively use PCD and similar tools.

With this as a backdrop I'd like to express my appreciation for the insightful feedback I've already received. Many thanks, Chris, for the, "Aha!" moment regarding the baffle offset and "zero points" and for providing some sign-posts that I can use to cross-check my phase calculations. Also, Jeff, thanks a zillion for your reply. It will take me weeks to learn enough to digest your comments but I am absolutely certain it will be worth it. And, finally, John, thank you for sharing your experience and encouragement.

Judd

[Chris Roemer]

Re: TriTrix crossover design: gaps in understanding

Google "FRD Consortium" (you might have to use the Wayback Machine - as that site is no longer hosted where it originally was) and see if you can find "XOverSim.exe". It's a standalone sim tool that's really easy to use, especially if you're new to all this. If you download it, I can send you my F/Z data files for the TriTrix drivers.

The DCR of inductors is a fairly important factor in both crossover AND box models, as it reduces a driver's output (just from the parasitic resistance) and also effectively alters a driver's "Q" in a box model (which alters both the optimum box volume AND the shape of the rolloff curve).

Chris

[johnastockman]

Re: TriTrix crossover design: gaps in understanding

Nice post Judd! I'm certain now that you already knew what I was conveying, so I sincerely hope that I did not insult your obvious further-than-me learning curve/knowledge level. While I am also not where I can grasp PCD, the XOverSim program Chris mentioned is quite good and uses freq. response and impedance measurement files for it's calculations. I have my copy and it is easy to get a handle on, you just have to get familiar with the procedure for how it needs, interprets and processes the data. Chris has been generous with his tutoring time, helping me wade through it's own requirements. I'm still making those procedural mistakes, but I do get it...practicing with it goes a long way towards becoming familiar. I think it's a great program by itself, and if your goal is to get proficient with PCD, it is an excellent place to start. Keep us posted on your progress, as I'm sure I can learn from your own process.


John A.

[juddwilcox]

Re: TriTrix crossover design: gaps in understanding

I haven't made much progress since my post on 12/26. As before, I calculated, (complex) voltage drop across (and current through) the drivers, as functions of frequency, after the crossover network. My quest was, and is, to convert these into acoustic power or, ultimately, SPL. This quest led me into several rather enjoyable rabbit holes learning about what audio amplifiers actually *do* but this hasn't helped me, yet. Any reference that might help me would be appreciated.

Chris - I would very much like to take you up on your offer to share your XOverSim simulation of the TriTrix. I did look, unsuccessfully, for XOverSim.exe. If you have one, would you share a working URL for that?

I *did* find an excellent reference that cleared up my question about summing coherent sound pressures. The paper, in its entirety, entitled _Fundamentals_Of_Acoustics_, by Prof. Colin H. Hansen is excellently written and cleared up lots of other questions I had, too. Since I found it so enlightening I thought I'd share it here.

http://www.who.int/occupational_health/publications/noise1.pdf

I don't know the protocol here in the forum about sharing URL's - hopefully I won't get banished for sharing...

Judd

- "What is sound to one person can very well be noise to somebody else.", Prof. Colin H. Hansen

[juddwilcox]

Re: TriTrix crossover design: gaps in understanding

In a PM, Chris R. encouraged me to find and download xoversim.exe from the web. From http://users.on.net/~isaacmcn/audio/...ewxoversim.htm I found and downloaded is "Crossover Simulator" Beta Version 1.0 by Isaac MCN. Also, in PM, Chris shared ZMA and FRD for drivers similar to those found in TriTrix as well as an xoversim primer which helped me get started with that program. (Thanks, Chris! You should think about posting that primer if you think others might benefit.)

In parallel, I was able to learn the basics of PCD7 - I shared that experience in another thread: http://techtalk.parts-express.com/sh...igner-7-(PCD7).

I am now able simulate TriTri XO and drivers both in xoversim and PCD7. I am now studying differences in their simulations to get a feeling for the relative strengths of the tools. This experience has been pretty rich for me and I'm thankful to all of you for that.

I am still baffled (no pun intended) by the physical meaning of the 3rd column in the .FRD files. I suspect it's the physical phase, relative to input, of the drivers, measured close to the cone. I'm not sure of that, though, and, until I get that sorted out I won't be able to understand how to sum SPLs myself and, as I shared already, understanding is my goal. I consulted the web but am yet to find a clear description or detailed (underlying) method of measurement. Can anyone comment on the physical meaning of the 3rd column and/or provide references to the method of measurement?

[Jeff B.]

Re: TriTrix crossover design: gaps in understanding

In a PM, Chris R. encouraged me to find and download xoversim.exe from the web. From http://users.on.net/~isaacmcn/audio/...ewxoversim.htm I found and downloaded is "Crossover Simulator" Beta Version 1.0 by Isaac MCN. Also, in PM, Chris shared ZMA and FRD for drivers similar to those found in TriTrix as well as an xoversim primer which helped me get started with that program. (Thanks, Chris! You should think about posting that primer if you think others might benefit.)

In parallel, I was able to learn the basics of PCD7 - I shared that experience in another thread: http://techtalk.parts-express.com/sh...igner-7-(PCD7).

I am now able simulate TriTri XO and drivers both in xoversim and PCD7. I am now studying differences in their simulations to get a feeling for the relative strengths of the tools. This experience has been pretty rich for me and I'm thankful to all of you for that.

I am still baffled (no pun intended) by the physical meaning of the 3rd column in the .FRD files. I suspect it's the physical phase, relative to input, of the drivers, measured close to the cone. I'm not sure of that, though, and, until I get that sorted out I won't be able to understand how to sum SPLs myself and, as I shared already, understanding is my goal. I consulted the web but am yet to find a clear description or detailed (underlying) method of measurement. Can anyone comment on the physical meaning of the 3rd column and/or provide references to the method of measurement?

The two programs differ in this way - Xoversim.exe uses a nodal analysis and can handle almost any circuit you can dream up if it is within its parts count and node count. PCD, on the other hand, works with a fixed circuit so you are limited a bit more with it, but for the most part it works with 95% of the speakers being built out there. The advantage of PCD is that it can include the relative offsets between drivers and calculate the summed response accordingly. This is a real miss by Xoversim in my opinion.

The third column in an frd file is the acoustic phase of the driver. It may be minimum phase or it may be measured phase with time of flight included, but it is phase. You should do a little search online for information about understanding acoustic phase. There is a lot of info out there.