Cauer-LSPCad question

[JohnL]

Hello Guys, I just downloaded the demo of LSPCad last night to play with doing some Cauer filters. How long should it take to optimize a 2-way network? I set the thing up with a cauer on the LP and a 3rd order electrical on the HP and got it fairly flat, set it to optimize last night at about 9:30pm and it was still optimizing this morning at 6:30am. It's only a P3 1.5 ghz, but does this seem a bit long to anyone? I've never used this particular program before, I was just wondering if I was doing something wrong?

Thanks,
John

[JonMarsh]

Hello John, and welcome to Missio Possible DIY!

LspCAD never stops optimizing until you hit the stop function; it's not like the versions of SoundEasy or my old DOS based CACD. It reports on the degree of error and just churns away.... Now, are you trying to optimize the whole design at one pass (high pass and low pass?) or are you setting the acoustic transfer function targets for the high pass and low pass seperately and optimizing those... the latter is the recommended procedure. I rarely rely on LspCAD for doing a complete "flat response" optimization, becuase the crossover points could wander, the filter transfer function could wander, etc. This isn't the way to use the tool. You want to consider what your goal is and set the acoustic transfer function for each driver, knowing how they should sum in the final system.

Don't forget to specify the right driver polarity for complete SPL summation- for example, for L-R 4, thats positive polarity on both drivers; for Butterworth 2, L-R 2 and L-R 8, that's inverted polarity for the tweeter. Third order can work either way, chose that which produces the best power response for the specific front panel and driver acoustic offsets.

If you're used to SoundEasy (or at least the older versions I'm familiar with - haven't used it in years), this behavior may seem strange, but it you can adjust the range of optimization steps while optimizing and tweak how it settles in... typically, you'll start with the steps set fairly large, then bring the step size gradually down, until there's no real improvement to the fitting error. This shouldn't take more than a couple of minutes for each filter section with a computer like yours. Optimize HP and LP individually.

Now, all that said, let me say a few other things about the optimizer- getting the most out of it requires perhaps a bit of thought and care, and it should not be depneded on too often. It's just a curve fitting optimization program, and as regards speaker design or your overall goals, it can be called dumb as dirt.

An important thing to do is to set a minimum impedance target, because depending on your network configuration and driver characteristics, the optimizer is quite capable of coming up with a network that hits your targets quite well, but has some wicked impedance characteristics- low Z, high phase, etc.

There are other guidances that are quite common recommendations - if the network design your'e trying out is a conventional crossover and has an inappropriate number of "orders" to the combination of acoustic target, you may see series caps or shunt inductors become quite large- this is a hint to take them out.

Good luck, and have fun- there's a bit of a learning curve if you're new to this, but LspCAD 6 is a very capable tool- I'm still uncovering features and thoughtful things Ingemar built in.

~Jon

[JohnL]

Hello Jon, and thanks for the help. I was trying to optimize the whole design at once (I'm a SoundEasy user). I'll try fiddling with the transfer function; that was the reason I went to 3rd order on the highpass, the curves didn't fit right. I'll go back to a 4th order electrical on the highpass, invert the polarity on the tweeter and optimize for the transfer function.

Now, do I optimize for 8th order LR or variable slope 48 db/octave when tweaking the cauer filter?

Thanks again
John

[JonMarsh]

Well, the way my designs are done is that I'm setting up the cauer-elliptic filter to mimic an 8th order L-R for the first 40-50 dB. This produces a nice corner characteristic that isn't too high a Q, and it sums well- plus requires only minor tweaks to compensate for driver acoustic center offsets in the Z axis. But feel free to experiment... I'm not a "it's my way or the highway" kind of guy...

You can play with other settings; the topology doesn't change, it's just the tuning for the transistion band characteristic.

[Dennis H]

for L-R 4, thats positive polarity on both drivers; for Butterworth 2, L-R 2 and L-R 8, that's inverted polarity for the tweeter

I thought it was:

LR 2, 6, 10, etc. inverted
LR 4, 8, 12, etc. positive

[JonMarsh]

LR-8 is not something widely discussed...

Never been able to get an LR8 to work with positive polarity.... always been inverted.

Have deep nulls on connection with positive, both in simulation and speaker builds.




Maybe I'm doing something wrong... all constructive comments welcome.

~Jon

[Dennis H]

Well, far be it from me to challenge the EE Poohbah.

I guess the phase shift of a Cauer filter with an initial 8th order rolloff is less than an LR8 at Fc?

Okay, that was making my brain hurt so I just kludged a Cauer together with the QSC software and I see what's going on with the phase. These are 4th order Butterworth lowpass and highpass filters at 1K with notch filters an octave above/below to emulate a 1K Cauer.

[JonMarsh]

Well, the amplitude transition, if it matches the nominal function, especially down to ~ -48 dB as I do, "should" have close to the same phase characteristic. Maybe there's some excess phase due to the higher transistion rate just past that-

I should research by taking the same driver data and doing a true "ideal" LR-8 as per an active or DSP network. You shure wouldn't want to try to build one of those in a conventional ladder network- the insertion loss and component sensitivity would be something awful.

Of course, maybe the technique I'm using is like a bumble bee. It's not supposed to fly, but it does, anyway.

[Dennis H]

Yeah, maybe you could model an active filter into a pure resistance so you can see what the filter's phase is doing. I imagine LspCAD can automate it but, just in case, SL says to use these Q values for the 2nd order filter stages to get an LR8.

1 - 0.54
2 - 1.34
3 - 0.54
4 - 1.34

Unless I'm all screwed up on the theory, the LR8 phase should have spun 360 degrees at Fc and 720 degrees at light. The Cauer seems to only spin 360 at light, half as much, but it takes a crooked path getting there, and the highpass doesn't match the lowpass, so I can see how reversing the leads might be necessary.

[JonMarsh]

Well, I'm "fitting" against the LR8 transfer function target in LspCAD, so it's the combined filter and driver transfer function which is matching the transistion band characteristic and fall off for the first octave quite closely...

Oh well, something else to do in my copious spare time....

[Dennis H]

Okay, Jon, you shamed me with the spare time comment so I decided to take a crack at it myself.

An aside, I downloaded the LspCAD demo but I couldn't get it to run on my XP machine with all the latest updates. The splash screen comes up and then it shuts down with an "abnormal program termination" error message. But I remembered I had an old, old Adire version of LspCad so I did the best I could with it.

The pic is an IB Shiva (theoretical response) with LR8 highpass and lowpass added. The phase crosses (almost) through zero at the 1K Fc. There's a bit of excess phase due to the driver's highpass behavior. Anyhoo, it looks like you'd wire it in phase.

[Paul H]

The crossovers I'm modelling for my dipole (https://www.htguide.com/forum/showth...9&page=3&pp=35)
have cauer filters (4th order with additional capacitor inserted). The tweeter rolloff is very close to 8th order, and the mid roll-off is slightly shallower. I get very close phase-matching and good response when one driver is phase-inverted, and I get nothing to work with positive polarity to both - and I've tried.

Paul

[JonMarsh]

Paul's comments mirror my experience- I've tried mightily to get it to work in positive phase, no dice.

I suspect what I should do is dig up my old Class D filter design in MathCAD and write out the network transfer functions in MathCAD for both the "standard" LR8 using the idealized description, and compare the phase against the MathCAD analysis of the Cauer-elliptic. That would make an interesting thread, huh guys? Something light to help you fall asleep in the evening...

[JohnL]

When I got home last night I redid the model for my two-way (AMT/RS225x2) optimizing for the 8th order xfer function, cauer elliptical on the LP, 4th order electrical with a notch on the HP. It did end up much better looking, with a deep null when I put the tweeter in positive polarity. I got done modeling, talked to the neighbor for about an hour about the virtues of biasing his amp after replacing the tubes, finally hooked everything up and had enough time to listen to one song before I went to bed. It didn't sound that good compared to the other side with a LR4 type crossover. I didn't have time to set up the measurement equipment, but just wrote it off to needing to do a little tweaking. As I started typing this, I remembered that when I hooked up the prototype xover, I connected the tweeter in positive polarity :thud: . So much for prototyping when you need sleep. I'll reverse that tonight and try to get some measurements.

[JonMarsh]

Sounds like you're making good progress... I know that I have my limitations with regards to accurate work when I'm tired beyond a certain point, so I just stop, or work on something less taxing...

Keep us informed how it goes and what you think....

Where are you crossing over the AMT, BTW? My measurements on the RS225 show the first major cone mode (which is a dip) at 1.5 kHz, so staying well below that is a good idea- 1 KHz with the LR8 should be OK, I think... I'm trying that in my M8ta. Lower wouldn't hurt, though.


~Jon

[Dennis H]

Nah, Jon, you've got more important stuff to do with your time.

I've pretty well convinced myself what's going on. My quasi-Cauer with the QSC software showed the "pure" highpass and lowpass filters, driving a resistive load, to be about 90 degrees out of phase at Fc (actually 360 + 90). The highpass shows 45 degrees less shift than an LR4 and the lowpass shows 45 more. Now hook those up to real drivers with their rolloffs and acoustic-center offsets and it's natural to keep shifting another 90 degrees to 180 out of phase rather than try to go back to zero.

[JohnL]

Well... it works much better with the tweeter reversed. Jon, this really cleans up a lot of the breakup I was hearing with the LR4. Furthermore, it really didn't need any tweaking. The cauer did exactly what it was supposed to do on the RS225s, and Heils are basically resistive like a ribbon so they do pretty much what they model. I love it. Can we start calling this an 8th order Marsh filter? I'll post some more info later, but I ended up crossing the RS225s at 1200. The AMTs get a little funny under 1000, so I figured it was a fair trade off. Thanks for all the help, this was much easier than I thought it would be. Heck, it was easier that the LR4 I did for it previously, and I finally got the bump in the passband out.

[JonMarsh]

Thanks for the feedback and kind words, John. Now, I think you're getting why I like this approach- it IS pretty easy to implement with good results once you get the gist of it. :T :T

Glad to hear it cleaned up your RS225's but not at ALL surprised.

Just think of it as being like Col. Sanders secret recipe... but for making speakers that "shouldn't" work with conventional techniques play nice together for not that much more money...

~Jon

[capslock]

Jon, one thing occurred to me. SL with his active LR4 designs always uses an allpass to delay the tweeter signal by the physical offset. It makes sense to me that an active filter that does not interact with the driver impedance and that uses textbook coefficients will only work correctly if you take care of the delay.

Does your design approach address this explicitly or is this something that the optimizer takes care of automatically when it optimizes for target response, by fooling with the great number of components and interactions?

By the way, I located the W12 review, will scan for comparison to RS125. Better unload your mailbox quick!

[JonMarsh]

It's 4:30 AM and I'm unloading my mailbox.... sheeeeshh!

I do take into account the acoustical offsets in the crossover design process; normally I manually tweak the transfer function on the LP slightly to get phase tracking through the crossover region and a deep null in ant-phase connection; typically all it takes is a slight modification of the corner shape and roll off rate, and I mean slight, to make the transistion regio phase OK.

[Dennis H]

Cauer better than LR8?

I was just reading a thread over on the Mad board. Paul Hilgeman did a month-long listening test to different filters using the DCX. He can't quite put his finger on it but he says something just sounds wrong with the LR8. It was the one filter of the bunch that really stood out.

http://www.madisound.com/cgi-bin/discuss.cgi?read=339768

That reminded me of a comment SL made on his filters page. "Crossover filters of higher order than LR4 are probably not useful, because of an increasing peak in group delay around f0."

So, using my crude tools (wish I could get LspCAD6 to run) I looked at the group delay peaking of an LR4, LR8 and a Cauer. Turns out the Cauer has the best group delay behavior of the bunch. The magnitude of the peak is about equal to the LR4 and much smaller than the LR8. However, the peak of the Cauer is very broad and it has a shallow slope well into the stopband. By contrast, the LR8 has tall, narrow peak with steep slopes. Looking at group-delay behavior, best to worst, it's Cauer, LR4, LR8.

Now how all this translates into sound, I don't know. But everyone seems to like the sound of Jon's XOs and at least some people don't like the sound of a true LR8.

[JonMarsh]

Very interesting research on your part, Dennis. I looked at the cauer group delay when I first started working on this crossover design years ago- it seemed pretty reasonable, so I didn't think much of it, and didn't try to specifically compare it with the standard LR4 or LR8.

When I can find a littel extra time I'll try replicating and posting what you've done using LspCAD 6.

BTW, what kind of problems are you having getting LspCAD 6 to run? The only real caveat I'm aware of is that you MUST install the software first before plugging in the dongle (yeah, it's more like play and plug, than plug and play), or things get hosed configuration wise. I've had similar problems with the Audiophile USB; especially if you disconnect it from a notebook (after it's been working a while), than re-connect it, often, mostly, it doesn't work any more- just makes static. VERY annoying.

OTOH, I've had no problems at all with my LSPCAD6 installs, as long as I install the software completely first, then plug the dongle in after that's finished.

~Jon

[Dennis H]

Thanks Jon. It will be interesting to see what you come up with, especially comparing LR4 and Cauer. I was looking at graphs with very different scales so it was a bit hard to judge shapes.

I'm trying to run the LspCAD demo so no install and no dongle. Just double clicking the executable. The initial small logo screen comes up and then it shuts down with an "abnormal program termination" error message. The whole thing only takes a couple of seconds. I'll have to try it on a different computer and see what happens. I gather from JohnL's initial posting that it works for him.

[Feyz]

So, using my crude tools (wish I could get LspCAD6 to run) I looked at the group delay peaking of an LR4, LR8 and a Cauer. Turns out the Cauer has the best group delay behavior of the bunch. The magnitude of the peak is about equal to the LR4 and much smaller than the LR8. However, the peak of the Cauer is very broad and it has a shallow slope well into the stopband. By contrast, the LR8 has tall, narrow peak with steep slopes. Looking at group-delay behavior, best to worst, it's Cauer, LR4, LR8.

Dennis, did you try these filters with ideal resistive loads as the drivers? If so, could you provide the component values you used for the Cauer filter? I tried to come up with a flat summing LP-HP cauer filters, using 8 ohm resistors as loads, but couldn't reach a flat sum, there is ripple to left and right of the xover frequency. And if I am not mistaken the group delay is neither smoother nor less than LR4 or LR8 in my example:

max Group Delays: (900Hz xover freq filters)
1.9 msec Cauer
1.4msec LR8
0.6 msec LR4

This is the same filter that I had posted the burst signal ETC results in another thread. (BTW, I checked the contribution of FR non-flatness to the ETC behavior, and that seems to be minor wrt to the phase or group delay issues. Same FR amplitude but minimum phase system displays much better ETC.)

I don't have my SE working right now, and I don't have any other filter optimizer software, so I am curious to find out how an optimized "text-book" cauer filter sums up. I tried searching the 'net, but couldn't anything like LR4 text book coefficients for elliptic-cauer. Trying to optimize them by hand is no fun either, so I would very much appreciate if you could give more information on what you have used as an example.

I suppose when used with real drivers on baffles, it may be a very different thing, for one thing I get a dip to the left of the xover frequency, which I think could be tuned as BSC.

TIA

[Dennis H]

Feyz, I was just using the QSC DSP software like the thumbnails above. I kludged up a Cauer by starting with a 4th order Butterworth and adding a notch filter an octave above/below. The software lets you tab between mag, phase and GD.

[Feyz]

Feyz, I was just using the QSC DSP software like the thumbnails above. I kludged up a Cauer by starting with a 4th order Butterworth and adding a notch filter an octave above/below. The software lets you tab between mag, phase and GD.

How well does the LP-HP sum (or subtract) up?

[Dennis H]

Feyz, I just read your posting more carefully. That filter you are using is a "bad" one - at least Jon said he didn't like it a while back. You should go for a transfer function like the ones Jon is using. Scroll through any of the design threads he started to see the plots. Maybe someone will send you FRD files for one of the designs so you can model the whole enchilada.

I can't see the summed lowpass and highpass with my software. However, my sims of just the filters show them in phase quadrature so I'm assuming you need to apply them to real drivers with rolloffs and AC offsets to get the extra 90 degrees of phase shift to put them 180 apart requiring you to reverse the tweeter.

[Feyz]

Scroll through any of the design threads he started to see the plots. Maybe someone will send you FRD files for one of the designs so you can model the whole enchilada.

I would appreciate if someone shares the resultant FR amp and phase measurements of a finished speaker using these filters on both LP and HP. I am just curious, they look pretty cool with just one additional component to a LR4 you get very steep transfer functions. But usually there is always a trade off, and reading your post saying that it was better in the phase area than an LR4 somehow didn't sound right to me with my trade off logic that I am used to.

I can't see the summed lowpass and highpass with my software.

Forgive my ignorance if I am displaying any, but then how did you see the end result's group delay to make comparisons to LR4 or LR8? I quickly tried simulating something like what you mentioned, and it did qive group delay like you are mentioning, BUT with a wide dip of 5db order on the xover point. I don't think this would be fair to compare it to a LR that sums flat. My guess is, which I may be wrong, if you try to make it sum (actually substract) flatter, you will see the group delay rising. I am not even sure it will ever sum flat, even after optimization, there may always be residual ripples. With real drivers used, this may not be the case, depending on the FR (amp+phase) of the driver and may display good group delay. But something in me still says, everything comes with a price

I will look at Jon's design here on the board for more info. I am just curious and trying to learn more.

[Feyz]

Dennis you were right

That example I used is not a good one.

I have been able to get my SE going again. And after a few minutes of optimization, I was able to get practically flat sum and a group delay that's looking much better. I need to spend more time playing with it to have a better grasp, but it is really nice.
I just had to see it for myself!

[capslock]

Feyz, I was just using the QSC DSP software like the thumbnails above. I kludged up a Cauer by starting with a 4th order Butterworth and adding a notch filter an octave above/below. The software lets you tab between mag, phase and GD.

Interesting! So you used textbook BW4s with the same nominal XO frequency? And the low pass path was made up of the BW4-LP and a notch an octave aboce and the high pass vice versa? What Q did you use on the notch?

Did you have to optimize?


Greetings,

Eric

[Feyz]

Some graphs that I came up with

Thanks to Dennis H's correction and guidance, I started using one of Jon's Mt8a 2-way filters I found in the threads. Jon had Zobel networks which I suppose had made the load look very much resistive already, so I omitted the zobels and used 6 ohm resistors instead of speakaers. After a little optimization with SE, mostly to get rid of BSC built in the the LP section, I had a flat cauer elliptic sum of LP and HP sections. I used 1100Hz 7th order BW as target, cause that's the highest suitable target curve supported in my version of SE. The resultant group delay is pretty much same, if not better, as a same frequency LR 4th order sum, as can be seen below (Yellow is Cauer's GD, Red is LR4):



A few days ago on another thread I had posted a graph of shaped burst tone ETC of the elliptic xover circuit I had found at Diyspeakers.net, and that looked ugly. But as Dennis H pointed out, that really is because that particular circuit is not well optimized and problematic. This time, here is the ETC of the xover that gave the above group delay plot, yellow is Cauer's ETC to 1100Hz shaped burst tone, red is the ETC of the shaped burst tone itself. That looks not bad at all IMHO, as would be expected from the GD graph.



I think what's going on is, the extra phase rotation caused by the initial steeper slope is then compensated by the shallow slope followed after the lobe. The initial slope gives faster phase rotation than an LR4, the following slope gives slower phase rotation than an LR4, as a result the group delay comes up to be almost same. This is pretty darn cool. Jon, you do know this stuff!

[JonMarsh]

Wow, a lot has happened here since yesterday lunchtime!

Thanks for the kind words, Feyz...

As I think you're seeing here, with your investigations with Dennis, "cauer-elliptical" just describes a network topology, not a filter type per se, apart from some very basic properties. A cauer-elliptic is described as an equal ripple voltage filter, as the ripple in the stop band is the same as the ripple in the pass band. This is why my normal target is for the ripple voltage in the stop band to be around -50dB or lower if possible, consistent with other targets (like putting the notch on driver breakup mode- the latter doesn't work with drivers like the RS180 which have a wideband of "excess" HF output.) Then it's impact in the passband is of little consequence, compared with everything else going on. Next most important is controlling the shape of the transistion band, which gives the phase properties and group delay.

What I've been using for a number of years now is a very specific implementation with the pass band, transistion band, and stop band tuned for very specific characteristics for a high slope speaker crossover (primarily the tweeter-midwoofer transistion), which is usually often a difficult crossover to handle well musically, becuase of the narrowing dispersion in the midwoofer, flare in the tweeter, and incipient cone problems in the midwoofer. No matter what you do, there's going to be some compromise compared with, say, a good full range ESL. But how to get the best out of the drivers? And keep non-linear distortion down (unlike early Avalons, for example, which had low crossover freuqencies using conventional approaches, and rather high distortion even with a fairly robust tweeter).


Well, this is probably a moot point after the investigation you've done on your own, but here's an SPL plot on axis of one of the recent designs using this crossover approach- can you guess the crossover frequency from the amplitude response? The response above 14 kHz is an artifact of the mic used.





I'm hoping to upgrade my measurement capabilities this spring. For now, I do look at the group delay in the crossover design predictions, but I unless I see something unusual, I don't pay as much attention to this during the design process as the SPL magnitude, off axis response, vertical window, etc.

Here's the predicted group delay of this same design.




Crossover frequency is 1400 Hz. Stopband ripple on the woofer crossover transfer function is better than -55 dB; on the tweeter its -50dB. Attenuation still continues after that, but at a reduced rate, of course. DCR in shunt inductor tends to be a limiting factor, which is why I like manly wire gauges.


Maybe I should right a paper about this crossover technique some day (in my day job I write several conference papers a year), but generally I'd rather be building speakers than writing papers...

[Dennis H]

Capslock, I was just eyeballing things on the dinky QSC graph that only goes to -30dB so I can't give any specific guidance. If you were going to implement it with a DSP box, you'd need to measure the actual response, or use better software than I have, and optimize all the parameters from there. The notch is very high Q, I used 30, because the passive circuit uses an L and C with no R.