Phase, Impedance, FR Importance

[paul_n_oneal]

What do you consider the most important piece when modeling a crossover. Do you always try to have the phase right on or do you care more about a flat FR or impedance, etc. Long writeups welcome. Please explain why you choose one over the other. Just trying to increase my knowledge of who, what, where, and why...

[kenc]

> What do you consider the most important
> piece when modeling a crossover. Do you
> always try to have the phase right on or do
> you care more about a flat FR or impedance,
> etc. Long writeups welcome. Please explain
> why you choose one over the other. Just
> trying to increase my knowledge of who,
> what, where, and why...

Hmmm, good question. Without a bunch of tecnical gobbleygook, I think isolating any of these three without giving consideration to the other 2 is a recipe for disaster. You already knew that though.

I'm curious to see what people respond. I've heard a lot of speakers that had great phase or great fr plots, but just didn't sound right for whatever reason. I've also heard some speakers that didn't measure so well that sounded pretty darn good.

I'll be very surprised if someone picks impedance. Who can hear impedance? Assuming it's the amp is up to the task...

[paul_n_oneal]

> Hmmm, good question. Without a bunch of
> tecnical gobbleygook, I think isolating any
> of these three without giving consideration
> to the other 2 is a recipe for disaster. You
> already knew that though.

> I'm curious to see what people respond. I've
> heard a lot of speakers that had great phase
> or great fr plots, but just didn't sound
> right for whatever reason. I've also heard
> some speakers that didn't measure so well
> that sounded pretty darn good.

> I'll be very surprised if someone picks
> impedance. Who can hear impedance? Assuming
> it's the amp is up to the task...

Impedance isn't my highest priority either but I do look at it frequently during modeling. The impedance indicates a number of things that I use. If it's a ported design, the impedance will show the tuning frequency and wheter ported or sealed will show approximately where the xover point is. IIRC, I read a paper awhile back that said something like keeping the impedance phase between +/- 30 degress should be a design consideration. For what reason, I have no idea. I usually go for phase first, FR second, and impedance last. I am curious to see what other do though.

[romanbednarek]

> What do you consider the most important
> piece when modeling a crossover. Do you
> always try to have the phase right on or do
> you care more about a flat FR or impedance,
> etc. Long writeups welcome. Please explain
> why you choose one over the other. Just
> trying to increase my knowledge of who,
> what, where, and why...

Impedance is the lowest priority. I usually just check to make sure that it doesn't dip too low. However if you are using a tube amp it is beneficial to have a flatter impedance response so the speaker doesn't react with the output impedance of the amp and influence the frequency response output.

I like to keep the phase aligned at the listening height. If the phase isn't aligned you aren't getting the maximum added contribution from both drivers. This can be an issue because there will probably be a listening height where the phase is aligned and if you designed the response to be flat at a listening axis where the phase wasn't aligned, it may now be aligned at this height and you will get a peak in the response. Also having the phase aligned across a wider range in the crossover region should improve the imaging.

So that's my take on the subject.

[andre]

> Impedance is the lowest priority. I usually
> just check to make sure that it doesn't dip
> too low. However if you are using a tube amp
> it is beneficial to have a flatter impedance
> response so the speaker doesn't react with
> the output impedance of the amp and
> influence the frequency response output.

> I like to keep the phase aligned at the
> listening height. If the phase isn't aligned
> you aren't getting the maximum added
> contribution from both drivers. This can be
> an issue because there will probably be a
> listening height where the phase is aligned
> and if you designed the response to be flat
> at a listening axis where the phase wasn't
> aligned, it may now be aligned at this
> height and you will get a peak in the
> response. Also having the phase aligned
> across a wider range in the crossover region
> should improve the imaging.

> So that's my take on the subject.
Paul , another look !!! After years of DIY speakers I'm sure the best crossover is

"no crossover" . Some manufacturers in the past (SPICA, EPOS, and few others)have made outstanding speakers without crossover or at most a Cap on the tweeter ! I'm assuming you have to match the right tweeter with the right tweeter !I'm still looking for such a DIY desing.

[paul_n_oneal]

> Paul , another look !!! After years of DIY
> speakers I'm sure the best crossover is

> "no crossover" . Some
> manufacturers in the past (SPICA, EPOS, and
> few others)have made outstanding speakers
> without crossover or at most a Cap on the
> tweeter ! I'm assuming you have to match the
> right tweeter with the right tweeter !I'm
> still looking for such a DIY desing.
JohnK built an MTM with a single cap and inductor using vifa woofers and a seas 27TDFC.

[andre]

> JohnK built an MTM with a single cap and
> inductor using vifa woofers and a seas
> 27TDFC.
Paul , sorry but I'm not able to find the reference you gave me ! Is it on his site?

[curt_c]

IMO:

#1 is easily flat response. Who cares about the rest if the sound is colored? But of course it isn’t just the on axis response, but the power response that is important. Consequently driver capabilities, driver spacing, transfer functions etc. get thrown into the mix. Sometimes you will have to compromise a flat on axis response to get the best power response, but obviously we really want both.

#2 Is phase tracking. Although many of my earlier ‘tuned by ear’ designs sounded good, but obviously had phase all over the place. I generally find that designs that don’t track phase well will not have pinpoint imagining and soundstage, and the instrument locations will drift around depending on the frequency played. Of course this ‘only’ occurs through the transfer bands of the crossover networks. If you don't care about soundstage, -well then your job just got a lot eaisier.

#3 Impedance. Since most of us use solid state amplifiers, and those are voltage sources, impedance variations within reason do not affect the resultant sound. Sure, you can easily ‘optimize yourself into a corner' and get phase and response perfect, but then you find out you are left with a 1 ohm impedance. The trick is finding the combination of topology, crossover frequency, drivers, etc., to get all three al close as possible.

C

[Andy_G]

>"The trick is finding the combination of topology, crossover frequency, drivers, etc., to get all three al close as possible."

then why the heck aren't more of you using series x-os !! ;-))))

[Andy_G]

http://users.tpg.com.au/users/gradds/SeriesXO/image001c.JPG

[Andy_G]

http://users.tpg.com.au/users/gradds/SeriesXO/image001b.JPG

[paul_n_oneal]

So does power response indicate off axis response?

[paul_n_oneal]

> Paul , sorry but I'm not able to find the
> reference you gave me ! Is it on his site?

Here ya go.
<A HREF="http://www.zaphaudio.com/audio-speaker16.html">http://www.zaphaudio.com/audio-speaker16.html</A>

[paul_n_oneal]

> Here ya go.
>
> <A HREF="http://www.zaphaudio.com/audio-speaker16.html">http://www.zaphaudio.com/audio-speaker16.html</A>

Wrong link sorry. Look in his blog.

[unknownuser]

> So does power response indicate off axis
> response?
as it was explained to me, it refers to driver integration - can you tell which driver the sound is coming from, or is the sound just _there_?

I understand little of this stuff, but sometimes remember what I hear.

j.


(Originally posted by: Joshua Layne)

[dlr]

> So does power response indicate off axis
> response?

Yes, but maybe not the way you might think. Power response is essentially the response integrated over a sphere that encapsulates the system. The more important aspect is probably the front 2-pi. The more reverberant a room or the closer reflecting surfaces are, such as floors, walls, etc. the more important it is.

The off-axis is important, some say more so than the direct response, but not in my experience. But it depends on what is affecting the on-axis response.

If you go to my web site, you'll find a very old section on "Windowed averaging". This was one way I worked some years ago. I found that if I used a raw measurement that was a simple average of three axes (-15, 0, +15 degrees), that I can a more acceptable result. This left some non-linearities in the on-axis response, but it "averaged" out in the power response. You'll see reference to this in things such as Stereophile's plots of normalized off-axis plots, most importantly the in the horizontal plane.

This was before I used any diffraction control. What this did was balance the on-axis and off-axis response do some degree. Was it the optimal way? I don't know, it just worked for me.

Now that I use extensive diffraction control I have found that I don't need this. The off-axis is smoothed as well as the on-axis with diffraction control. This lets me concentrate on the on-axis only and know that the off-axis should follow reasonably well.

The caveat here is that there's still the aspect of driver directionality that you can't account for in the on-axis. Choice of drivers and crossover are key to this. Integration is still a bit art, especially for a DIYer, since we can't conduct large scale auditioning for feedback. But if you choose drivers and crossover and cross at or below the point that the lower driver is about 3db or less off-axis at Fc, then you'll be in the ballpark.

You may ask why I bring all of this up. Well, it's because it all influences the power response.

dlr

[dthomas]

Provided Link: http://www.tolvan.com/edge


dlr,

Well said and written. Especially the part about selecting drivers based on their off-axis performance specifically in the passband. I see a lot of designs that are based on too high of crossover points for midwoofers especially in terms of off-axis performance.

But to go a step further, I too have become very fascinated by baffle step. More in understanding how the affect occurs. One thing I noticed in using the standard calculation... we all know the one 4560/Width. And then calculate for an inductor. Well I found some real anomolies using this, especially just slightly off vertical axis. I was getting the step correction but also other bumps in response that are not as expected nor as explained in all the white papers I have read.

A baffle typically a rectangle, the BSC formula assumes that your baffle is round. None of the BSC documents discussed this. As a matter of fact the common equation for BSC corrects for only a small area of the baffle. Then I moved on to studying baffle diffraction and it all came together. While the baffle width gives an inductor value it corrects only in narrow horizontal axis or worse yet, it is assuming that your baffle is round. A rectangular baffle has many different distances from the driver to it's edges. I have been using a baffle diffraction program on my last two designs and using the BSC calculator in it. The values are greatly different from what the standard calculations give but the performance is more acceptable. It attempts to account for width and height of the baffle in calculating the correct values for BSC. The inductor values get increasingly larger for increases in height even when the width remains the same. I have had very good luck with this with the only variable being the resistor value which can be varied depending actual in room response.

It is worth a try it is a freeware program.

Dave

[paul_n_oneal]

Wow, I just read that twice. Hehe, I have some measuring to do my friend :-). I like the visuals. The one with on-axis and the L/R off-axis looks like sine waves going through each other and if you look at it just right, you can average by sight. You can also see the dips and peaks and how each axis is affected. Pretty darn cool.

Take this as constructive critism as it is meant. I would junk the frames and go with divs and layers. Much neater looking and fairly easy to accomplish. Thats just me though.

Again, thanks for that. As I said, I'm going to be a measuring fool this weekend. One question. Do you move the speaker and how do you just best guess the 15 degress? I know you're not supposed to move the mic.

[Jeff B.]

> IMO:

> #1 is easily flat response. Who cares about
> the rest if the sound is colored? But of
> course it isn’t just the on axis response,
> but the power response that is important.
> Consequently driver capabilities, driver
> spacing, transfer functions etc. get thrown
> into the mix. Sometimes you will have to
> compromise a flat on axis response to get
> the best power response, but obviously we
> really want both.

> #2 Is phase tracking. Although many of my
> earlier ‘tuned by ear’ designs sounded good,
> but obviously had phase all over the place.
> I generally find that designs that don’t
> track phase well will not have pinpoint
> imagining and soundstage, and the instrument
> locations will drift around depending on the
> frequency played. Of course this ‘only’
> occurs through the transfer bands of the
> crossover networks. If you don't care about
> soundstage, -well then your job just got a
> lot eaisier.

> #3 Impedance. Since most of us use solid
> state amplifiers, and those are voltage
> sources, impedance variations within reason
> do not affect the resultant sound. Sure, you
> can easily ‘optimize yourself into a corner'
> and get phase and response perfect, but then
> you find out you are left with a 1 ohm
> impedance. The trick is finding the
> combination of topology, crossover
> frequency, drivers, etc., to get all three
> al close as possible.

> C

Regarding your #2 - why don't we start by you telling me what you mean by "phase tracking". I want to make sure we are talking about the same thing before I make a few points along those lines.

[curt_c]

http://www.geocities.com/cc00541/NicktriuneMTM27TDFCphase.gif


> Regarding your #2 - why don't we start by
> you telling me what you mean by "phase
> tracking". I want to make sure we are
> talking about the same thing before I make a
> few points along those lines.

Hi Jeff! Thanks for endeavoring to clear up any misconceptions I may have caused.

What I mean by phase tracking is that the phase rotation of the individual drivers will be aligned through the transition band of the crossover network, as suggested in the phase plot below.

C

[Chris Roemer]

[Jeff B.]

> Hi Jeff! Thanks for endeavoring to clear up
> any misconceptions I may have caused.

> What I mean by phase tracking is that the
> phase rotation of the individual drivers
> will be aligned through the transition band
> of the crossover network, as suggested in
> the phase plot below.

> C

Well, I kinda thought that's what you were saying, but that means also that you are saying only even order Linkwitz-Riley acoustic crossovers will have stable images, because they are the only crossover types that behave as you have described. No offense, as I am not pointing this comment directly at you but at what seems to be the fascination amoung DIY'ers toward this type of crossover, as this fascination is evident by the "reverse nulls" displayed so often. It's kinda like, I'll show everyone how deep my reverse null is so they will know how in-phase the drivers are the other way. This is fine if the goal was a Linkwitz-Riley crossover, and there is nothing wrong with that, but it is not the only crossover type out there, nor is it arguably always the best. I do realize, however, that for beginners it is probably the easiest crossover type to target because of these characteristics, especally fourth order L-R's.

First, I would ask, does this mean that you feel that a system with good phase tracking between the two drivers (L-R types, as mentioned) would have better imaging than systems that were time aligned with minimum phase type crossovers that sum to a minimum phase response? In other words, is it how the phase tracks individually or how it sums together that matters (or neither), because with minimum phase crossovers the individual drivers are typically 90 degrees apart (albeit, they would be tracking each other at this differential ;-).

Also, there has been some mention regarding smooth power response, which as dlr states is essentially the sum of the response on all axes, but it wil be weighted by the direct forward radiation more than anything else. But with in-phase systems like the L-R crossover the power response is not flat, it dips 3 dB in the crossover region. This may be fine, but I was just pointing out that you can't have in-phase on axis and flat power response at the same time, although a second order L-R will have much smoother power response than a fourth order will.

Now, if you want to talk about producing the best imaging we would need some discussion on diffracton control, and maybe even more importantly, reducing response variations between the left and right speakers, to go along with discussions on frequency response and phase alignments.

Just throwing some thoughts out there.

Jeff B.

[dlr]

How's the next version of the PCD coming along?

dlr

[dlr]

All good points. I've got the Edge. It's a nice, fast piece of software. My preference is still for the Baffle Diffraction Simulator over at the FRD Consortium. But that does require Excel.

dlr

[paul_n_oneal]

Say I measure a nearfield and a gated farfield and splice them together using Speaker Workshop. I've been told that this messes up the phase so it can't be used for that purpose. To get around this, I usually export the data, import the data into FRC and then extract min. phase and reimport back into Speaker Workshop. I then offset the woofer with a negative value to correct the Z-axis. Is this the best way or is there a better way to get nearfield and farfield data combined for a better picture of what's happening below say 500hz?

[paul_n_oneal]

I was thinking about the averaging aspect of your technique last night. Do you just export the .frd file and import into excel the 3 files and then use excel to average the data and then save that as a new .frd file and import back in for modeling or is there a different way say using SW?

[dlr]

> Take this as constructive critism as it is
> meant. I would junk the frames and go with
> divs and layers. Much neater looking and
> fairly easy to accomplish. Thats just me
> though.

I use a simple, freeware HTML tool that is fairly basic and creates bare-bones, purely functional files. I like 'em compact and not fancy. Since I'm more interested in just providing info, I haven't looked into any of the newer stuff. If there's some good freeware available, I'll look into it, but I won't be buying any software packages.

> Again, thanks for that. As I said, I'm going
> to be a measuring fool this weekend. One
> question. Do you move the speaker and how do
> you just best guess the 15 degress? I know
> you're not supposed to move the mic.

It doesn't really matter which one you move, as something has to move. I measure from the tweeter center for all angles. Some setups rotate a box on an axis down the center of the box, like a lazy susan. I prefer the tweeter reference and move the mic, partly because of space limitations and proximity to walls and such.

I'm in my basement, so I can hang things from the ceiling. I bought one of those large, plastic triangles available in Home Depot that are marked for degrees, highlighted the angle slots for each test angle for easy viewing, then hang it just over the tweeter, flush to the baffle surface, with the origin touching the baffle surface. My mic, though, is mounted so that I can slide it in and out a fair amount for easy distance setting. I also adjust the stand with multiple bubble levels so that it's nearly perfectly vertical, so raising the mic to sight it on axis is easy as well. I don't have to re,measure the mic vertical position doing it this way.

This gets +/- 1 degree, but does require moving the mic. It takes a while to move, set up and re-measure, but for the occasional times I'm doing this, it's OK.

If you're using a mic on a mic boom, you may want to work up something different, I suppose, such as rotating the speakers then re-setting the distance.

dlr

[cjd]

> What do you consider the most important
> piece when modeling a crossover.

How it sounds. :)

er... you said modeling. ;)

I have to agree, I think, that it's frequency response first. And last.

Impedance, well - If you're not careful it can, of course, get away from you which may cause issues with some amplifiers (even solid state). I am pretty sure it was Wayne J (speakerbuilder.net) that wrote about trying to keep impedance phase +/- 30 degrees.

Phase integration, as has been mentioned, only works the way many look at it working with even order, yadda yadda.

FWIW, I had two late variants on the big RS 3-way towers I tried - one was clearly an even order slope, nice reverse null. It did not sound as good, and most interesting it imaged and staged far worse than the version I tried that presented slightly better impedance and a very sad little reverse "null". In fact, I had previously blamed the less than great imaging on the room and placement issues - the speakers are just TOO big for my room, too close to walls, too close together. So, when a wonderful performance and only good recording of mahler's 8th laid an orchestra in front of me, as soon as I craned up what I thought would be the less ideal crossove, well... Guess which I stuck with! :) Only just dips below 3ohm as well, and it's pretty much within that impedance phase tracking model too. ;)

It measures well also, so it's not just a "it sounds good" thing, but in the end I think your ears can tell you things that you can NOT learn by looking at simulations.

C

[paul_n_oneal]

> How it sounds. :)

> er... you said modeling. ;)

> I have to agree, I think, that it's
> frequency response first. And last.

> Impedance, well - If you're not careful it
> can, of course, get away from you which may
> cause issues with some amplifiers (even
> solid state). I am pretty sure it was Wayne
> J (speakerbuilder.net) that wrote about
> trying to keep impedance phase +/- 30
> degrees.

> Phase integration, as has been mentioned,
> only works the way many look at it working
> with even order, yadda yadda.

> FWIW, I had two late variants on the big RS
> 3-way towers I tried - one was clearly an
> even order slope, nice reverse null. It did
> not sound as good, and most interesting it
> imaged and staged far worse than the version
> I tried that presented slightly better
> impedance and a very sad little reverse
> "null". In fact, I had previously
> blamed the less than great imaging on the
> room and placement issues - the speakers are
> just TOO big for my room, too close to
> walls, too close together. So, when a
> wonderful performance and only good
> recording of mahler's 8th laid an orchestra
> in front of me, as soon as I craned up what
> I thought would be the less ideal crossove,
> well... Guess which I stuck with! :) Only
> just dips below 3ohm as well, and it's
> pretty much within that impedance phase
> tracking model too. ;)

> It measures well also, so it's not just a
> "it sounds good" thing, but in the
> end I think your ears can tell you things
> that you can NOT learn by looking at
> simulations.

> C

Would you say that even or odd xovers present better imaging or is it just a model/listen thing. I've had FR that look pretty flat and the slopes look pretty close to LR4 but the null looks like crap as you stated above. I've never ended up with a xover that has more than a 30db null. Sure I can make them go down to 60+db but I haven't noticed that this sounded better.

I know I said I was finished playing around with my RS150_MDT20 combo but last night I could't stop myself. Partly because the boxes are apart awaiting the RS28 tweeters. I changed the cap values to 7.5uF and 30uF, kept the inductor the same, took off the shunt resistor and went with a basic L-Pad and it sounded just as good if not better than what I've been listening to for awhile now. I think it's really just me nit picking now as the sound was still full and imaged well. It did raise the mid and treble up about a db or so, so they sound a little more forward instead of laid back.

[Jeff B.]

> Say I measure a nearfield and a gated
> farfield and splice them together using
> Speaker Workshop. I've been told that this
> messes up the phase so it can't be used for
> that purpose. To get around this, I usually
> export the data, import the data into FRC
> and then extract min. phase and reimport
> back into Speaker Workshop. I then offset
> the woofer with a negative value to correct
> the Z-axis. Is this the best way or is there
> a better way to get nearfield and farfield
> data combined for a better picture of what's
> happening below say 500hz?

Actually, this sounds like a good way to accomplish your goal, and should work fine for you. I would add one more step to it too. In order to ensure that you are dealing apples to apples in your summed response I would also extract the minimum phase response from the tweeter as well, just as you did with the woofer. Then you know your phase relationships are correct and controlled by you through your off-set settings. This should reward you with the most predictable results.

Jeff B.

[Jeff B.]

> How's the next version of the PCD coming
> along?

> dlr

Everything was sent to webmaster Paul a few days ago and by this weekend version 4.0 should be up and available to all. (I will formally announce it when the time comes). By the way, Dave, I think I figured out how to work everything you recently requested into the file, as well as almost everything everyone else was asking for too. See, it pays to suggest improvements, and I am happy to comply if it's not a big re-write or something I don't know how to do (even then, I am still up to the challenge).

Jeff B.

[dlr]

> Everything was sent to webmaster Paul a few
> days ago and by this weekend version 4.0
> should be up and available to all. (I will
> formally announce it when the time comes).

Looking forward to it.

> By the way, Dave, I think I figured out how
> to work everything you recently requested
> into the file, as well as almost everything
> everyone else was asking for too. See, it
> pays to suggest improvements, and I am happy
> to comply if it's not a big re-write or
> something I don't know how to do (even then,
> I am still up to the challenge).

I'll second that latter part.

dlr

[dlr]

> I was thinking about the averaging aspect of
> your technique last night. Do you just
> export the .frd file and import into excel
> the 3 files and then use excel to average
> the data and then save that as a new .frd
> file and import back in for modeling or is
> there a different way say using SW?

What I did then (I no longer need to average) was to use the built-in function in LAUD for multiple measurements.

You have more to consider, though. First, you need to determine acoustic offset with single measurements (whether by my method or another). When you average, you must average magnitude only. Then you generate phase from the resultant SPL magnitude. Using phase in averaging is problematic as frequency goes up because it's pretty near impossible to get a perfect 1m distance for the mic from the acoustic center, especially since no one has yet been able to determine it precisely. :)

dlr

[alann]

Provided Link: Mlssa Acoustic center (http://www.mlssa.com/pdf/DRA-MLSSA-Manual-10WI4.pdf)


Some aoustic center information, page 182 of the manual Section 6.4 Loudspeaker Phase & Acoustic center.

For what worth.

Alan

[curt_c]

Ha! Ha!

You caught me big time here, Jeff! It was one of those ‘last minute’ posts before I dashed off from work, and well, I had my phase quadrature blinders on I guess. While I didn’t specify, my example indicated even order, and to be honest I, was thinking only even order at the time I wrote the post.

Yes, my idea of phase tracking includes odd order networks that would track in quadrature as well, and that one is no more advantageous than the other in this regard. My intent was to say that networks that sum flat on axis, but do not ‘track’ through the transition band may suffer more significant off axis response abnormalities, and hence, localization issues as the phase of the driver/filter networks change with respect to each other. Granted, this presumption may not be the most significant cause, and other issues have a more significant effect on the localization issue I attributed to the phase variation. As you indicated, It is more likely the direct sound and the delayed sound from the baffle edges arriving at the listener out of phase, or the direct sound and the delayed sound from the sidewall would have more effect, but I would think if the power response irregularities were significant, then this would be a factor as well.

I certainly do not want to disseminate incorrect information on the forum, and I appreciate your keeping me honest. You ‘throw out those thoughts’ anytime.

Thanks

C

[cjd]

> Would you say that even or odd xovers
> present better imaging or is it just a
> model/listen thing.

I have no clue. To be honest, I don't target specific slopes beyond initial transfer function setup, from which I tweak, tweak, and tweak. Build, be disappointed, tweak, build, tweak build... some measuring thrown in there for good measure. . .

I'm one of those people that really doesn't care about staging. :) In fact, I was never sure what was considered good staging till listening to systems that were declared "good" in that department.

And, my ears have VERY different training from most people. Translating the things that I pick up on into "audiophile" language is tough still.

Not sure if I really know what I'm saying, actually. :) ANy more than I'm sure I have a clue what I'm doing.

C

[dlr]

> Some aoustic center information, page 182 of
> the manual Section 6.4 Loudspeaker Phase
> & Acoustic center.

> For what worth.

The acoustic center can be approximated, but not determined precisely. They are using "excess-phase curves", but the problem is that to remove the precise amount of excess-phass to remove you have to first know the acoustic center, Catch-22. What they show is close enough for design work, though.

dlr

[dthomas]

> Looking forward to it.

> I'll second that latter part.

> dlr

What is you web page address?

Dave

[dlr]

Provided Link: Dave's Speaker Pages (http://www.speakerdesign.net)