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A K-402-Based Full-Range Multiple-Entry Horn


Chris A

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The La Scala sounds very good outdoors... for casual listening such as a neighborhood block party or while working in the garden. It also sounds very good outdoors, compared to how it sounds when played at high SPLs in a small reverberant listening room. 

 

This is going back 30 years, but I can attest to this. I had my pair in the back of my house on top of a hill sitting on concrete and against a brick wall firing into a forest down an acre of hill. It did not result in my neighbors calling the cops, but the sound was impressive and memorable to everyone at the party.

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Let's take two horns both using the same driver:

Horn A has an area expansion slope of X starting at the throat.

Horn B has an area expansion slope of X starting at some distance away from the throat.

They both have the same final mouth area (which means Horn A is longer than Horn B ).

 

At the point where the driver enters the horn, the actual cross-sectional area will be smaller on Horn A than on Horn B. Doesn't this mean Horn A has a larger compression ratio than Horn B? And by extension, wouldn't that mean Horn A will have a higher throat impedance, and overall be a more efficient horn?

 

Am I missing something?

 

While I don't have the closed formula for a finite conical horn resistive impedance, loaded at the throat and then loaded a some intermediate position between the throat and the mouth on the horn's wall, I can say the following:

 

1) It is the resistive part of the impedance that counts for efficiency loading, not the reactive part, so that portion of the impedance equation for a conical horn for reactance must be subtracted out.

 

2) the formula for a finite conical horn throat impedance can be found on the bottom of the 126th page of Olson's Acoustical Engineering

 

The plot of throat resistance and reactance for a finite conical horn is shown on the 128 page of that same book. 

 

I don't have the formula for the off-axis port impedance vs. frequency for a finite conical horn, but my guess is that a little massaging of the two referenced resources above will yield at least an approximation for the impedance at any point along the horn walls, which is what Danley's plot is basically showing: relative port impedance cut-off levels for off-axis ports along the horn. 

 

Chris

Edited by Chris A
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On 1/22/2016 at 2:12 AM, Khornukopia said:
The La Scala sounds very good outdoors... for casual listening such as a neighborhood block party or while working in the garden. It also sounds very good outdoors, compared to how it sounds when played at high SPLs in a small reverberant listening room.

 

In my various discussions with Roy on this subject, he said the following:

 

Quote

 

"Imaging and creating it by having two varying acoustic signals is an interesting undertaking. I have found that a smooth, unobtrusive boundary between the two speakers works very well with well-behaved and consistent polar patterns [of speakers]. The other thing that I have noticed that works well is no boundaries--like playing the speakers outside. Both do a very good to excellent job of accomplishing the imaging goal, but the caveat is that no boundaries forgives non-consistent polar patterns while a smooth boundary is a strict enforcer of consistent polar patterns. Pretty cool how that happens."

 

I think that you're listening to the La Scala midrange (and to some extent the bass bin and tweeter) that has very uneven polars in the vertical direction, and probably uneven polars in the horizontal direction.  Then listening to La Scalas (or any of the Heritage loudspeaker types for that matter) in the "outdoors" case of Roy's comment above applies: horn-loaded loudspeakers really sound quite good outdoors, even if their polars aren't very good. 

 

I've found the same indoors by applying a sufficient amount of absorption around the midrange mouth of Heritage models to absorb at least a portion of those uneven polars that are illuminating the room at different coverage angles vs. frequency, thus helping the polars look more and more like those found in the K-510 (above 700 Hz) and the K-402 (above 200 Hz). 

 

Chris

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Chris, You put some MONEY and time into this new path, just as I have in 2014. Even though hearing is believing, living with this type of point source speaker for a long time tells a better story than a quick demo and makes it difficult to go back, so to speak.

 

Like my comment to Mark above on the subject of listening impressions and how long it takes me to form those opinions, I've found that it didn't take me very long at all to hear the differences, and that I wasn't going to revert back.

 

 

 

And no, the SH-50 was also designed to be used at home, since it outperforms 99 percent of the overpriced "pretty" speakers at Axpona at a fraction of the cost and is quite competitively priced against Khorns and LaScalas, even in the used market. Tom Danley has his original prototypes in HIS living room

 

Actually, I have to agree to disagree here.  While Tom Danley does use SH-50s in his own listening room, that doesn't mean that they were designed for that, and especially that they are optimal for that environment.  It just means that he's using SH-50s in his living room.  He has said multiple times that he hasn't been able to convince Hedden to allow him to design home hi-fi loudspeakers.  I can see why he chose SH-50s for his living room, but I very much prefer the configuration that is the subject of this thread, and for many reasons, over that for SH-50s.  The coverage issue alone is a huge difference that I've found is critical.

 

Unfortunately, until both loudspeakers (an optimized New Center and the SH-50) are in the same room to listen to, this argument (...a logical argument, that is...) won't be resolved. 

 

I know where I'd put my money, however...

 

Chris

Edited by Chris A
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Unfortunately, until both loudspeakers (an optimized New Center and the SH-50) are in the same room to listen to, this argument (...a logical argument, that is...) won't be resolved.    I know where I'd put my money, however...

 

I should have both in my living at some point this year so I can answer that question. The best sounding SH-50's I've heard were at Artto's house. He no longer uses twin Khorns and sold his center belle. His sound room is the best ever heard by me and he claims part of the reason for superior imaging is the narrow dispersion of the speakers "keeping it off the walls."

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I know where I'd put my money, however...

 

Although we have had different starting points, I'm hoping we will both end up with the same conclusions eventually. In my case, my money is in 3-4 places, depending on how that definition breaks down, not just 1 or 2.

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I think the compression presented by the "smaller than average throat" multiple entry apertures loads the driver just fine

Think all you want, but a proper understanding of something includes measurements and/or equations to describe that behavior. Are you able to quantify how much of a load the front chamber and port entry is providing at low frequencies?

 

This is what engineers do - we understand the world through equations and measurements, and communicate it to each other through equations and measurements. The math/science here is the language of understanding, which is very different from armchair engineering. I can't help but notice a massive amount of defensiveness from you, which doesn't improve anyone's understanding. It just makes everything personal and combative. Nothing about the equations and trying to understand the design and its tradeoffs should affect someone else's subjective impressions. It certainly never affects my own subjective impressions - which is important because an unbiased correlation between the subjective and objective is incredibly valuable.

 

It's also my opinion that to spend so much time analyzing a design is really the best compliment an engineer can give. Chris is/was an engineer so I hope he feels much the same way.

 

All that to say - my only intent here is to further understand the mechanisms at play. Even after I get my own units to play with myself, I am still going to ask myself the same questions and do the same exploration. What we're doing here is sharing in that quest. It's boring running off and doing things on your own, and the reason I've stopped sharing my explorations here is because they have nothing to do with Klipsch and nobody here can relate. Here we have a common love for the K402.

 

So again I ask - how much loading are we getting from the front chamber area and its port entry into the horn? "Enough" is such a boring answer :P

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Well, I had a little time with just the pets today, so I improvised a polar turntable--a bar stool base--and eyeballed the off-angles.  You can see a bit of angle error in the distances between the traces at the larger angles - out to 90 degrees in this case.

 

But the objective was achieved: the polars of this loudspeaker are (IMO) exceedingly good.  Roy did an outstanding job.

 

New Center Polars - Hor (10 Deg Incrs).png

 

New Center Polars Vert (10 Deg Incrs).png

 

The compression driver used was a K-69-A.  The noise background is shown in each chart.

 

Chris

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Just in case you're looking at the crossover region, here is the on-axis frequency response and phase plot at a little higher resolution for reference.  Note that I still haven't settled on the crossover settings and the PEQs in that area.

 

10394696_K-402-MEH(onaxismid-wall)frequencyresponseandphasewithminphase.thumb.jpg.4297ca0b3ba6ef05f873d2bef0d225fe.jpg

 

Chris

Edited by Chris A
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How anechoic would you say these measurements are Chris? It's frigid cold up here in Chicago so I'm having a hard time picturing you taking things outdoors, haha.

 

Those polars are indeed impressive. The differences in the ~15kHz region are kinda interesting.

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It is the resistive part of the impedance that counts for efficiency loading, not the reactive part, so that portion of the impedance equation for a conical horn for reactance must be subtracted out.
 

For that to be true, wouldn't the acoustic impedance of the driver also need to be entirely resistive? Doesn't the driver impedance change with frequency, and does that not therefor require a reactive portion to its impedance? When I have some time this weekend I can go find the actual equation. I seem to recall that being why we talk about everything in terms of ka.

 

Also, I think we're looking for maximal power transfer here - not necessarily efficiency:

https://en.wikipedia.org/wiki/Maximum_power_transfer_theorem

 

...but thinking about this some more, the Maximum Power Transfer Theorem assumes infinite current capability in the voltage source. In the case of an audio amplifier, we get more power transfer with a higher load impedance than our source impedance because our output stages have limited current capability (we can achieve the same current at multiple voltages).

 

In much the same way, we have limited excursion capability in our drivers. Shouldn't we be addressing the acoustic output as a function of driver excursion instead of input power?

 

 

Btw, there's a lot of thought behind these questions - it's actually a pretty loaded topic when you start thinking through the implications. The next piece in my measurement rig will be a laser to measure cone excursion, so I can start correlating designs to the cone excursion requirements for a given target SPL. My thought is that we don't necessarily want to maximize efficiency of the system, but rather want to minimize excursion.

 

The part that applies here is whether moving the driver down the horn actually reduces the excursion requirements for a given SPL versus having the driver at the throat (the Horn A and Horn B examples I gave). In the horn I build (after my tenants get caught up on rent), I'm thinking about trying to move the port closer to the throat so I can have a higher xover frequency. I also don't need as much low frequency extension since I have some crazy potent subwoofage already (othorn). However, I'm intrigued by the idea that moving the driver port closer to the throat will actually increase cone excursion for the same SPL. I don't think that's true, but if what you're implying from Danley's comments in true, then that would certainly be the case. In other words, is there an ideal location in the horn for a given low frequency corner?

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This is what engineers do - we understand the world through equations and measurements, and communicate it to each other through equations and measurements. 

 

 

 The noise background is shown in each chart.s

 

 

 

 

 

This is my mathematical equation asking you if the noise in your background was from your wife...  :ph34r:

post-12967-0-37500000-1453507210_thumb.p

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How anechoic would you say these measurements are Chris? It's frigid cold up here in Chicago so I'm having a hard time picturing you taking things outdoors, haha.

 

It was in the upper 40s today, sunny and protected from the gentle northerly breeze.  Nice, really. 

 

The measurements are what I'd call "verification level", but not development-level tests, in terms of quality.  You can see a lot more in the K-402/K-69 plots that were posted earlier in this thread.  Those plots done in the chamber are much, much better, and I'd refer to them for what they're actually doing.

 

For that to be true, wouldn't the acoustic impedance of the driver also need to be entirely resistive? Doesn't the driver impedance change with frequency, and does that not therefore require a reactive portion to its impedance?

 

This isn't electrical resistance, but rather acoustic.  It changes with frequency.  See the Olson plot referenced above--the so-called "A" factor is plotted as the resistive part, and the reactive part is the "B" part, is also plotted vs. frequency.  The acoustic resistance is the part of the energy that goes out the mouth of the horn, while everything else just gets stored and returned to the driver/amplifier. 

 

Chris

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Think all you want, but a proper understanding of something includes measurements and/or equations to describe that behavior. Are you able to quantify how much of a load the front chamber and port entry is providing at low frequencies?

 

Of course I can, but I choose not to since I prefer listening to those adequately loaded woofers rather than calculate or measure them........for the moment. 

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It certainly never affects my own subjective impressions - which is important because an unbiased correlation between the subjective and objective is incredibly valuable.

 

No defense here, it's just that no one can truly have a valuable,  unbiased correlation between the subjective and objective until they have actually heard a pair with Roy's test CD's.

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Let's take two horns both using the same driver:

Horn A has an area expansion slope of X starting at the throat.

Horn B has an area expansion slope of X starting at some distance away from the throat.

They both have the same final mouth area (which means Horn A is longer than Horn B ).

 

At the point where the driver enters the horn, the actual cross-sectional area will be smaller on Horn A than on Horn B. Doesn't this mean Horn A has a larger compression ratio than Horn B? And by extension, wouldn't that mean Horn A will have a higher throat impedance, and overall be a more efficient horn?

 

Am I missing something?

 

While I don't have the closed formula for a finite conical horn resistive impedance, loaded at the throat and then loaded a some intermediate position between the throat and the mouth on the horn's wall, I can say the following:

 

1) It is the resistive part of the impedance that counts for efficiency loading, not the reactive part, so that portion of the impedance equation for a conical horn for reactance must be subtracted out.

 

2) the formula for a finite conical horn throat impedance can be found on the bottom of the 126th page of Olson's Acoustical Engineering

 

The plot of throat resistance and reactance for a finite conical horn is shown on the 128 page of that same book. 

 

I don't have the formula for the off-axis port impedance vs. frequency for a finite conical horn, but my guess is that a little messaging of the two referenced resources above will yield at least an approximation for the impedance at any point along the horn walls, which is what Danley's plot is basically showing: relative port impedance cut-off levels for off-axis ports along the horn. 

 

Chris

 

 

I don't know what equations Hornresp is using, but it does provide acoustic impedance plots.

 

Attached is a PDF comparing a few different horns:

  • Normal = Crites driver firing into throat of 40Hz Fc Conical horn with a length of 40cm.
  • Offset1 = Same driver horn, but 10cm down the horn.
  • Offset2 = Same driver horn, but 5cm down the horn.
  • Direct Radiator = Acoustic impedance of just the driver itself.

Acoustic_Impedance_Comparisons.pdf

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Thanks - that was a nice comparison, Mike.  That second graph looks just like that in Olson's 1957 text, Acoustical Engineering.  Looks like Mr. McBean worked out the math. 

 

I wish that he'd open the source, or at least publish an analyst's manual for each modeled capability.  He's steadfastly refused to document such things, it seems. 

 

While his freeware application is certainly useful for DIY, it doesn't engender a lot of confidence in its validation/limits to its methodology.  It also doesn't tell you much about coverage angles and SPL, at least for multiple-entry horns.  It doesn't presently model tractrix mouth flares, either.

 

Chris

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Those polars are indeed impressive. The differences in the ~15kHz region are kinda interesting.

It's pretty good out to 80 degrees (included angle), or 40 degrees off-angle.

 

I remember Roy mentioning that anything above ~8kHz is really controlled by the driver itself.  My own calculations have shown that to be a true statement--it's related to the phase plug geometry. I'm sure that the last few notes above 10 kHz that are audible will be different with a TAD driving the horn.

 

Chris

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While his freeware application is certainly useful for DIY, it doesn't engender a lot of confidence in its validation/limits to its methodology.  It also doesn't tell you much about coverage angles and SPL, at least for multiple-entry horns.  It doesn't presently model tractrix mouth flares, either.

 

 

Indeed. But wouldn't take take some of the fun out of building and measuring stuff in the real world, which is different for all users? I'm just sayin'.

Edited by ClaudeJ1
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