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Old 24th January 2015, 03:47 AM   #1
xrk971 is offline xrk971  United States
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Default XKi - X's ab initio Karlson 6th Order Bandpass

Update (3/23/16): Srednivashtar's wonderful dual PA130-8 XKi

Click the image to open in full size.


Click the image to open in full size.

What's the deal with a Karlson aperture in front of the driver? Won't that mess up the polar dispersion? That's a great question, and no. The aperture actually improves the uniformity of the polar response compared to the bare faced driver:

Click the image to open in full size.

This thread found its beginnings here: A Speaker that Kicks Butt in Large Spaces. The finding was interesting enough that I decided to put it on its own here.

I will recap:

Properly scaling the Karlson K15 cabinet to work with smaller drivers has been an elusive goal for over 50 years. If you are at all familiar with the K15, you know that the moment it is scaled below a 12/15 scale, the bass extension suffers. The cabinet excels at efficiently controlling cone motion and channeling what little motion there is into high SPL levels, albeit, with some warts in the way of the famous Karlson "W" dips and peaks in the mid-bass region. Nonetheless, the speaker sounds very good and has a devoted following.

I recently have been working on developing 6th order bandpass subwoofers over in the subwoofer forum, especially slot-loaded push-pull bandpass subs. This alignment is very good at controlling cone motion and in many ways reminded me of the topology of a K15. So I got to thinking that I could develop a K15 style cabinet for any size driver, if they satisfy some basic T/S parameters needed for a 6th order bandpass box (moderate to low Qts, low Vas, strong motor, high sensitivity, etc.). I would design the new box from the ground up, or as they say, "from the beginning". The "i" is for ab initio, or from the beginning. I have figured out how to design a new type of "K" box with deep bass, good cone control, for any size driver with appropriate T/S parameters. There is no scaling of the K15 design involved, and it begins with the design of a 6th order bandpass alignment optimized for bass extension, flat response, and good control of cone motion, all properties that a 6th order bandpass alignment is known for. The difference is that the output port is simply a Karlson aperture of appropriate cross sectional area, and the chambers are designed with angles to avoid rectangular volumes that may have resonance modes.

As a test case, I designed a box that can reach 50Hz using a nominal 3.5in driver - the Dayton RS100P-4 (paper cone). This driver has a suitable moderate Qts to allow fb to set below fs and has good xmax of 4mm and a relatively powerful motor. The 6th order bandpass design was a 4.0 liter rear chamber and 1.0 liter front chamber with a 0.5in x 5.0in x 9.0in long vent, and a front chamber vent consisting of a 5in dia aperture.

I converted these volumes and vent dimensions into a box that has internal dimensions of 5in wide x 9.0in tall x 7.5in deep which then provides the correct volumes once the vent volume and driver volumes are subtracted. The front K-aperture is sized to have the same cross sectional area as a 5in dia hole, which was approximated by the area of a triangle that is 5in wide x 7in high, accounting for the curvature and offsets near the bottom.

The box design looks like this:

Click the image to open in full size.

Here is a photo of the inside during construction showing the bracing and folded vent arrangement leading to the top of the front chamber (although not ahown, there is a piece of open cell foam on the bottom and I put a wad of pink fiberglass in the main large volume to damp the HF's from reflecting back onto the rear side of the cone):

Click the image to open in full size.

Here is the completed speaker - still retains the look of a very small K15:

Click the image to open in full size.

And here is the measured frequency response about 0.5m away along the axis of the driver centerline - it has the characteristic Karlson "W" dips and a falloff near the bandpass followed by the direct radiator output which lets it reach up to the HF limit of the driver (about 14kHz in this case). The measured f3 is 51Hz! An amazing concept for anyone who has ever tried to scale a K15 down will realize. Predicted max SPL at 4mm xmax is 98dB in 2pi space:

Click the image to open in full size.

How does it sound? Very nice - sound clips attached below. Dispersion was very good as evidenced by the polar data showing very little variation in the response from 0 deg to 45 deg (or 90 deg full cone, and even out to 60 deg the variations are quite small). This is one of the biggest advantages of the Karlson aperture is a uniform polar response:

Click the image to open in full size.

The transients are also clean as you can see from the measured impulse response. Furthermore, because the polar response is so uniform, the impulse response is also uniform along different angles. Many open face speakers will exhibit vastly different impulse responses because they have beaming or cone breakup modes that are angle dependent.

Here are the IR's for 0 deg to 45 deg (note the similarities from 0 deg to 45 deg):

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This is a tiny speaker with a tiny driver, but it sounds quite big. Now, the neat thing about this methodology is that if a 3.5in driver can hit 51Hz, a 6.5in or 8in can probably do 40Hz. This can also be used for a sub woofer with a good pro audio 12in driver like the Faital Pro 12HP1030 and achieve 120dB SPL and mid 30Hz...

I applied a -24dB/oct high pass filter at 47 Hz to reduce cone excursion and some EQ to see if we can't make the response less bumpy. Here is the result of the HPF and EQ:

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Here is the impulse response after the EQ has been applied - a little cleaner:

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Here is the harmonic distortion - a lot of this is the result of the foam core cabinet vibrating. CLD can knock this down quite a bit but I have not done that yet:

Click the image to open in full size.

If you are interested in this speaker and would like to design a box around your favorite driver, follow along and I will detail the process and methodology for designing the XKi for your driver.

Briefly, the process starts with a design of a quasi 6th order band pass box with your favorite driver, but with these guidelines:

1. Set the rear chamber volume to front chamber volume ratio at 4:1
2. Set the output vent to have a cross sectional area equal to at least 2x Sd if you plan on using full range drivers
3. Using a quasi 6th order bandpass simulation program (Akabak, Bassbox, etc) adjust the vent length and chamber total volume to provide the optimum balance of bass extension, SPL output, and flat response.

Akabak script for 6th order band pass is available here: XKi - X's ab initio Karlson 6th Order Bandpass

4. Convert the volumes and vent length to a box with a total volume equal to 5x the front chamber volume PLUS the driver magnet/basket/cone volume and the vent volume
5. Set the width of the cabinet based on driver bezel width plus an inch or so of margin, set the height at an aesthetically pleasing ratio (golden ratio is good), Fibonacci, etc.
6. Calculate the depth based on known volume and height and width
7. Calculate the front chamber volume using the area of a triangle - this calculates the setback of the angled V in the front chamber.
8. Make the vent a channel vent leading from the top to the back and wrapping down. Note that the final build tends to have a deeper tuning than predicted due to the additional losses in the narrow aspect vent walls, so you may want to reduce the vent length by about 15% or so in the build.

Edit Jan 25, 2015: effects of EQ, high pass filter, and aluminum vs paper cone - aluminum cone seems to have more bass.
Click the image to open in full size.
Attached Images
File Type: png xki-rs100p-4-polar.png (120.4 KB, 3282 views)
File Type: png xki-rs100p-ir-0-deg.png (50.0 KB, 3034 views)
File Type: png xki-rs100p-ir-15-deg.png (51.1 KB, 3018 views)
File Type: png xki-rs100p-ir-30-deg.png (52.1 KB, 3004 views)
File Type: png xki-rs100p-ir-45-deg.png (59.2 KB, 3012 views)
File Type: png xki-rs100p-effect-of-hpf-eq.png (96.9 KB, 3011 views)
File Type: png xki-rs100p-ir-eq.png (43.7 KB, 3007 views)
File Type: png xki-rs100p-hd-eq.png (169.8 KB, 4130 views)
Attached Files
File Type: zip XKi-RS100P-4-RP-01.zip (932.1 KB, 203 views)
File Type: zip XKi-RS100P-4-ZB-02.zip (944.7 KB, 69 views)

Last edited by xrk971; 3rd April 2016 at 01:06 AM.
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Old 24th January 2015, 03:56 AM   #2
freddi is offline freddi  United States
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(Howard Beale's response to Arthur Jensen's rather forceful speech comes to mind ) - - lacking good software for BP6A, perhaps a list of suitable drivers might be compiled. Will Visaton's modestly priced BG20 fit into a reasonable sized cabinet? Should we have a rule to set the front chamber's aspect to allow a useful aperture and not unduly impact response with its own potential resonance?

how does this little Dayton XKi sound compared to a little Karlsonator alignment with similar size driver? (I hope the readers have been following the spinoffs from GregB's clever Karlsonator.)

I've W8-1772, Beta8cx, Beta10cx, and more which might fit into this new recipe.

are there a number of possible alignments for any given driver whose T-S meets the basic criteria?

is Hornresp suitable to sim the possibilities ?

Last edited by freddi; 24th January 2015 at 04:07 AM.
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Old 24th January 2015, 04:13 AM   #3
xrk971 is offline xrk971  United States
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Quote:
Originally Posted by freddi View Post
(Howard Beale's response to Arthur Jensen's rather forceful speech comes to mind ) - - lacking good software for BP6A, perhaps a list of suitable drivers might be compiled. Will Visaton's modestly priced BG20 fit into a reasonable sized cabinet? Should we have a rule to set the front chamber's aspect to allow a useful aperture and not unduly impact response with its own potential resonance?

how does this little Dayton XKi sound compared to a little Karlsonator alignment with similar size driver? (I hope the readers have been following the spinoffs from GregB's clever Karlsonator.)

I've W8-1772, Beta8cx, Beta10cx, and more which might fit into this new recipe.

are there a number of possible alignments for any given driver whose T-S meets the basic criteria?

I have not tried the RS100-4 or RS100P-4 in a Karlsonator yet, but I know that the Karlsonator will not have as deep of bass extension for the similar volume box size. The Karlsonator also does not have as good of cone motion control so max SPL's will be lower and harmonic distortion will be higher due to more cone movement. I really like the sound of the Karlsonator, and it is hard to tell the difference without more listening or an A/B test. My initial reaction to listening to this little XKi with the RS100P-4 is that it sounds surprisingly good - there seems to be more punch and sharper sounding transients.

I think we are looking for low to moderate Qts, lower Vas, higher sensitivity, moderate to high Bl, large xmax not an absolute requirement but always nice. W8-1772 should work but I would caution use of any very light mass cone driver as there are substantial pressures involved here that may collapse the cone if a sufficiently high amplitude transient came through. I fear the Beta10cx and BG20 have to large of a Vas and the cabinet will be too big. I would look for pro-audio drivers with Qts in the 0.35 range and a heavier cone.
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Old 24th January 2015, 04:24 AM   #4
freddi is offline freddi  United States
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fwiw, plug in Beta10cx - Beta8cx should have enough motor - not sure of vas - what fullrange might we find to fit?
https://www.youtube.com/watch?v=NKkRDMil0bw
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Old 24th January 2015, 11:32 AM   #5
BYRTT is offline BYRTT  Denmark
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Impressive polar response the measured speaker and interesting cleaner FR and IR after hands on EQ.
Expect sound clips is EQ'ed speaker and sounds good.
Well perceive less open sound micro detail and 3D depth, if this could be a outcome of the very good polar response making off axis reflections to recording microphone more even as the direct sound is just a thought.
Some of the sound comments above is based on comparing first sound clip to exactly same track in the first sound clip this thread FAST with TL?.
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Old 24th January 2015, 02:26 PM   #6
xrk971 is offline xrk971  United States
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Byrtt,
I think much of the less micro detail may be result of RS100P-4 paper cone driver as it falls off at 13.5kHz. The specs do not claim it to be a full range but a mid range driver. Also, you are comparing it to the Vifa TC9FD in the Dagger TL with a 5in helper woofer in FAST mode. That Dagger is perhaps one of the best technically flat and clean response speakers I have made with lots of attention paid to reducing baffle and driver edge diffraction effects. Here we have the K aperture blocking the driver - you would expect less of an open sound. The thing to listen for is how clean and deep the bass goes in the XKi without a helper woofer. My DCR with a Vifa can go deep too but is a much bigger box and the polars are not as uniform. As always, thanks for the great feedback.

Last edited by xrk971; 24th January 2015 at 02:30 PM.
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Old 24th January 2015, 06:19 PM   #7
tb46 is offline tb46  United States
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Hi X,

You have been busy! I like the idea of the XKi. It's a logical extension of the Karlsonator.

How about a center aperture port (like the original Karlsons)?. Can that be simulated?

Regards,
Attached Images
File Type: png k15i-rs100p-4-plan_mod_center_port.png (28.1 KB, 347 views)
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Old 24th January 2015, 06:42 PM   #8
xrk971 is offline xrk971  United States
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Tb46,
It could be done this way, but GregB indicated that a top entrance for the vent helps with reduced peakyness and inproves the sound. I would have to say that I like the idea of the back vent flow having to traverse the narrower part of the slot before reaching the wider area. It is consistent with the idea that the K aperture provides a gradual impedance termination. My model is very basic - I am only modeling the 6th order band pass with no consideration for the K aperture. I have found that the front chamber is a complex 3d problem that is tough to capture properly with a 1d lumped element model. If I ever figure out how to use Abec3 it can be done.
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Old 24th January 2015, 08:04 PM   #9
freddi is offline freddi  United States
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thanks for reminding, I need to document the response and tuning of a tall K-type with horizontal slot vent when tuned lower

its tall so probably would be tuned quite low if 3/4" x 12" vent area is maintained
Click the image to open in full size.

Last edited by freddi; 24th January 2015 at 08:09 PM.
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Old 24th January 2015, 08:04 PM   #10
xrk971 is offline xrk971  United States
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Default XKi for W8-1772

Quote:
Originally Posted by freddi View Post
(Howard Beale's response to Arthur Jensen's rather forceful speech comes to mind ) - - lacking good software for BP6A, perhaps a list of suitable drivers might be compiled. Will Visaton's modestly priced BG20 fit into a reasonable sized cabinet? Should we have a rule to set the front chamber's aspect to allow a useful aperture and not unduly impact response with its own potential resonance?

how does this little Dayton XKi sound compared to a little Karlsonator alignment with similar size driver? (I hope the readers have been following the spinoffs from GregB's clever Karlsonator.)

I've W8-1772, Beta8cx, Beta10cx, and more which might fit into this new recipe.

are there a number of possible alignments for any given driver whose T-S meets the basic criteria?

is Hornresp suitable to sim the possibilities ?
Here is what I came up with for the XKi with a W8-1772. The Vas on this driver is rather large so the cabinet is rather big, in my opinion for something that has an f3 of 43Hz.

The design ended up at 60 liters of active volume for the front and rear chambers with a vent of 12in wide x 1in high x 8.5in long. This translates to a box of internal dimensions of 12in wide x 20in high x 16in deep. Is this size still suitable for you?

Here is a sketch:

Click the image to open in full size.

Here is the predicted bass extension and max SPL at 9.2 volts to hit xmax - ignore the peak at the upper bandwidth - that goes away when you have the Karlson aperture, I think 103dB is a respectable number for the 1772 and should be great for home listening. Additionally, the beaming normally associated with a 8 in full range will be greatly reduced with more uniform polars due to the K-aperture:

Click the image to open in full size.

Here is the predicted cone displacement with a -24dB/oct HPF at 37Hz:

Click the image to open in full size.

So, what do you think? I think keeping this speaker small will require one to use lower Vas pro audio coaxials.
Attached Images
File Type: png XKi-W8-1772-Plan.png (81.4 KB, 3126 views)
File Type: png XKi-W8-1772-Freq-at-xmax.png (28.6 KB, 2860 views)
File Type: png XKi-W8-1772-Displ-at-xmax.png (26.8 KB, 2830 views)
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