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Constant directivity 2-way à la Geddes

bmc0

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I thought my recent speaker project might be of some interest to the members of this forum. This is largely copy-pasted from my post at diyaudio.com.

The waveguide profile is oblate spheroidal with an angle- and curvature-matched Euler spiral (a.k.a. clothoid) termination starting at 40% of the total depth. Throat angle is 10°, which matches the compression driver I'm using (Celestion CDX1-1747). Here's the completed speaker:

finished_speaker.jpg


The cabinet is 73cm x 41cm x 30cm (approx. 29in x 16in x 12in). Obviously inspired by Earl Geddes' designs.

It took me a while to figure out how to make an accurate waveguide of this size since I don't have a big lathe or CNC router. I have a 3d printer, but I wasn't too keen on the idea of printing the whole waveguide due to the time required and the fact that the finished product would be a bit flimsy unless a lot of material was used. The basic process I arrived at is gypsum cement (basically plaster of paris, but much harder and stronger) over an MDF substrate coated with a suitable bonding agent. After some experimentation I found that type II water resistant yellow (carpenter's) PVA glue works remarkably well as the bonding agent (more on this later).

I shaped the gypsum cement using 3d-printed running molds that pivot on a 1/2in stainless steel rod held in place by this jig (which is also 3d-printed):

jig.jpg


Here are the running molds:

templates.jpg


Two of the running molds have a wide angled edge which helps to spread the plaster, kind of like a plasterer's trowel:

template_detail.jpg


I applied the plaster in two coats, similar to two coat veneer plaster. The basecoat is about 3mm thick, cut 50/50 by weight with fine silica sand and the finish coat is 1mm neat. Here's the bare plaster waveguide. You can see the stainless rod in the middle:

plaster.jpg


This particular one was actually a failed attempt as the plaster didn't bond properly to the substrate. Due to the fact that gypsum plaster expands slightly as it sets, you need a bonding agent that provides some bond strength even when damp to prevent the plaster layer from lifting off the substrate near the waveguide mouth. For the attempt above, I sealed the MDF with a waterproof primer and then coated that with Elmer's Glue-All (a white PVA glue without water resistance). The problem is that the Glue-all turns back into a PVA emulsion on contact with the wet plaster and thus has no bond strength until dry. What I found works well is two coats type II water resistant PVA (I used Gorilla wood glue (NOT the polyurethane stuff), but Titebond II or any other similar product should work just as well), sanded lightly between coats, and one coat of Elmer's Glue-All. The Glue-All is probably not required, but I figured it would improve the bond once dry. Type II PVA adhesives get a bit soft when exposed to water, but don't completely re-emulsify. This property appears to be what makes it work so well for this application.

The gypsum cement I used is a G-P product called Densite (K-5, I think), which you can buy in small quantities at dickblick.com. USG Hydrocal White should also work well. Do not use USG Ultracal 30 or any other gypsum cement with portland cement (check the SDS). Based on my experience with Ultracal 30, it will shrink slightly over time and crack.

So how does the final product measure? Very well, in fact. The data seems to agree pretty well with the ABEC3 simulations I did. The measurements were done inside with a short window, so resolution is limited. Data below 500Hz or so are invalid due to the time window. Also, there's a slight problem with the vertical measurements, which caused the small peak off-axis at around 650Hz. I'm planning to do new, better measurements before too long, but I haven't gotten around to it yet. Needless to say, having a Klippel NFS would be nice :). Anyway, here's the data I have:

directivity.png


directivity_h_pos.png


directivity_contour_h.png


directivity_contour_v.png


I generated these graphs using a python script I wrote. The crossover is LR6 acoustic at 1050Hz, implemented with my DSP software.
 
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Webninja

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Looks similar to the Dutch & Dutch 8c. As someone doing house projects using wood, plaster and glue, I’m very impressed with the quality and final look of these. My square built ins are no where near this quality, and I have easy straight lines. You should send one in for testing.
 
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bmc0

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Thanks :). There are some visual similarities, I suppose. My speaker is a monopole, while the 8c has cardioid radiation at LF. Also, mine is significantly larger (the woofer is 12 inch). I'd like to experiment with a cardioid design at some point, but it's much harder to implement well (especially passively like D&D does).

I probably won't send one in for testing any time soon, unfortunately. Shipping would be difficult and expensive due to the size and weight and it'd be a huge inconvenience for me if something happened to it in transit. As you might imagine, building them wasn't easy and it's not like I can just buy a new one.
 

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Hi bmc0,
have you considered to move the crossover frequency a bit higher? Kimmo Saunisto persuasively suggests a crossover frequency of 1.2 lambda is best for optimized Directivity Index. fluid brought it up here and recently, Kimmo wrote about this over at HTGuide: optimizing center-to-center distance for in-room response. With your driver spacing of 32 cm, 1.2 lambda is roughly achieved at 1250 Hz (1286 to be precise, but I would perhaps restrict it a little due the 12" woofer and also because of number aesthetics :p). I use this crossover frequency at the moment with my own prototype. Yours featuring a very good performing waveguide could improve quite a lot on a more gradual DI transition between the woofer and the compression driver.

On another note, I was wondering what your impression with tonal balance were. There was a small exchange between Earl Geddes and Martijn Mensink from Dutch & Dutch about attenuating the high frequency response of a constant directivity speaker deliberately (and therefore seemingly violate HiFi neutral response goals) to reach a balanced sound. I have run my speaker with filters flat and it sounded a tad bright, indeed, but was not really able to EQ for listening window yet. Yet, reducing the high shelf on the compression driver was helping. What are your experiences so far?
 
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bmc0

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Thanks for the links. I'll have to look at that idea a bit more closely to determine whether it applies to a design like mine. The examples given are quite different: omni/low directivity and LR4 slopes (I use LR6).

The DI transition looks worse than it likely is in reality due to the off-axis peak at ~650Hz in the negative vertical measurements. If we assume that this is a measurement error, which I think it is, the DI transition would look much less abrupt. My measurements are very low resolution at that frequency so I'd be hesitant to draw any sweeping conclusions from them. Unfortunately, I still haven't done the outdoor measurements I intended to do so I don't have better data. In-room measurements don't show any obvious problem around that frequency.

I roll off the treble a little as well (about 2dB at 10kHz) for the same reason. On average (there is considerable variation between recordings), commercial recordings seem slightly too bright with a flat listening axis response.
 

Skeptischism

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These are some great looking speakers and your solution a very clean, hands on maker solution to the problem. Nice hack for construction using 3d print to augment a process, rather than replace.The results speak for themselves. Congratulations.
 

voodooless

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Wow! Missed this one on DIY-Audio and here as well it seems. Very smooth and nice-looking monstrosity you've made :cool: Really impressed with the plasterwork. It also shows how good simulations are nowadays. Do you have any in-room measurements to show that the DI shelve is indeed a measurement error? What woofer did you use?

I'm still really torn on what to do.. build something like this (I'd probably use an off the shelf horn), a synergy, or go for a 12" coaxial. The coaxial is the simplest solution, but it will not have such a smooth response due to the cone profile. Synergy is complex, especially if I want to keep it a 2-way. Yet this design is relatively simple, yet does an extremely good job. To many choices :facepalm:
 

changer

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I roll off the treble a little as well (about 2dB at 10kHz) for the same reason. On average (there is considerable variation between recordings), commercial recordings seem slightly too bright with a flat listening axis response.

Thanks for the affirmation. I would find it interesting to learn more about it with a more solid foundation. For example, when Harman build the M2, which allegedly looses in A-B listener preference to Revel Saloon2, they did not shelf the HF, maybe because they deduced from experience (with mostly direct radiator speakers) a flat on-axis is correct. Would love to know how a slightly shelfed M2 would have performed and what this means for the widely believed cause for listener preference, apparent source width, as this seems to be a joker nowadays.

On the crossover slopes: I am not sure if Kimmo's rules only apply to certain slope crossovers. I have not learned how to use optimizer tool for such tasks in Vituix, but obviously, it can be simulated. The slopes do not affect pattern width and this rule is all about (vertical) pattern width at crossover frequency.

Do you have any in-room measurements to show that the DI shelve is indeed a measurement error? What woofer did you use?

There will usually be a shelf-y transition with such designs, but it can be optimized, i. e. see Gedlee NA-12 sound power curve. But even M2 is not showing a continuos slope like in three way direct radiator designs. On another note, in-room response cannot supplement a true DI curve, because DI is SP x LW, in-room on the other hand is additionally weighting in ER.

I agree, these are very well executed speakers. The great thing about them is the waveguide is also tall vertically, which is decisive.
 
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bmc0

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Do you have any in-room measurements to show that the DI shelve is indeed a measurement error?
It's not the shelf that's that error, it's the bump at ~650Hz in the negative vertical measurements. Here's an idealized representation of what I'd expect the real DI to be:
idealized_di.png


What woofer did you use?
Eminence Deltalite II 2512.

I'm still really torn on what to do.. build something like this (I'd probably use an off the shelf horn), a synergy, or go for a 12" coaxial. The coaxial is the simplest solution, but it will not have such a smooth response due to the cone profile. Synergy is complex, especially if I want to keep it a 2-way. Yet this design is relatively simple, yet does an extremely good job. To many choices :facepalm:
Most of the big pro audio coaxes I've seen don't really perform very well, unfortunately. The termination of a waveguide is very important, but even more important is the throat. Both of these things tend to be done poorly in coax drivers compared to dedicated waveguides.

I'd like to try doing a multiple entry horn design at some point, but as you mentioned it is difficult to do. There's also the question of whether the diffraction/HOMs you get from the midrange and woofer ports is an audible problem.

what is happening below 1KHz though?
The measurements were done inside so they have a rather short time window (gate) applied, so they are very low resolution below 1kHz and invalid below ~400Hz. The real F3 is about 70Hz. In my current setup I use two 15 inch sealed subs below 85Hz.
 

abdo123

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It's not the shelf that's that error, it's the bump at ~650Hz in the negative vertical measurements. Here's an idealized representation of what I'd expect the real DI to be:View attachment 144569


Eminence Deltalite II 2512.


Most of the big pro audio coaxes I've seen don't really perform very well, unfortunately. The termination of a waveguide is very important, but even more important is the throat. Both of these things tend to be done poorly in coax drivers compared to dedicated waveguides.

I'd like to try doing a multiple entry horn design at some point, but as you mentioned it is difficult to do. There's also the question of whether the diffraction/HOMs you get from the midrange and woofer ports is an audible problem.


The measurements were done inside so they have a rather short time window (gate) applied, so they are very low resolution below 1kHz and invalid below ~400Hz. The real F3 is about 70Hz. In my current setup I use two 15 inch sealed subs below 85Hz.

How does it sound since the PIR is flat like the anechoic on-axis?
 

Jim Matthews

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I'm still really torn on what to do.. build something like this (I'd probably use an off the shelf horn), a synergy, or go for a 12" coaxial. The coaxial is the simplest solution, but it will not have such a smooth response due to the cone profile. Synergy is complex, especially if I want to keep it a 2-way. Yet this design is relatively simple, yet does an extremely good job. To many choices :facepalm:

A Deltalite 2512 and SEOS-12 with a Peerless 1" CD would be cheap and cheerful. Simple is good, if you're after a proven design.

https://www.parts-express.com/Peerl...tanium-Dome-Compression-Driver-8-Ohm-264-1464

The Deltalite 2512 is very good in the vocal range. It's not ideal as a midbass driver, but it gets a lot right. The 99.9 dB sensitivity and solid response down to 100 hZ is a terrific combination..

https://www.eminence.com/speakers/speaker-detail/?model=DeltaliteII_2512
 
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bmc0

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How does it sound since the PIR is flat like the anechoic on-axis?
Sounds good to me. Very clear and non-fatiguing with excellent imaging. Hardly an unbiased opinion though :). As I mentioned above, I usually roll the treble off very slightly (about 2dB at 10kHz). Some recordings sound balanced with a flat response while others sound quite bright; the roll off is a compromise.

The Deltalite 2512 is very good in the vocal range. It's not ideal as a midbass driver, but it gets a lot right. The 99.9 dB sensitivity and solid response down to 100 hZ is a terrific combination..
It requires a little massaging above 800Hz, but this is easy to do with DSP. If using a passive crossover a different driver may be a better choice. Note that the real mid-band sensitivity is more like 96-97dB/2.83V@1m. Eminence computes the average over the "usable frequency range", so in this case the Deltalite's rising response inflates the figure.
 

abdo123

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@bmc0

do you think it’s possible to make holes in the cabinet so out of phase sound leaking out produces cardioid directivity below 1KHz and the speaker basically becomes a better Dutch & Dutch 8C?
 
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bmc0

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It's theoretically possible, but achieving a good result would probably require a lot of experimentation and multiple prototypes. I'd like to try this at some point, but it probably won't happen anytime soon.

Edit: For a speaker of this type, I'd be inclined toward super- or hypercardioid. These speakers, like Dr. Geddes designs, have the design axis at about 20° horizontal (18° to be more precise) and are intended to cross in front of the listener. The nulls in super- and hypercardioid patterns are at good angles for this kind of configuration. In addition, the DI is higher than cardioid so there would be even less mismatch between HF and LF DI.
 
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abdo123

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It's theoretically possible, but achieving a good result would probably require a lot of experimentation and multiple prototypes. I'd like to try this at some point, but it probably won't happen anytime soon.

Edit: For a speaker of this type, I'd be inclined toward super- or hypercardioid. These speakers, like Dr. Geddes designs, have the design axis at about 20° horizontal (18° to be more precise) and are intended to cross in front of the listener. The nulls in super- and hypercardioid patterns are at good angles for this kind of configuration. In addition, the DI is higher than cardioid so there would be even less mismatch between HF and LF DI.

that would be a great design choice anyway as it makes intensity time trading not just desired but also necessary.

This design is so good that i would honestly consider going further with it (polish LF) and monetizing it.

You might consider it ‘too difficult to be mainstream DIY’ but if you would build plans in a way that anyone in the world can 3D print them and they just have to glue everything together this would change the world of home audio as we know it.
 

ctrl

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Obviously inspired by Earl Geddes' designs.
This is a very nice project with a "modern" waveguide design.


do you think it’s possible to make holes in the cabinet so out of phase sound leaking out produces cardioid directivity below 1KHz and the speaker basically becomes a better Dutch & Dutch 8C?
The approach of controlling the cardioid with additional drivers is probably more promising - as with the Kii.

Let's not forget that with the 8C, due to the slot approach, the third order harmonic distortion at 86dB was 3% around 100Hz and at 96dB it was already at 9% - that's ... really not good.

One would have to look in simulations at @bmc0's project how the cabinet depth affects the radiation pattern in the range 500-1000Hz. There could still be potential for optimization.
 

voodooless

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It's not the shelf that's that error, it's the bump at ~650Hz in the negative vertical measurements. Here's an idealized representation of what I'd expect the real DI to be:View attachment 144569

I did not mean error as in non-existent, but exactly as you showed: different Q.

Most of the big pro audio coaxes I've seen don't really perform very well, unfortunately. The termination of a waveguide is very important, but even more important is the throat. Both of these things tend to be done poorly in coax drivers compared to dedicated waveguides.

Indeed the list of halfway decent ones is very short. Of many you can’t even see the throat due to the dustcap covering it up, and you also don’t know the sample to sample variation. The newer BMS coaxes seem to have it covered quite well though. And then you have the breed of awkward looking horn protrusion coaxes. They have their own issues..
 

voodooless

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@bmc0

do you think it’s possible to make holes in the cabinet so out of phase sound leaking out produces cardioid directivity below 1KHz and the speaker basically becomes a better Dutch & Dutch 8C?

I’ve been thinking about this for a while. In a synergy this would be a very interesting concept. However for a 2-way, you’d probably loose to much bass response to be very usable.. maybe not, takes lots of time to experiment with.
 

abdo123

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The approach of controlling the cardioid with additional drivers is probably more promising - as with the Kii.

are there any realistic 'driver based' cardioid designs that doesn't involve a dipole and an omni-directional speaker?

6 channels of amplification is a little bit of an overkill.
 
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