I'm using a 4 channnel VTV amp only 12"x13"x3.75" with a Motu Ultrlite Mk4 sitting on top. For cardioid I would need a second amp. This is nicely compact. Unfortunately, the computer it connects to is bigger than one of my speakers
but at least its fanless.So not to clutter up here I've created a new thread for project2 - https://www.diyaudio.com/community/threads/ath4-waveguide-inspired-multi-way.384410/
In case you have not seen the discussion of cardioid cabinets in chapter 9 of my book, let me paraphrase:
- active cardioid works best, and can be as simple as a single LP filter on one driver (as shown in my text,) but passive methods can be found, for example, one is shown at the end of the chapter. This chapter is free on my website. As is the whole book if I am not mistaken. They are no panacea because with directivity comes lower efficiency - no radiation mode can be more efficient than a monopole at LFs. If efficiency is not an issue (when is it not at LFs?) then cardioid, etc. can be attractive. I do think that to be really effective, they need to be active.
- No solution can lower the DI once the system reaches the main drivers ka=1 region. The DI of the main (direct) source will dominate above ka=1. Hence, a small "main" speaker is still going to be the limiting factor to matching DI at the crossover.
I don't see the crossover region as problematic, neither with a monopole nor a cardioid. The thing is that a monopole approaches an omni source (i.e. low DI) quite quickly with decreasing frequency below that. With a cardioid, this can be somewhat improved - at least that's my view and my understanding. Of course the efficiency is lower - that doesn't have to be a problem for a home use.
Yes, by giving up efficiency as I said. The crossover situation depends on what kind of DI one is looking for. A High DI is much harder than a low DI.
My point is that the cardioids DI does not hold at Higher frequencies because the drivers DI will dominate. If the main drivers DI suits you for the crossover and desired DI then all is good.
But as you said, the directivity around a typical crossover is given mainly by the source radius - we don't loose DI with cardioid, do we? It's only better, i.e. better controlled below the crossover point.
- I see a cardioid as an extension of an existing DI from the crossover point to lower frequencies (at least not so quick widening as with a monopole).
- I see a cardioid as an extension of an existing DI from the crossover point to lower frequencies (at least not so quick widening as with a monopole).
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The DI of a cardioid is 4.8dB, super cardioid a bit more, for smaller woofers there may be no less DI but for bigger one there will be less DI higher up. It wouldn't be too hard to get a nice match between a cardioid woofer and a smoothly increasing DI waveguide.
I thought you were wanting to go smaller with the cardioid construction but I see what you mean now, here is an example (active) of what you are describing. A 15" woofer in a box that is not as deep as it is wide gives almost the same response down to 300Hz at full output, the example below extends it to 100Hz but chews a lot of output, there is a 19dB difference in gain between the two drivers.
If the waveguide has a DI of 10 then yes or use a bigger woofer to match at a lower frequency, but why does it need to be 10? Your own NS15 is 8.6dB (according to the image on your website) which would match what is in the sim above at 800 to 900Hz and where you chose to cross it.
I'm confused by your question as you already know the answer.
Yes but only basic edge diffraction.
I wasn't comparing it to anything in particular, only pointing out how it gets much harder to do with a higher DI. But just to be precise, the NS15 is more like 700 Hz. Xover, but that's hard to define when the crossover is asymmetric. Its much lower for the woofer than it is for the waveguide. And 8.6 in your example would be about 1 kHz, so our view of the numbers don't quite agree. And anyway your comparing sims to real data the two thing don't always agree. Does the edge diffraction take into account of the boxes total volume? Or just the edges? A sphere has no edges, but it still has diffraction.
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I was only trying to give a frequency region where a reasonable directivity match would likely occur. With fully synthetic data it's still only an educated guess.
This is how the author describes it
Simulation is based on simple ray theory: each driver is a point source sending 72 rays towards baffle edges with fixed 5 deg steps. Path lengths of shortest 1 st order diffractions are calculated and summed with delay i.e. phase information in a listening point. Magnitude of diffracted rays is frequency dependent. Weighting factors are calculated from radiator dimensions and edge radius
I have full 3D sims of 15" woofers in various cabinets where the responses are much more closely aligned with reality, but none of those include a cardioid component which was the point of the graph.