To see how things work, the last few days (since the thread started--thanks Gus for bringing it up!) I spent playing with this type of arrangement about 10 hours every day.
At first, I used a Chinese backplate to see what happens bringing things to extremes, so I used the side with blind holes, and then its flat side. I drilled 4 bigger diameter holes for a phase shift network, and then plugged certain pattern of holes to see how they influence response and pattern.
[quote author="PRR"]> I see the basic idea. Same as a dynamic cardioid: delay the back-wave in an R-C network and let it cancel the front-wave. When the R-C delay matches the delay in the air-path from front to back, you null the rear of the pattern. Slight shifts of delay give hypercardioid or fat-cardioid, still with significant directionality?..
?.But I don't have the intuitive "feel" to know if the Williamson can be a good cardioid, or just an omni with an attitude. [/quote]
Although in my latest version (see below), I took a long deviation from Williamson arrangement, I feel the last should work fine, especially if well tuned. First, with different "plugged holes" arrangement, the pattern would change significantly. In its "optimal" position, the pattern is close to fig8 in low band with close micing, turning into nice cardioid with increased distance from the mic, which actually is one of the properties of the single diaphragm capsule. In my capsule the omni was OK. Williamson might be also fine.
[quote author="PRR"]
So the back-gap, and the ratio of gap-volume to hole-volume, are key parameters.
[/quote]
Precisely!
[quote author="PRR"]> Operation without the through-holes is quite clear. It is omni. The resonance is controlled by the diaphragm mass/area and the total stiffness. The total stiffness appears to be 90% trapped air. The mass/stiffness ratio seems to point to the top of the audio band, as it should: any lower and you lose treble, any higher reduces sensitivity without audio-band advantage. If un-damped, the resonance would bump-up the top of the audio band. Damping is gotten by putting about 85% of the back-volume down in holes, thus making most air displacement wheeze through the thin gap between diaphragm and backplate before reaching a hole. [/quote]
That?s what I have read, but have some confusion, as I got completely opposite results in practice. When flipping the backplate to its flat side, intuitively I feel that diaphragm stiffness should increase significantly, due to very thin layer of air trapped between diaphragm and backplate, and top end should be flat, with a bump due to undamped tuning resonance. However, in omni mode, the top end was completely gone, whereas putting the backplate the other way around (with blind holes towards diaphragm, I got nice top end, but the low end was gone.
Obviously I am missing something here?how the thin air vs. viscosity of the air in the holes contribute to the stiffness and damping?
[quote author="PRR"] The number of holes is not, of itself, a first-order parameter. We want damping distributed all over the diaphragm, but up to 5KHz-10KHz the dimensions are "small". Some designers use hole-drag for damping, requiring a large number of small holes to also get a reasonable back-volume with a reasonable back-gap. That might even work better. But as others have noted, huge numbers of teeny holes means hours of tedious labor, drilling and breaking bits. [/quote]
I took this route, and made a new backplate. I started with smaller number of holes, and listening to the result, little by little drilled the new ones, until I felt the capsule sounds about right to my ears. Needless to say, I have never had such a frustration, and done such a tedious and hellish work?to audition each additional drilled hole requires dismounting the mic, taking off 12 screws to dismount diaphragm, drilling the hole, and then putting everything back together... just to realize it still did not sound how I wanted to....