Topic: Omnis to figure of eight

[heva]

Things one learns on social media …..

[Gutbucket]

Doing that is something I've wondered about for long time.  Doing it well enough to be useful for recording is the key.  I've been meaning to start a thread to further discuss it.  Now we have one.

[Gutbucket]

The goal is creating a fig-8 pattern by combining a pair of mics of some other (more available) pattern.. in this particular case, two omnis.

I've brought this up with a couple acoustics PHDs who sort of "yeah, but.." dismissed it, but I've yet to be fully convinced it can't be used as a practical work around for the lack of a miniature figure-8.  If it works in theory we might get it to work well enough in practice to be useful.  So lets break it down in theory, then figure how that might translate to a practical realization and what the caveats of doing so might be.

I started thinking about doing this in terms of how any 1st order polar-pattern can be generated by the combination of omni and fig-8 patterns and manipulation of their levels and polarities.  A cardioid pattern results from the sum of a coincidently placed omni and fig-8 summed together in equal amounts (presuming both mics have equal sensitivity and response).  Going the opposite way, we can derive a fig-8 pattern from two well matched cardioids placed as close together as possible, facing in opposite directions, by inverting the polarity of one of them and summing them.  Due to the inverted polarity, the omni components from the two cardioids cancel each other out, while the figure-8 components reinforce each other.  The result is a virtual fig-8 sensitivity pattern.

We know from experience that producing a figure-8 using two cardioids works because there are plenty of examples of it.  Leaving out large diameter mics with electrically switched patterns that operate using this principle and sticking with examples using small diameter cardioid capsules, I have a couple fig-8s that operate in this way: The Naiant X8, and the Side channel of the AT BP4029 Mid/Side stereo shotgun.  Both use a pair of cardioid capsules arranged back to back and connected out of polarity to produce a fig-8 pattern.  There are others manufacturer as well. Similar to the Naiant, Octavia makes or used to make an amplifier body or capsule adapter that used two of their SD cardioid capsules to produce a fig-8.  Neumann made/make stereo Mid/Side microphones that operate on the same principle as the AT as do others.

Doing the same using other patterns-
I'd expect that approach to work even better if super/hypercardioids are substituted in place of the two cardioids, because those patterns are "more fig-8 than omni" to begin with, so there is less omni component that gets canceled out and more fig-8 component that gets added constructively, which should improve noise performance.  But going the other way in pickup pattern doesn't work as well. A subcardioid consists of more omni component than fig-8.  The stronger omni part cancels out leaving the relatively weaker fig-8 signal to add constructively, but so does the noise.  If we go all the way to using two coincidently placed omnis, the two signals cancel out entirely (assuming everything is matched and set correctly). Hmmm that doesn't work..

Lets go deeper..

If we think of an omnidirectional microphone as a sensor which measures a "change in pressure" at a single point in space, and a fig-8 as a sensor that measures the "differential change in pressure on the opposite sides of a single diaphragm", it would seem we should be able to place two miniature omni "single-point change in pressure sensors" on either side of that fig-8 diaphragm and achieve an alternate method of measuring the same change in differential pressure across the diaphragm.

What's different that before? Not much except that the two omnis are now physically separated by the diaphragm.  The diaphragm acts as a barrier which creates a path length difference to the two sensors for any wavefronts arriving normal to (on-axis with) the diaphragm and the bezel to which it is attached.  There is no path-length difference for a wavefront arriving on-edge to the diaphragm, so for "on-edge" arrivals we get full cancellation, equating to the null plane of the fig-8.  From all other directions there is a some path length difference, and that difference will be greatest for a wavefront arriving directly at the diaphragm on-axis from either side, equating to the fig-8 lobe axis.

OK, so we should be able to use two coincidently miniature pressure omnis to produce an fig-8 response pattern as long as we place a baffle between them which substitutes for the missing diaphragm.  Ok I accept that (although I still don't understand a key detail which I'll bring up in a following post..).  Or, instead of a baffle we might space the two omnis apart from each other and produce a path length difference in that way.  I think spacing the omnis apart is how DPA suggests doing it "for fun" (I didn't read the social media post but came across a similar / the same? post on the DPA website a few months back).

More tomorrow..

[EmRR]

Yeah....that doesn't work, someone totally boned the post at DPA.  The number of times I've put 2 omni mics together with one opposite polarity to match gain by looking for the lowest combined sound output is not small.  Moving them apart to become some version of AB omni with one polarity flip then summed mono does not make a figure eight pattern unless by extraordinary unrepeatable accident, and I doubt it even then. 

A pair of opposite facing cardioids, sure. 

[goodcooker]

This doesn't seem like it would work with an omnidirectional polar pattern.

[Gutbucket]

Ok good, we all agree it won't work with the two omnis immediately adjacent to each other. 

However it seems it should work if we arrange it so that the path-length to the two omnis is identical for some angles of approach (forming the null plane) and differs for other angles of approach (forming the lobes), at least to some degree.  We can achieve that in two different ways, either spacing the mics apart from each other or by keeping them immediately adjacent with a barrier between them.  Either way a wavefront approaching from "side-on" reaches both simultaneously, while one approaching from any other angle reaches one before the other. 

Let's setup speaker emitting a 1kHz test tone as the source to be recorded, and set up the two omnis so that the spacing between them or the distance around the baffle between them creates a maximum pathlength difference which equates to exactly half a wavelength (wavelength of 1kHz = 34cm, x 0.5 = 17cm).  Arrival along that axis will produce a signal at each mic that's 180-deg out of phase, and since the output of the second omni is connected with inverted polarity, the summed signal from both mics reinforce maximally.  We get a figure-8 shaped sensitivity pattern..  at 1kHz.
 
Ok that works. Problem is it would seem to produce that perfect fig-8 full sensitivity pattern only at 1kH.  At lower frequencies where the wavelength becomes significantly longer I suppose a clean fig-8 shaped pattern is still generated but with decreasing sensitivity - side-on arrival still cancels out, while on-axis arrival produces a phase shift of less than 180degrees so there is less constructive summing resulting in less output level.  OK I suppose that equates to the -6 dB/octave dipole roll off of a fig-8 at low frequencies.  At frequencies higher than 1kHz we start to get a phase shifts that exceed 180 degrees.  Rather than retaining a fig-8 pattern with decreasing level, that should equate to increasing numbers of lobes and nulls which no longer line up with each other but shift position as the frequency increases above 1kHz.

I suppose that means that we need to choose a upper frequency for which the figure-8 pattern will remain consistent and setup the path length to corresponds with that frequency. We then get a -6db/octave rolloff response below that frequency, but a consistent pattern.  Above that frequency we get no roll off (on average) but a chaotic polar pattern.  ..and I suppose that's what happens with any fig-8.

Ok I think I'm getting it now.

What I didn't understand about directional microphones (mentioned in my post yesterday) is how the phase offset between arrival at the the front and backside of the diaphragm is somehow kept the same throughout the usable frequency range of the microphone.  Apparently, the answer seems to be that it isn't!  If we set it up so that the critical frequency point is just above the highest desired frequency response, we retain pattern and live with a constantly decreasing sensitivity as frequency decreases from there.   OK that makes sense.

What I still don't understand is why the rolloff slope doesn't extend all the way up to that high frequency point above which the pattern breaks down - in any directional mic.  I understand how the slope of the rolloff changes with pattern, due to the change in ratio of the absolute pressure [omni] response verses pressure gradient [fig-8] response in the collective sum.  But the response of real-world directional microphones always has some corner frequency where the low frequency roll off starts that's significantly lower than the highest intended response of the microphone.  Regardless of pattern that generally seems to occur between about 300hZ and 500Hz or so.  Why is that?

Why doesn't the -6db/octave rolloff response of a fig-8 microphone extend all the way to the highest frequencies of its response curve?

[EmRR]

I think the low mid rolloff corner is a function of the phase differences used to shape pattern in any directional mic. 

Single element figure 8's win the pattern control contest; ribbons or SDC's. 

The MKH 30 response plot is about as ruler flat as they come down below 50Hz.  Different capsule tuning approach with equalized output. 

Can of worms, the Neumann KM-86 with it's pair of KM-84 cardioid capsules and a purposeful space between them, a compromise position designed for most even target response. The Oktava MK-012 figure 8 adapter, with even wider spacing between the SDC cardioid capsules.  I have that one, and it works, but the pattern consistency doesn't compete with a ribbon or a Sennheiser MKH 30.   

Spaced omni is a basket of snakes with no certified outcome.  We can't forget the directional aspects of an omni with increasing frequency. The Grateful Dead '70's vocal dipole omni cancellation works on the idea of both being on-axis to the sound to be rejected (the Wall of Sound), but would have low level comb filtering in the off axis response to the sides, not of much importance there.  180 degrees would reject as well too, and it sounds 'kinda' figure 8 but it would be sloppy anywhere in between, and with differing 90 versus 270 treble response (calling the nulls 90/270).

LDC's?  I only use them in figure 8 on-axis, never for MS.  The upper registers are just too uneven in pattern with an LDC. 

[VibrationOfLife]

I would think that a Jecklin Disc would get you closer to a fig. 8 rather than close summing 2 omni's which I would think would have the effect of combining both resulting in more of a single source recording.

[Gutbucket]

I think the low mid rolloff corner is a function of the phase differences used to shape pattern in any directional mic. 

^
Yes, it's details concerning this about which I'm curious. Specifically, what explains the multiple octave region (something like 4 to 7 octaves) of relatively flat response that lies above the low-mid roll-off corner and extends up to the mics upper frequency limit where pattern and response are no longer well behaved?

Some of that is probably the result of using the influence of diaphragm/housing geometry/size on high frequency response/directionality.  Might use that to flatten the dipole peak and extend it a bit before it starts rolling back down aggressively into the first combing notch. But I can't imagine that alone flattening the peak enough to extend flat response across that many octaves.

Classic dipole response curve-

[Gutbucket]

In searching for the above dipole response curve, I realized I should go back and review the excellent write up about modeling dipole speaker design at the Linkwitz website.  Mr. Stan Linkwitz had a real gift for figuring out and clearly explaining what's going on.  I miss that guy and am very pleased that all the good work he did on his website remains accessible.  Same for Eberhard Sengpiel.

Dipoles are figure-8's, figure-8's are dipoles.  Sources and sensors, speakers and microphones, the fundamental interaction remains the same.

Lots of good stuff on this page:
https://www.linkwitzlab.com/models.htm

"Here is the basic model for dipole radiation and the only one that has a readily calculated closed form solution. Everything beyond this leads to complicated mathematics or approximations with limited range of applicability.



Take two point sources, like two small closed box speakers. "Small" means that all the speaker dimensions are small compared to the wavelength radiated. These are monopole, omni-directional sources. Space them at distance D apart and drive them with opposite polarity (=180 degrees out-of-phase). The acoustic path length difference to the two sources is d = D*cos(a) when listening from far away."

^ Substitute small pressure omnidirectional microphone sensor for "small closed box speaker"

[Gutbucket]

I would think that a Jecklin Disc would get you closer to a fig. 8 rather than close summing 2 omni's which I would think would have the effect of combining both resulting in more of a single source recording.

What we are trying to do is make one mono fig-8 microphone.  We can then take that and use it along with another microphone to make a stereo recording

But you are thinking along the right path.. A stereo Jecklin Disk setup could easily be repurposed for this purpose..  To do so you would invert polarity of one of the omnis and sum their outputs together.

Found this sketch on the Linkwitz website, which nicely shows how an identical path-length between the two sources (sensors in our case) can be achieved by either spacing them apart or by placing a flat "Jeklin like" baffle between them (in our case the baffle would presumably be significantly smaller in diameter than a Jecklin disk). Drawing shows the transformation from one into the other while retaining the same path length-

[VibrationOfLife]

^^^ That is exactly what I was thinking.  I've got my own design for disk I have to get around to making.  Really psyched to try it out once I do.

[voltronic]

I find it very amusing that this post comes from DPA, who may be the only upper-echelon mic manufacturer who doesn't offer a fig8 option. It also is a bit disconcerting that a manufacturer as highly respected as DPA would recommend such a janky setup.

Lots of great info on this subject from John Willett may be found in this thread (starting reply #10):
https://gearspace.com/board/high-end/1283650-small-diaphragm-figure-8-other-than-km56.html

[rocksuitcase]

I find it very amusing that this post comes from DPA, who may be the only upper-echelon mic manufacturer who doesn't offer a fig8 option. It also is a bit disconcerting that a manufacturer as highly respected as DPA would recommend such a janky setup.

Lots of great info on this subject from John Willett may be found in this thread (starting reply #10):
https://gearspace.com/board/high-end/1283650-small-diaphragm-figure-8-other-than-km56.html

Great explanation(s) by WIllet. THANKS for the link

[Gutbucket]

I find it very amusing that this post comes from DPA, who may be the only upper-echelon mic manufacturer who doesn't offer a fig8 option. It also is a bit disconcerting that a manufacturer as highly respected as DPA would recommend such a janky setup.

DPA is not suggest this for serious use.  The blurb about it can be found on a page of their website titled Twelve Fun Ways To Use Miniature Mics.  I find it rather refreshing that they entertain this sort of thing at all.

https://www.dpamicrophones.com/mic-university/audio-production/twelve-fun-ways-to-use-miniature-mics/

Creating a figure-of-8 from two omnis

Sometimes, it is fun to experiment with extreme directionality of microphones. For instance, you can create figure-of-eight characteristics by connecting two miniature omni microphones to one input! All it takes is that the microphones have a balanced output – which they don’t… However, if you use an XLR-adaptor (for DPA miniatures,  DAD 6001), you can apply two identical miniature mics and a phase inverter (swapping pin 2 and pin 3 of the XLR) on one of them. Add the two signals using a passive summing device. Or if you have the luxury of possessing a small sound mixer, use two channels, both panned to the center (or the same side). If this mixer has an inverter on the inputs, use it on one of the channels (to avoid the cable inverter). Experiment with the distance between the mics and/or add a disc between the mics. Now you just made yourself a pressure gradient microphone!

Thanks for the link to to GS thread, even though there really isn't anything in there particularly relevant to this discussion.  It's more or less the same discussion about existing fig-8s that we've had here at TS several times in the past. I did download John's AES paper linked there on the Sennheiser RF-based symmetrical backing-plate design since I've not actually read it, even though I'm familiar with the unique design features of that mic.

This isn't about creating a high-performance top-quality fig-8, but rather is rooted in the active and long running DIY taper sub-culture here at TS.  Heva starting this thread was timely, as I've been thinking more about a potential application of it where it would be uniquely applicable.   
^
I'll go into that in a later post.  First I wanted to explore what's going on at the fundamental level, prior to getting into how it might be optimized.  Next logical step is probably just trying it out just to see what happens as that should be simple for me to set up, but I won't have time to play around with that for a couple weeks.  As a rough test I might try gaff taping a pair of 4060s to opposite sides of the AudioTechnica BP4029 stereo shotgun body next to its Mid capsule grill openings.  Should at least provide some idea of how well it might work as an alternate Side channel and allow for comparison of the two.