Topic: Next step up in omnis from 4061's?

[Gutbucket]

An interesting thing to me is the nature of the directionality of the DPA 4015 verses the 4006 when the 4006 has an 'Acoustic Pressure Equalizer' installed.  That's a hard ball-like attachment which slips onto the 4006 omni to make it behave more directionally (this only works on a true 'pressure omni'; it wouldn't work on a dual diaphram or dual capsule omni and would block the openings of any side vented directional mic, screwing it all up).

With the ball attchment installed, the 4006 behaves more directionally, but not in the same way as the 4015.  As mentioned before, the 4015 maintains a quite consistant front back difference through most of the frequency range down to the lowest octaves, but I'm sure you noticed it's pattern progressively narrowing on-axis at high frequencies above about 10kHz, and the frequency where that starts to happen is related to the capsule diameter.  A ball attachment placed on a 4006 extends that phenomena somewhat lower down the frequency range.  It doesn't extend the directionality all the way down in an even way like the 4015, instead the pattern changes with frequency down to a few kHz.  It also creates an on-axis boost in the frequency range where it makes the microphone more directional.  DPA makes three different sized ball attachments for the 4006.  This is the response with the largest of the three, which changes the response the most-






In contrast, your 4061s are so small that when mounted in free-space, they are truly omnidirectional to a far higher frequency than omnis with larger diameter diaphrams like the 4006.  But if you mount them on something, or next to something which acts like a baffle, that will significantly change their polar pattern and response.  Here's the polar for the 406x-




I played around with a poor man's DIY version of those APE balls on 4060s about 5 or 6 years back, made from hard-foam balls with a hole through the middle so the microphone capsule is effectively flush with the surface of the sphere-

More on that in the Oddball Mic Techniques thread.  That worked to roughly approximate the polar pattern behaviour of a 2006+50mm APE, but doesn't make it a poor mans 4015.

[Ultfris101]

gutbucket,

That just clicked for me seeing your 4060 in the green ball. So the ball blocks the waves from behind but given that it's spherical they don't get sharply rejected. About right (in a very simplistic way)?

So for curiosity sake, if you replaced the green ball with a disk the same diameter and had the mic in the center of it then it would be more directional? Rejecting more of the rear waves but with the disc being small it's not going to have the boundary mount effect? Maybe more like the mk22 plot above?

And more curiosity, if you shove an SDC omni like an Schoeps mk2 or the 4006 all the way through a nerf softball so it just comes out the other side are you going to start getting something approaching an mk21? and then using a disc get something akin to an mk22?

[Gutbucket]

It blocks the highest frequencies arriving from behind and boosts those arriving on-axis, as determined by the relationship between the wavelength of the sound and the size of the attachment. 

The on-axis boost is the boundary effect, only manifesting over a very small surface area so it only effects the high frequencies as determined by the surface area and shape of the attachment. 

But there is more going on than small baffling and boundary effects.  Sounds from sources off-axis diffract around the attachment and re-combine at the diaphragm.  When the differences in path-length around the attachment correlate closely enough to the wavelength of a frequency, it causes degrees of cancellation which is maximized when the difference in path length corresponds to a 180-degree phase difference (and I suppose reinforcement at 360-degree phase differences and varying combinations between). So those reinforcement/cancelation angles vary with frequency. 

Notice the lobes in the 4006 with APE polar plot above.  They are somewhat similar in appearance to the nulls and lobes in the polar plots of directional mics, but all the lobes are positive polarity, and they shift with frequency, and it’s all happening at upper-mid and higher frequencies. Long enough wavelengths don’t ‘see’ the small attachment so it has no effect below the frequency where the microphone reverts to normal omni behavior.  In the plot above that transition is complete by 1kHz so the 1kHz plot line is a perfectly round circle.  All frequencies below that will also be picked up omni-directionally.  With a smaller ball attachment all that stuff happens at correspondingly higher frequencies.

That’s very different than the way non-pressure omni microphone like a cardioids (or subcards, supercards, figure 8s, etc) derive their directionality.  The directionality of those microphones can be much more frequency independent down to the lowest frequencies.  How frequency independent the directional pattern of any particular microphone is and how little it’s response varies off-axis is all part of the art, science and cost of microphone making.  Take a look at the general trends in shape of the 4011 and 4015 polars (and mk21, mk22) posted above and notice how the pattern isn’t exactly the same across all frequencies, but maintains something of the same shape. Contrast that with the 2006 and the 2006 with APE polars which show directionality at the highest frequencies and a complete transition to omni response below that.  You won’t get anything like the response of a mk21, mk22, mk4, mk21, etc from putting attachments on an omni, instead you will get an omni that shows some directionality (and response differences) only in the upper mid and higher frequencies.

A sphere produces the smoothest response of all attachment shapes because it is the same shape from all angles and has no discontinuities or edges, but attachments can be found in other shapes such as disks and cylinders.  Niant makes (made?) an omni intended for instrument and maybe vocal mic’ing with a detachable wooden disk as do other manufacturers.  A disk produces a more pronounced on-axis boost but a more ragged off-axis response, and the diameter of the disk determines how low in frequency that boost occurs.

The idea of mounting an omni capsule flush in the surface in a spherical housing goes way back to the Neumann M-50, which was used for orchestra mic’ing and was the apparently the favored mic for use with the Decca Tree when that technique was first conceived.  Neumann currently produces a titanium skinned version of that in the M-150 (I think).

[Gutbucket]

Here's a couple graphs showing amplitude reponse ripples corresponding to off-axis defraction around different shaped solids.  These are for speaker drivers mounted in various shaped baffles, but the phenomena is more or less the same for microphones in reverse-

Cylinder, cube, and sphere, from Stan Linkwitz's website-


This only appears to show on-axis response variations, but for various shapes.  It was a sidebar in a Sound on Sound article-

[MIQ]

Hi Gut,

The diffraction graphs are interesting.  Both the ones from Siegfried Linkwitz's site and those from the SOS article can be found, with more info, in Harry Olson's book "Elements of Acoustical Engineering" 1957.  There are PDF scans of it floating around, like here:  http://www.scribd.com/akaliabetsos/d/51369856-olson-1957-I
Check out pages 21-23 (pages 41-43 in the pdf).

As you pointed out, the freqs at which these effects happen are dependent on the size of the shapes.  You can see that the horizontal axis of the graph for spheres is labeled (D/lambda), where D is the diameter of the sphere and lambda is the wave length of sound. 

For spheres you can see that the onset of the on axis freq response boost starts to happen at about D/lambda = 0.1, gets up to +3dB at D/lambda = 0.3, and reaches nearly +6dB at D/lambda = 1.

I'm not very familiar with thinking in terms of wavelength so I made an Excel sheet to help figure out at what frequencies these on axis boosts would occur depending on the diameter of the sphere.  Here's some common sizes for the balls used on Omni mics and also the human head.

Sphere Diameter = 30mm,  Onset of Lift = 1150 Hz,  +3dB Boost @ 3450 Hz,  +6dB Boost @ 11500Hz
Sphere Diameter = 40mm,  Onset of Lift =   860 Hz,  +3dB Boost @ 2560 Hz,  +6dB Boost @   8600Hz
Sphere Diameter = 50mm,  Onset of Lift =   690 Hz,  +3dB Boost @ 2070 Hz,  +6dB Boost @   6900Hz

  Head Diameter =160mm,  Onset of Lift =   215 Hz,  +3dB Boost @   650 Hz,  +6dB Boost @   2150Hz

Looking at the response measurements of the 4006 with these different sized Acoustic Pressure Equalizers (balls) shows similar trends, but they don't achieve the theoretical amount of boost (+6dB).  Not sure why.     I get that reality doesn't always match theory but the responses DPA show fall back to 0dB at very high freqs.  Wonder why?

Miq

[Gutbucket]

Thanks for the reference and numbers Miq, that helps a lot.  I can never remember the math describing this stuff so I tend to read what I can find, look for trends, attempt to distill the basic principles of what's going on, and if it's applicable to what I'm doing and easily achievable, try things out and listen to the results.  Thanks for backing up the empirical take with the mathematics describing these effects.

Not sure why the measured boost response isn't quite as much as the model predicts, maybe one of the more knowledgable experts here can comment.  Not sure either about the fall back to 0dB at the highest frequencies, perhaps that is part of the microphone's normal high-end response roll-off?

I'd assume the mathematical decription to fit more closely for the hard plastic balls with the microphone capsules flushmounted in them, and the human head sized approximation much more prone to variation for the way people use them around here, but it's very interesting to see the mathematical prediction for a head-sized sphere.  I think one could find measurement data for the Schoepes KFM spheres that are head-sized with two omnis flush mounted at the opposite poles.

Big water-filled hydrophone sphere attachments for underwater stereo and surround recording from Ambient-

[Gutbucket]

And that takes us pretty far from the original question.
Appologies for the off-tangent!

[Gutbucket]

As long as I've veered this far, how about lots of omnis arrayed over the surface of a very big sphere-

[yates7592]

As long as I've veered this far, how about lots of omnis arrayed over the surface of a very big sphere-

All 4006C's no doubt.

[Ultfris101]

thanks for taking the time. the graphs with the different shapes are really interesting. Now to find something like that with off axis.

And that sonar array....

I think a thread like this is really meant to meander anyway since it was stated up front this was basically a theoretical exercise barring a lottery windfall