Small diaphragm capsule design help needed

[Marik]

If and when I start with 10u spacing I don't have to mess too much before I have to lap the surfaces again to keep things in alignment. This might be the biggest problem affecting the accuracy of a series of measurements in my plan.

I really would like to have reliable method for measuring the diaphragm resonance before screwing it to the capsule. The impedance method sounds quite good, but then I have to build an acoustically transparent backplate for that job only. Worth the trouble I guess.

I'll keep you posted, for sure. From this point on it will take some time to get results.

The first capsule will be assembled in a couple of weeks or so. I hope it is not a total disaster.

Well, unless you are incredibly lucky and all the stars got crossed, most likely it might be... not a disaster, but something to start with. Just think that if you get at least some sound, then life is already good. You might find that the sound will be wheather too shrill, or way too mellow. Depending on the one you will just need to get little by little to go the other direction.

The 10um look little thin, but again, the final result will be the fine balance between capsule tension and diaphrang damping, which depends on the amount of air cution (i.e. spacing) and backplate drilling. With that spacing you might find that you will need to put much less bias on the capsule, and/or will be able put much more tension on the diaphragm. On the other hand, if you'd like to go Al (which I also tried), you cannot go way too much with the tension, because of the material fragility.

So all depends on the compromises you are willing to take. There are way too many variables to give you something more specific.

Best, M

 

[PRR]

I don't have the dimensions. I believe they may be calculated for any specific goal. I sure am not the person for that.

Basic principles.

We want a Low-Mass, Large-Area diaphragm.

It must conduct electricity, but very-poorly is good enough.

It must be air tight, at least so its leaks against the back-chamber are slower than the lowest frequency we want caught.

Oh, but it must be small to stay semi-omni to high frequencies. We could do math, but we know what to expect from 50mm and 6mm capsules. Dime-size is in the ballpark. 2:1 variations matter, 10% variations (16mm vs 18mm) really don't.

And if this is ball-mounted, I submit that the actual diameter is even less fussy than a stand-alone wave-catcher, as long as it is "small" against the ball.

The most natural configuration is Stiffness Controlled, Voltage Output.

Such a system will Be Flat. No tricks needed.

However high stiffness gives low output. So it seems we want low stiffness.

Stiffness may be self-stiffness (quartz, multiply supported plastic film) or induced stiffness (tension).

But all real materials have Mass. Stiffness and Mass makes Resonance.

When the frequency is above resonance, the system is Mass Controlled, voltage falls with frequency. To a first approximation, we want that to happen "above" the highest frequency we want caught.

When the frequency is AT resonance, it resonates. And because most suitable materials have nearly no self-damping, it will peak-up 10dB or 20dB.

OK, let's try some random known values. Fostex FE-103 loudspeaker with 69 cubic inch back-volume resonates at 180Hz, where the stiffness is nearly all back-volume. It is a 3" cone, and a 10" long 3" tube is 69 cubic inches. If we shorten to 1", resonance moves as square-root of 10, 3.16, to 570Hz. And if we dice the cone and chamber axially, no change in resonance. A 1" cone-paper diaphragm on a 1" diameter 1" deep tube will resonate at 570Hz.

We want at least 10 times higher, 5700Hz. That means the tube is 100 times shorter, 0.010". This is just to get cone-paper and chamber stiffness to resonate "above" (most) of the audio band.  

We may want something lighter than cone-paper.

We will need "some" mechanical stiffness in addition to air-stiffness. The polarization will suck-in. We can't make the system so air-tight that it won't bleed-out in minutes or hours.

We want lowest possible mass and significant mechanical stiffness. For tension-stiffened systems, this leads to high strength/mass materials. Metals are possible. Plastic films are nearly as strong and much lighter. We could hunt around, but better brains than we have beaten the bushes and the "good" materials are well established.

Let us suppose we get a reasonable mechanical stiffness with low mass, a reasonable air stiffness. It will resonate, big narrow-band peak. Bad for music, awkward for measurement, and possibly shifting all the time.

We need resistance.

Some mikes have used fuzz in front of the diaphragm. This must be very close, falls out, tends to be unpredictable.

If we put a narrow passage between diaphragm and back-chamber, air drag will add resistance. There are several possible schemes. The most common one puts the back-plate very close to the diaphragm, with grooves or slots to give the desired total back-volume. Much of the air must travel "sideways" in the narrow clearance to reach back-chamber. This gives drag.

 

[PRR]

The number of variables is fascinating, but plagiarism narrows the hunt.

Diaphragm size is the #1 variable for output versus bandwidth (see B+K range of big-small capsules); plagiarizing known-good audio mikes gives a target.

Diaphragm material is critical, and I think you must simply steal this BoM item from existing designs using available products.

You need a back-electrode. The polarizing voltage and electrode spacing are inter-related. However high voltage is annoying, and I think damping will lead to small back-spacing. Steal these values.

Build a capsule with an adjustable-spacing perforated back-electrode and a large back chamber. Use plagiarized film, stretch until it breaks, do again to say half the breaking point. Raise voltage well above target, reduce back-spacing until fall-in, reduce voltage to target.

Measure mechanical resonance. This may be obvious by listening (big 2KHz peak, some bass, no highs). It may be found by electrical impedance measurement, with and without DC polarizing voltage, although this will be very fussy.

Adjust back-volume to bring resonance "near the top" of the audio band.

For dead-flat response we would put resonance far above the band; but this conflicts with sensitivity. And in practice, wave-size gives directivity which raises on-axis response at the expense of off-axis, which is annoying, but useful. Unlike speakers (which may work up into the very-beamy range) "omni" mikes generally won't want more than a few dB of beaming; this still allows resonance to be low in the top-octave rather than at the far end.

So you know a back-spacing for no fall-in, and a back-spacing for a good resonance frequency. In practice, you will need to add volume. You want to do this so that most of the air has to drag through clearance. Holes or slots.

Hole/slot area "wastes" electrical power. If the holes were half the total area, you'd get full voltage via half the capacitance, half the output power. We are committed to a head-amp, but still power is too teeny to squander. 1/3rd of area is not much power loss. 1/10th of area is 23% better but may lead to excessively deep holes/slots which may display wavelength effects or be so narrow that air-drag swamps back-volume effects.

Given extra volume needed, and percent of area, the hole-depth is obvious.

Where to put holes?

A hole in the middle wastes the best part of the diaphragm's motion.

A moat around the back-electrode is electrically best, but begs for circumferential air-modes. If present for mechanical reasons, it should be small-clearance to damp roundy-modes.

Any single hole/slot will give no-uniform damping, we want to spread it around.

Between these extremes, I suspect hole size and location is not very critical.

Now after all that, we have good resonance and a good electric source but no idea if resonance damping is correct. I think it will come out useable, because we have stolen or inferred most dimensions from Known-Good designs. It may peak or slump, but not no 20dB like an undamped diaphragm. Maybe +/-6dB, added to several dB of directivity rise, plus your ball-size.

 

[leswatts]

Wow, great observations as always PRR.
You're getting tons of good information now, huh Jonte?

I've steered things sort of toward the the analytical end with the Zuckerwar equation, but it's about the best condenser mic analysis we have. Yes, lots of math!

But in practice, we usually just make simple lumped parameter networks to model the device and experiment a lot. (including the ultrasonic microphones I make)

We just use a few simple heuristics.

Transducers are separated into to basic types... those using rigid structure in bending mode (like plates and bars) and those using tensioned members likw membranes.

For rigid structures we usually select materials with the highest stiffness to mass ratio. This is because phase velocity involves the term SQRT(E/rho) where E=youngs modulus and rho = density. The winning material is usually BERYLLIUM.

For tensioned structures we select materials with highest strength to mass ratio, because transverse phase velocity involves the term SQRT(T/sigma) where T is tension, and sigma is mass per unit area.
Winning materials are things you would make aircraft/spacecraft out of...aluminum alloys, titanium, carbon,
iron/nickel/chrome, some polymers.

Given that, and that we are talking about tensioned stiffness controlled devices, many separate the microphones into two broad categories:

Type I:
The majority of the stiffness is supplied by mechanical diaphragm tension rather than air in a cavity.
The diaphragm is often highly tensioned metal foil.
This is the type typical of the B&K measurement mics and the TAN paper mic. The backplate is thin and has through holes and an anular slot to a back chamber due to the backplate being smaller than the diaphragm. (backplate d=0.82 diaphragm d as calculated by some as optimum) A limiting factor for full range audio use is that it's hard to make these bigger than about 15-20mm diameter.

Type II: The majority of the stiffness is supplied by the air (in a cavity). The diaphagm tension is lower.
The backplate has no slot and the holes are blind. There is no "rear chamber". Jonte, your design is of this type as are many if not most studio microphones. Limiting factors? One big one. The air can be a stiff spring where the vent hole impedance is high, but at very LF it can just flow out, causing the diaphragm to suck in toward the backplate from the electric field force. So larger gaps and lower polarization voltages are generally used, with the usual consequences. One "advantage" though...you can make them big if you want. Also, they are easier/cheaper to make.

Anyway, those are the broad categories I use. There's one other thing that comes to mind:

I really would like to have reliable method for measuring the diaphragm resonance before screwing it to the capsule. The impedance method sounds quite good, but then I have to build an acoustically transparent backplate for that job only. Worth the trouble I guess.

Here is what I do to solve that when doing impedance runs: I put the assembled microphone in a vacuum.

I have some pictures of impedance testing of microphones in my lab, but will only show them if someone wants/needs to see them.

Les
L M Watts Technology

 

[burdij]

Here is what I do to solve that when doing impedance runs: I put the assembled microphone in a vacuum.

D'oh! That's why you get paid the big bucks, I'm sure.

Possibly a reason for going back and re-evaluating my suggestion about not worrying about a relief hole. Putting it in the spacer ring is not a good idea as the material I use is about as stiff as a well cooked noodle. Guess it will have to go elsewhere.

 

[leswatts]

D'oh! That's why you get paid the big bucks, I'm sure.

HaHA well sometimes. Recently I had to forgive a lot of client fees due to the automotive industry stuff. So I kinda PAID the big bucks with some acoustics projects.

Anyway, Im glad to see consistent responses in this thread. I think we are all saying pretty much the same thing, with different words. That's good! Smart people here. None of the silly audiophool arguments.
Just proper scientific principles. (Even though it's an art)

Les
L M Watts Technology

 

[ioaudio]

I have some pictures of impedance testing of microphones in my lab, but will only show them if someone wants/needs to see them.

hi les,

would be great to see those pics.
great discussion!

-max

 

[leswatts]

hi les,

would be great to see those pics.
great discussion!

-max

Well, I have one picture of measuring microphone impedance and plugging in values to the lumped parameter model.

In this setup I am measuring radiation resistance. To separate it from internal electromechanical resistance, I fire the highly directional microphone at a boundary certain wavelength multiples away.
This creates a standing wave, so radiation resistance goes away...it's all radiation reactance. Remaining resistance is just the internal stuff.

This is for ultrasonic microphones, but the gear is the same for audio. The problem is the cost of it. I'm trying to design up a low cost autonulling bridge impedance analyzer based on computer data aquisition
so I don't have to pay $1200/month rental on that damned Agilent stuff. If I get it done, I'll share the design if anyone wants.

My test station is in a cordoned off area in my machine shop building....a bad place. I hope to move it to it's own new separate room soon.

Les
L M Watts Technology

 

[Jonte Knif]

Thank you all, this is pretty unbelievable.

From AES library the paper by Roger S. Grinnip (2006) looks very good source for those who "do" math. Les?

Just out of curiosity, does stiffness to shear have any role in mic diaphragms? At least in many musical instruments it has.

None of the silly audiophool arguments.

Right on spot. This is why I stay away from a certain microphone forum. Even if someone there sometimes gives very good info especially about history, I don't like the "atmosphere" there. 80% of its content is needless self affirmation and "the old mics are best" lore without really explaining anything. One central figure told about his tube testing method for mics. No mention about testing Gm, grid leak etc, just going pretty directly to "listening" I bet his tubes sound different if they bias all over the place. Hmmmm.

Any how, I posted an inquiry to Kemet company about hand lapping plates and asked about their accuracy. Didn't get a reply yet. I hope 2 microns flatness for D=18mm piece is possible. Opinions? Their products look like pretty high in quality.

I'll go bankrupt with this project. I can see it.

-Jonte

 

[burdij]

I picked up some ceramic plates that are extremely flat and hard from a local company that makes slip rings for vacuum systems. They are about 2 inches in dia. I can send you one of those. Send your address in a PM. Don't buy a surface flat. Plate glass and jeweller's rouge works pretty well too. I start out with 0000 carborundum paper stuck to a piece of glass with 3M spray glue. I think you need better than 2 microns. Easy to do with glass and rouge. Another good source of flats are the defective slices and glass reticles from semiconductor manufacturing. These are extremely flat and made from silicon or glass. Electronics Goldmine sells them for $10-$20.

 

[leswatts]

From AES library the paper by Roger S. Grinnip (2006) looks very good source for those who "do" math. Les?

Just out of curiosity, does stiffness to shear have any role in mic diaphragms? At least in many musical instruments it has.

Jonte, I don't have that here and haven't seen it. If I did I would read it. Yeah, I do math. The Zuckerwar paper is the most comprehensive analysis I know of.

As far as the shear...sure stretched membranes can have shear stress. But the equations of motion for the stretched membrane just have the SQRT( T/sigma) figure of merit, so I think simple linear tensile strength to mass ratio is the goodness factor, as PRR and I both have mentioned. Also, I have only seen diaphragm failure in simple tension. Yes shear strength and modulus matter in many instruments. I build guitars. And wrote some papers.

I wanted to ask about your spark source. Don't automotive spark systems have a long burn time, like milliseconds? (fourier transform of a rectangular pulse is a very non flat sinc function) Don't some also do a rapid pulsetrain spark?

Les
L M Watts Technology

 

[Jonte Knif]

Hi Les,

Spark plugs in engines behave certainly not in an ideal way. I don't have the link at hand where it was explained, but I took a careful look at the principle and time values last year.
The main point was that there are 3 different phases in the discharge. Arch, plasma an glow if I remember. The whole process takes milliseconds, but sound is mostly produced in a very short time frame.

I get a nice 6dB/oct rising response from FFT, but I don't know the limit, I only have small panasonic capsule to measure it. Good enough for audio, probably not for ultrasonic mics.

Bubble plastic "explosion" on the other hand produces fairly linear response, but the upper limit is around 20k. Because of the flatness and high energy it is very well suited for fast measurement of LDC resonances and polar pattern.

Normal spark plug as such is poor source for controlled spark. I built a new electrode and modified the other in order to get the spark take the same route every time. Still not perfect and there are level and spectrum differences of several dB:s between each ignition. Could be better, but works for me.

-Jonte

 

[burdij]

Here is an article I stumbled upon while looking for something else that is related to the spark-gap problem. It talks about a spark gap apparatus that Boré at Neumann used for measuring transient response:

http://www1.neumann.com/download.php?download=lect0036.PDF

 

[PRR]

>> AES library the paper by Roger S. Grinnip (2006) looks very good source
> Jonte, I don't have that here and haven't seen it.

Advanced Simulation of a Condenser Microphone Capsule
An advanced numerical model of a pressure condenser microphone capsule is presented. The model divides the acoustic space into internal and external domains and couples the dynamic pressure in each domain to the capsule diaphragm motion. The external acoustic space is modeled using the boundary element (BE) method which allows for arbitrary geometry of the capsule/microphone external surface. The diaphragm is modeled as a circular tensioned membrane of negligible bending stickiness. The internal acoustic space (both the viscous air film and back chamber) is modeled as a cylindrical cavity with negligible axial pressure variation. Flow through the back plate is modeled as an annular array of circular pores with generalized functions locating each pore position. Although the presented model is specialized for a simple pressure condenser microphone, the numerical implementation is sufficiently generic to allow for a large variation in capsule parameters. The complete model, implemented in a software package called VC, is used to generate a simulated response curve that is compared to a response curve taken from an experimental prototype. The results show excellent agreement throughout the measured frequency range, indicating this new coupled model may be used for advanced microphone characterization and design.

Author: Grinnip, Roger S., III
Affiliation: Shure Incorporated, Niles, IL
AES Convention:117 (October 2004) Paper Number:6254

Permalink
http://www.aes.org/e-lib/browse.cfm?elib=12911

This paper costs $20 for non-members, $5 for AES members and is free for E-Library subscribers.

FWIW: my university is -apparently- not subscribed to AES.

 

[Jonte Knif]

FWIW: my university is -apparently- not subscribed to AES.

Too bad  
I have the subscription,  I have the paper and for me it is worth nothing because I just don't get the math and there are no generalizations in it. It is not that kind of paper.

It is only 9 days since I started this thread and things _are_ getting out of control. I have realized that the project (hopefully leading to 3 well made mics) does not make sense if I don't get a lathe. One thing leads to another. The price I got for 3 sets of capsule parts was too steep, and in addition to that I should machine the acrylic balls, (I just got them), make a nice conical support/holder for the capsule assembly, turn the tensioning  rings and mic body botton parts. Minimum. At this point the lathe has payed itself. Now the only question is whether or not I'm ready to learn a new craft. Fortunately all the parts are easy to machine, simple in forms. Brass is very easy, delrin is easy, acrylic needs a bit attention, but with a decent hobby machine this should be a piece of cake _for a skilled person_. Hmmm....

So far the only thing I have ordered from the micro mechanics school is the tool for positioning and drilling all the holes. Not really cheap, but without milling machine I couldn't make it. And it will be heat treated silver steel to last for ever.

But turning could be fun. Optimum Vario 180x300 or similar low cost - non China- lathe could work just fine. It is about 1300 euros with some extra accessories. (well, who knows how many parts of it really are made in Germany)

-Jonte

 

[audiox]

well, who knows how many parts of it really are made in Germany

None of them. A few years ago some of the electrical parts were made in Germany but not any more. Despite that you get a relatively good machine with very little money. A friend of mine has several Optimum machines in his shop and he is quite happy with them. I have used them too and I have nothing to complain. He told that there is one severe problem: the material of lead screws is too soft. If you adjust them to close zero backflash, they wear quite fast.

Those 1000 euro lathes are not designed for micromechanics machining. For the capsule parts in your drawing, you probably need a better machine or very skilled machinist (or both in worst case). And high quality bits (which are expensive).

For capsule hole drilling you need a dividing table if you already don't have one:
http://www.optimum-machines.com/products/accessories/1/circular-dividing-tables/index.html

 

[burdij]

I found a while ago that small round parts were easier and faster to machine on the mini-cnc mill than on the lathe. I make the Delrin body out of flat bar stock, 0.250 inches thick. The brass electrode is cut from a brass bar of the same thickness. The only capsule machining step I do on the lathe is the initial surfacing of the brass and Delrin assembly after I glue the two pieces together. The holes in the electrode and the holes for the mounting screws are done in two passes with the mill. The clamping ring is done on the lathe by boring the inside diameter into the end of a 0.750 brass bar that has the surface flattened. I then part off the .100 thick ring with a parting tool.

The lathe is a 9x20 inch China-brand. It was a suprising good deal for the money. I got the bigger lathe because I also wanted to do mike bodies. I have way more money invested in tooling than the lathe itself cost. I am planning on adding a Sherline lathe, the type Dale uses for the M7 capsules, because I want to be able to use collets for finishing small round objects. The collets are not as readily available for the larger lathes.

 

[PRR]

> That AIP (American Institute Of Physics) Handbook Of Condenser Microphones

I have a copy I would sell. ABE.com is listing copies at $140 and up and up. It is, as said, mostly about the W.E. condenser and calibration issues, narrow but deep. Mine is used, VG condition.

I also have:

A damaged but quite readable copy of Physical and Applied Acoustics, Meyer and Neumann, 1972, a very illuminating general course on acoustics with some pages on condenser transducers. Originally in German, well translated to English, and with a different emphasis from most US acoustics texts. A bookseller would say poor or very-poor condition, but that won't hinder your learning. ABE.com lists it at $120 in VG or Fair condition, which may be high, but it is rare.

Fundamentals Of Acoustics, Kinsler and Frey (NOT the Benade book!), 1962, a broad treatment of acoustics both in air and in water. Fair condition (spine wear, finger-smudge). ABE lists copies at $20 to $200. 

I'd love to do a deal with someone here who will really benefit.

PM me.

 

[Marik]

> That AIP (American Institute Of Physics) Handbook Of Condenser Microphones

It is, as said, mostly about the W.E. condenser and calibration issues, narrow but deep.

Well yeah, as well as buried in heavy math, etc. In any case, IMO, the introductory part alone is probably the most comprehensive source on omni capsule construction and theory, and is a "must read" for anyone who is interested in that. 

Best, M

 

[leswatts]

Jonte,

Too bad I'm half a world away. I own a commercial prototype machine shop. I'd let you use it.

Les
L M Watts Technology