Its getting a bit confusing because the 3 papers linked here deal with 3 different types of driver technologies, and many of the assertions made for each technology do not universally apply to the other two. Diaphragm mass plays a role in LF resonance, which may be used in the design of PM and dynamic drivers to improve LF response, whereas ESL drivers simply don't have driver mass in that order of magnitude - not to say that ESL drivers don't have panel resonance, but in headphones it probably isn't in the right region of the FR.

I'm no ESL or driver expert. Kind of getting an education here. But I think the mechanics behind it include compressing air much like other technologies. So fail to see how the laws governing dynamics and planar fail to apply to ESL. Also according to the linky below, it seems mass does play a role in how low in frequency ESL drivers go (excursion vs freq is also discussed):

http://www.audiodesignguide.com/esl/esl.html

I'm not saying that linky is right though. So if there are better explanations on the relationships between mass and ESL low frequency reproduction (including the lack of such relationship), feel more than welcome to prove the details.

Here is another reference with some discussion about mass effects and some plots on resonant frequency are given:

http://sound.westhost.com/project105.htm

BTW, from all the stuff I have read recently, panel resonance tends to be in the audible frequency region.

That is indeed a very good link.

I found very useful "The Electro-mechanical Analogy" Appendix B in Phillip Harvey's "Electrostatic Headphone Design" paper (original paper used in Chu Moy for his write up, and attached below).

The mass per unit area (M), the spring (stiffness S), and the damping (air 2Rm) are modeled as a second order electrical circuit. Mass per unit area corresponds to an M henries inductor (as you said), spring stiffness to a 1/S farads capacitor, and damping to a 2Rm resistor. The equivalent series RLC circuit has a well known resonant frequency of 1/sqrt(LC), which equal to sqrt(S/M). This in agreement with the description of resonant frequency in mechanical systems.

Appendix A is also very interesting. I think he used a flat baffle to measure his cans. This is a 1971 paper!

I also attached the original Pollock's "Electrostatic Headphones" paper (also used by Chu Moy for his write up).

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Tachioma, I feel my reply to your post was a bit confrontational. I'm not an expert in the field of transducers, and may form my own set of misconceptions as I learn. But I do try to make sense of what I read as best as I can, and I'm not that uncomfortable with the material. I perhaps reacted to what I perceived as an idealization of ESL drivers. But it maybe unfair of me push for proof that way, and for that I'm sorry.

I know the Graphene paper was brought up some time ago at Head-Case I think. I do read the information there from time to time. However, I just quickly skimmed it. Reading it more carefully, a lot of what they are describing seems cherry picked. I could say the same thing about that "Knurling" planar material patent.

The more I read though, the more I'm convinced that ESL, PM, and dynamic drivers have a lot in common. Their theory of operation might be different, but they all drive air by some mechanical means which can be roughly described by a similar set of differential equations. Note I said roughly.

   So I just read Bruce Thigpen's original 1997 "knurling" patent US6104825. The 1997 patent says nothing of compliance.

   US6104825 (1997) patents deforming the conductor and/or the substrate of a planar-magnetic driver for the purpose of "permit[ting] expansion and contraction of said conductor means and said active surface area".

Problem as stated in the Description:

'The heat causes the two materials [ conductor and substrate ] to expand at different rates resulting in a loss of tension or non-uniform tension over parts of the "active area" or "active surface area" of the diaphragm. ... The loss of tension across a diaphragm results in non-uniform displacement of the diaphragm during operation. Such non-uniform displacement of the diaphragm in turn causes several forms of distortion limiting maximum usable sound output.'

Solution as stated in the Description:

'At least a portion of the active surface area of the diaphragm and/or the electrical conductor runs carried thereby are deformed so as to create a plurality of ridges or grooves in the surface thereof such that, even though the diaphragm and conductors are mounted taut within a support frame, the areas which have been physically deformed remain and thereby create areas of expansion which allow the diaphragm and the electrical conductor runs to expand and contract during the operation of the transducer.'

Independent Claims of US6104825:

Is a copy of Dan Clark's supposed co -authored patent application with Thigpen circulating anywhere?  I wonder what they are trying to patent exactly, since US6104825 patents nearly all forms of deformation. The difference must be in the stated purpose. Are they simply going to copy the claims of the original patent and substitute "[deforming] so as to permit expansion and contraction of said conductor means and said active surface area when the transducer is in use" with "[deforming] so as to increase the compliance of the conductor/substrate combination"? Is the new patent simply a re-up of the expiring US6104825 with a new 'purpose'?

 

UB, thank you for the links, very informative post as usual!