On the film thickness of planar membranes

In discussions of various isodynamic and electrostatic headphone designs, you often see the statement that “the thinner the film, the better the sound”.
People sometimes ask me, “Is this true?”
To answer very briefly, no, it’s not true.

I will now explain why

1. I will start by explaining a certain theoretical limit for some ideal conditions beyond which reducing the thickness (and mass) of the film loses its meaning.

This limit is related to the ratio of the film mass and the mass of the most actively moved by oscillating air. If these masses are equal or comparable – this is the theoretical limit. Let’s assume that the film consists of lavsan alone and is actuated in some ideal way (it doesn’t matter which one, this is just to demonstrate the calculation).

The density of air is about 1.2 kg/mc, the density of lavsan is 1380 kg/mc. Let’s also assume that the lavsan is perfectly flat, solid, and that there are no obstacles in the transmitter design in the immediate vicinity of the diaphragm that create excess pressure during oscillations. Simplistically, we will assume that the diaphragm moves freely in ideal piston mode uniformly over its entire surface, and that the maximum amplitude at the peaks is 1 mm.

The calculation shows that, under these conditions, the mass of air being moved and the mass of the diaphragm will be equal at its thickness of about 0.87µm.
That is, in principle, a theoretical limit of about 1 micron. Below this limit, the “the thinner, the better” statement does not work in principle.
Let’s call it “the limit of the ratio of the mass of the membrane to the density of the acoustic medium.

2. Now let’s get closer to the real world in specific engineering solutions. In the design of any transducer and any headphone there are:

• Acoustic obstructions in the vicinity of the diaphragm in the form of magnets, protective mesh, transducer housing, cushion edges, damping, etc.
• Acoustic chambers of limited volume (cup volume, volume under the cushion).

Imagine a piston in a cylinder with a small exhaust port. The greater the difference in area between the piston and the orifice, the more resistance it needs to overcome. Roughly the same processes occur with diaphragm operation. The ratios of the area of the diaphragm to the actual emission area, the ratio of the conditional volume of the piston (diaphragm) movement to the volume of the cylinders (acoustic chambers) work.

Of course, for each of the designs of radiators and headphones for this reason, too, there is a theoretical limit, which differs from the described in paragraph 1 at least by an order of magnitude or higher. The calculations here are of course very complicated, taking into account many parameters of the system, and for each individual design the set of parameters is different.
This limit, depending on the specific design, can already be estimated at 8-15 µm of “conditional ideal lavsan”. Let’s call this limit the “transmitter design limit”.

Obviously, in more enclosed designs this limit is higher

3. Now even closer to the real conditions of manufacturing of concrete constructions and the materials used in them.
The technology of manufacturing films is such that even the most advanced manufacturers have very non-ideal technological tolerances. For example, the reputable company Dupont in the manufacture of films 10 microns operates with a tolerance of plus or minus 10% within a square meter of film.
The thinner the film, the greater this technological variation in percentage will be.
Given that the film in isodynamics is a “sandwich” of at least 3 layers (film, adhesive layer, foil), the tolerances add up.

In my experience and conviction, if the basic material parameter and tolerance do not fit at least in one order (10%), it leads to unacceptable (at least for me) instability of the result on the output, repeatability of quality, coordination of parameters of emitters of the left and right channels, etc.
There’s about 10 microns, in general, which provide at least some technological repeatability… Working with 6-8 micron film, for example, I have to throw away up to 40% of blanks. Working with 10 microns can be brought to acceptable technological 10% rejects, although this is also a lot…
And this is the “limit of technology”.

• Other than that:The film is made, stored, etc. in rolls. In their winding “floats” the tension force. When moving, tumbling, dropping, etc., the rolls are deformed, which manifests itself in the film in the form of internal stresses that lead to various unpleasant consequences in the final product. The thinner the film – the more noticeable the effect.
• Due to the specificity of the physical formula of lavsan itself and the technology of film manufacturing, it has a pronounced anisotropy (difference of properties from the direction). For example, tensile strength, elasticity properties in perpendicular directions differ many times. Remember, for example, how a lavsan bag tears. In one direction it tears very easily, in the other direction it does not tear at all. In thin films, the anisotropy is stronger. And this affects the vibration behavior of the stretched film. Such anisotropy is one of the causes of harmonic distortions.
  The distribution of the property over the area of the film is not homogeneous. The thinner the films, the higher the heterogeneity. This applies to the thickness, density, strength, and elasticity of individual sections of the film. This unevenness is also the cause of distortion.
• There is a lot of human factor in working with film. The operations of cutting, photolithography, tensioning, gluing, etc. The thinner the film, the easier it is to screw up. I worked with 2 µm films as well, to try it out. They deform at the slightest manipulation. The most problematic part is rinsing out the photoresist. A little tampon over the ribbon – stretched it by 1-2 mm. Only non-contact method of work… And the reliability of such a film. I, for example, managed to tear such a film glued to the frame, just by blowing on it well. The same effect can be achieved by simply moving the headphones, well “sucked” on the leather ear cushions.
  
  There are other factors that I have noticed, but these are enough to think about.

To summarize, the statement “the thinner, the better” definitely does not work here.

There is a certain optimum, which is made up of many factors, and which at the modern technological level can be estimated around 8-10 microns. If you try hard enough, you can get 6-8 microns. In presenting these facts, I have not specifically referred to the description of the physical processes occurring in the emitters of various designs, it will be quite “too much blah-blah-blah”. However, in all cases there is a growth of negative consequences with a decrease in the thickness of the film in the form of exactly the main parameters of the sound quality.

Well, the use of thinner films on the modern technological level turns both the process of production and purchase-use of headphones in an exciting lottery, where you can bet on

• How soon the headphones will fail;
• How much degradation in sound performance will occur over time;
• How lucky you will be to get an acceptable quality copy.

Author’s article (c) Snorry (Sergey Glazyrin)
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