Dr. Charles Chen PhD of Lauten Audio has written a software simulation program for microphone transducer capsule simulation. The results in this article are for pressure capsules only. A pressure capsule is the easiest to simulate and there have been simulation results in published papers. However, Dr Chen’s simulation software goes beyond any published results and provides a method for simulating pressure gradient capsules along with configurations of the back plate, such as the pore distribution affects on capsule behavior. These results will not be published due to trade secrets.
The capsules used for this article are all made by Western Electric. As to not reveal any information regarding our proprietary designs, we have used the capsule parameters for this simulation from a research paper (PhD thesis) published in The Journal of the Acoustical Society.
These capsules share the same back plate configuration (diameter, thickness, pore size and distributions), the only difference being the diaphragm (surface density and tension) and spacing between the diaphragm and the back plate. The 111070 with polyethylene membrane has the lowest tension, and the 11670 with metal membrane has the highest one. The capsule simulation results below are of these capsules.
In Figures 1 & 2 the top result is the output voltage of the capsule expressed as sensitivity. (click images to enlarge)
Fig. 1 (Western Electric 111070)
Notes: 0 dBV is defined as 1V output at 94dB SPL. All capsules can only output several millivolts so the sensitivity is always a negative number.
Fig. 2 (Western Electric 11670)
The second result shows the diaphragm displacement from its balanced position (determined by the bias voltage) in nanometer averaged over 15 rings of the diaphragm. The third and forth results show the sound pressure on the back of the diaphragm, amplitude and phase, respectively. You can see how the tension and the spacing affect their behavior.
Notes: Pressure capsules only receive sound in the front of the diaphragm because the chamber behind the diaphragm is sealed and no outside sound can reach the back side of the diaphragm. But as the diaphragm is driven by the front sound pressure, it suppresses the air in the chamber and produces the reacting pressure to the back side of the diaphragm. The net driving force for the diaphragm is the difference of the front sound pressure and the back pressure. For pressure gradient capsules, the back pressure is very important.
To see more details of the simulation, we have provided (Figures 3,4,5,6,7 and 8) six diaphragm movement results for these capsules at three frequencies, 100Hz, 1000Hz, and 10000Hz, showing the shape of the diaphragm and its movement in half a vibration period. You might expect all parts of the diaphragm (rings in the simulation) should move in the same direction, and for higher frequency, the only difference is all parts move faster, but still coherently. But it is not the case. At higher frequencies, the vibration of the diaphragm became more complicated. The neighboring rings can move in the opposite directions. This becomes more obvious when the tension goes down.
All these results are consistent with and even better than the published research papers and well supported by the real measurement data presented in various papers. Although the results are the same, Dr Chen developed a totally different mathematical method, which allows us to not only be able to simulate the pressure capsule, but also the pressure gradient capsule and dual diaphragm capsule, which no one to our knowledge has ever published.
Not shown are how the change in the configuration of the back plate, such as how the pore distribution affects the capsule behavior. These results have never been published in research papers and we can not publicly reveal these at this time.
Fig. 3 (Western Electric 111070 100Hz)
Fig. 4 (Western Electric 111070 1000Hz)
Fig. 5 (Western Electric 111070 10000Hz)
Fig. 6 (Western Electric 11670 100Hz)
Fig. 7 (Western Electric 11670 1000Hz)
Fig. 8 (Western Electric 11670 10000Hz)