## Friday, April 29, 2011

### Dr Chen on Pressure Gradient Capsule simulation for microphones – A Summary

Dr Charles Chen PhD provides a brief overview on capsule simulation and what we are doing here at Lauten Audio.

Condenser microphones consist mainly of two parts: capsule and preamp. For the preamp, there

is sophisticated commercial software, like PSpice, LTSpice, etc, which can be employed to study a preamp circuit before actually building it. The simulation results are quite close to the behavior of the actual circuits, because we know the mathematical formulas for all the components in the circuits: resistors, inductors, capacitors, diodes, transistors, etc. These formulas are the basis of all those circuit-simulation software’s.

Microphone designers have long hoped to have similar software to help them design condenser microphone capsules. But before we can have this highly demanded software, we need to know all the mathematical formulas describing the capsules. Physicists and mathematicians in acoustics started their research on developing mathematical formulas of condenser capsules half century ago. The first research article appeared in the Journal of Acoustical Society of America (JASA) in 1954. But the structure of the condenser capsules under study was very much simplified to allow a mathematical treatment. Since then, numerous papers published in JASA and more engineering-oriented JAES (Journal of the Audio Engineering Society). But all those mathematical models still contain too many simplifications about the structure of the capsules. For example, those models only study pressure condenser capsules, not pressure-gradient capsules and double-diaphragm capsules. Even for pressure capsules, they cannot describe the effect of the distribution of the holes on the back plate, and the thickness of the back chamber. So the power of those models in design-assistance is quite limited.

Here at Lauten Audio, we have developed and are still improving our own mathematical formulas and software which can simulate all kinds of condenser capsules. We can simulate how the thickness and tension of the diaphragm, the thickness of the air-film between the diaphragm and back-plate, the hole size and distribution on the back-plate, and the thickness of the back-chamber, the capsule shape, etc, effect the frequency responses and the polar patterns of the capsules. The simulated results provide us an excellent guide in developing our capsules.

In case you were wondering…