15.11. Negative compliance and stability

The negative capacitance  C E represents the electrostatic force of attraction. When referred to the mechanical side, it forms a negative compliance and must always exceed C MD in value to prevent the membrane from being attracted to whichever stator is closest. Hence, if there were insufficient tension to counteract this, we would have an unstable equilibrium in the central position, like that of a marble balanced on top of a dome. Therefore
CMD<d24CEEP2
image (15.67)
Although the force acting on the membrane is linear under dynamic conditions, because of the constant-charge principle mentioned at the beginning of the chapter, the resistance R P in Fig. 15.1 (together with any resistive coating) will not prevent charge from migrating to the closest stator during very slow or static displacements. Hence, the electrostatic force of attraction will increase as the membrane approaches the stator, causing it to stick. Hence, a reasonably thick layer of insulation is needed on the insides of the stators to limit the minimum distance between the membrane and the conducting parts of the stators. This is equivalent to driving the stators with series capacitors in which the insulating material forms the dielectric, but, for simplicity, we shall omit these capacitors in this analysis.
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