15.13. Dynamic membrane compliance and dynamic resistance

By similar argument, we find that the dynamic mechanical compliance is given by
CMD=α024CMD0=1πα02T
image (15.80)
and the dynamic resistance is given by
RMS=α024SDRS.
image (15.81)
However, it is inconvenient to have different circuit element values for static and dynamic conditions. Hence, we use the following bilinear approximations for hybrid static–dynamic compliances, which transition from static to dynamic at around half the resonance frequency f 0
CMD=1+2ff0α024+2ff0CMD
image (15.82)
CE=1+2ff0α024+2ff0(CE).
image (15.83)
We will derive an expression for the membrane resonance frequency f 0 further on. Note that we only apply this transformation to the negative electrical capacitance associated with the motional current, not the positive one associated with the static current. By applying the same bilinear approximation to both the negative and positive mechanical compliances, we are not changing the condition for stability of Eq. (15.74).
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