On the quality-factor of micro-resonators

Three measures of the dynamic response of micro-resonators are considered: gain, sharpness of peak, and quality-factor which is measured by logarithmic decrement. Analytic expressions for the three measures are derived and it is shown that they are not necessarily equivalent. The conditions for the equivalence of these three measures are discussed. A distinction is made between the response of one-port and two-port electromechanical resonators. The cause for the anti-resonance of a one-port electrostatic resonator is explained. The analysis is extended to distributed systems. In particular, the often-used measure of the product of frequency and quality-factor (f×Q) in distributed systems is reexamined. It is generally assumed that this product is constant for consecutive resonance peaks. In this work we show the conditions for which this assumption is valid.