Precise analytical evaluation of the ring shape anchored contour mode disk resonator for constructing a low noise UHF Pierce oscillator

Abstract

This paper presents an analytical evaluation of the previously demonstrated Ring Shape Anchored Contour Mode Disk (RSACMD) resonator and extracts its equivalent electrical circuit. In the next step, a series resonant Pierce oscillator is designed and parameterized based on the calculated MEMS characteristics. Due to the inherent 180° of phase shift in the RSACMD resonator equivalent circuit, a modified version of a Pierce sustaining circuit is introduced with two inverters (instead of one inverter in conventional Pierce oscillators) to compensate that extra phase shift and satisfy Barkhausen criteria. The designed circuit presents excellent phase noise performance because of a special design which results in small frequency pulling and enable the circuit oscillate close to natural frequency of the high Q resonator. The overall circuit consumes less than 257 μW from a 1.8 V power supply.