This paper discusses the conversion of voltage to frequency in surface-micromachined tuning fork oscillators intended as resonant transducers. First, the sources of nonlinearity in the mechanical structure and electrostatic actuation are discussed. These nonlinearities are analytically combined to show that low-frequency voltage drift in the sustaining amplifier is directly converted into a frequency shift in the oscillator output. Experimental evidence of this effect is presented, and it is shown that this is the dominant source of near-carrier frequency instability in the experimental system.
JntroductionA resonant sensor is a device whose output is a frequency shift. Resonant sensors are considered attractive for their dynamic range and sensitivity, as well as for their ease of integration into digital systems [l]. Quartz-based resonant sensors have been applied in a number of industrial applications, including high-dynamic-range pressure sensors and navigation-grade accelerometers [2][3]. Recently, the micromachining community has begun to look at using resonant sensing techniques, as well [4][5]. The work described in this paper is part of an effort to implement these techniques in an integrated surface-micromachining technology. This technology offers the advantages of low parasitics and good manufacturability, and the combination of surface micromachining and resonant sensing has the potential to produce high-quality, low-cost sensors.To this end, a number of sensors using resonant transducers have been fabricated in a commercial surface micromachining process [6][7]. This paper details the dominant source of low-frequency oscillator instability observed in the testing of these structures. A voltage-to-frequency conversion is found to take place that causes llfnoise from the sustaining amplifier to be directly converted into oscillator frequency drift. This llffrequency noise source determines the ultimate stability floor of the oscillator. Obviously, any 77 8 0-7803-3728-X/97/$10.00 0 I997 IEEE Figure I . Diagram of tuning fork resonatorsource of frequency instability in the oscillator is detrimental to the noise behavior of the transducer, so it is important that these sources be understood and minimized.
Oscillator DescriptionA diagram of a typical double-ended tuning fork (DETF) resonator is shown in Figure 1. The fork structure consists of two tines, each of which is rigidly clamped at both ends. The structure itself is anchored to the substrate on one end, while the other is left free for the application of an axial force. The natural frequency of the tuning fork is a function of this force, forming the basis for a resonant transducer.In the center of each tine is a set of electrostatic actuators, or combs, used to oscillate the structure. One set of combs is used to drive the tines, and the other is used to sense motional current. The drive and sense combs for
