Linearity and Stability of High Voltage Tuning Power Supply for Micro Electromechanical System Resonator
Micro electromechanical system resonators provide high quality factor frequency references for timing and filtering applications in communication systems, sensors, and signal processing. The resonant frequency of these devices depends on the mechanical properties of the resonator structure, which can be tuned through electrostatic softening effects by applying a bias voltage. High voltage power supplies for resonator tuning must provide exceptional linearity and stability to enable precise frequency control without introducing noise or drift that would degrade the resonator performance.
Electrostatic tuning of MEMS resonators exploits the voltage dependent spring constant of the electrostatic force between the resonator and adjacent electrodes. The electrostatic attraction force creates an effective negative spring that reduces the overall stiffness of the resonator, lowering the resonant frequency. The frequency shift depends on the square of the applied voltage, with higher voltages producing larger frequency reductions. This tuning mechanism enables post fabrication adjustment of resonant frequency to compensate for manufacturing variations or to implement voltage controlled oscillators.
The linearity requirement for tuning power supplies refers to the relationship between the control input and the resulting frequency output. While the physical relationship between voltage and frequency is inherently nonlinear due to the square law dependence, the power supply output voltage must be a linear function of the control input to enable predictable and controllable frequency adjustment. Nonlinearity in the power supply transfer function complicates the frequency control and can introduce distortion in modulation applications. Calibration and linearization techniques can compensate for power supply nonlinearity, but inherent linearity simplifies the system design.
Voltage stability directly affects the frequency stability of the tuned resonator. Voltage fluctuations cause frequency variations through the tuning sensitivity, which is the derivative of frequency with respect to voltage. The tuning sensitivity increases with the operating voltage, making stability more critical at larger tuning ranges. Low frequency voltage drift causes frequency drift that accumulates over time, potentially exceeding the allowable frequency tolerance for timing applications. Higher frequency voltage noise creates phase noise in oscillator applications, degrading the spectral purity of the output signal.
The tuning sensitivity of a MEMS resonator depends on the resonator design and the operating point. Resonators with strong electromechanical coupling have higher tuning sensitivity, enabling larger frequency tuning ranges but also greater sensitivity to voltage variations. The tuning range is limited by the pull in phenomenon, where the electrostatic force exceeds the mechanical restoring force and the resonator collapses into the electrode. The power supply must provide voltage control with resolution and accuracy sufficient to navigate the tuning range without approaching the pull in instability.
Temperature effects on both the resonator and the power supply affect the overall frequency stability. The resonator mechanical properties including elastic modulus and dimensions change with temperature, causing frequency drift. The power supply output voltage may drift with temperature due to component characteristics, adding to the frequency drift. Temperature compensation circuits can correct for these effects, but the residual temperature sensitivity after compensation determines the achievable stability. The power supply temperature coefficient must be small compared to the resonator temperature sensitivity to avoid dominating the overall drift.
Noise characteristics of the tuning power supply determine the phase noise contribution in oscillator applications. Voltage noise at frequencies near the carrier frequency creates phase modulation sidebands, while noise at frequencies near the resonator bandwidth creates frequency modulation. The noise spectral density of the power supply must be specified to enable prediction of the oscillator phase noise. Low noise design techniques including filtering, low noise references, and careful layout minimize the power supply noise contribution.
The settling time of the tuning voltage affects the frequency switching speed in applications requiring rapid frequency changes. When the control input changes, the power supply output must reach the new voltage with sufficient accuracy for the frequency to settle within tolerance. The settling time depends on the power supply bandwidth, the output capacitance, and the required settling accuracy. Faster settling enables more rapid frequency hopping in spread spectrum applications or faster calibration cycles in manufacturing test.
Power supply rejection in the resonator design can reduce the sensitivity to power supply variations, relaxing the requirements on the power supply. Differential electrode configurations can cancel common mode voltage effects, reducing the effective tuning sensitivity to power supply noise. The resonator mechanical design can minimize the electromechanical coupling to reduce sensitivity, though this also reduces the available tuning range. The system design must balance the power supply requirements against other resonator performance objectives.
Long term stability of the tuning power supply determines the frequency drift over the device lifetime. Component aging causes gradual changes in power supply characteristics, leading to voltage drift that translates to frequency drift. The aging rates depend on the component types, operating conditions, and environmental stress. Selection of low drift components and appropriate derating minimizes the aging contribution to frequency drift. Periodic recalibration can correct for accumulated drift, but the required recalibration interval depends on the power supply stability.
