MEMS Gyroscope Design

The MEMS gyroscope is an important class of inertial sensor and found in a wide array of consumer devices, including smartphones, cameras and navigation systems. Automotive applications find extensive use for gyroscopes and have requirements for high reliability. Additionally, industrial and especially defense markets demand high levels of accuracy, which fundamentally influence the design parameters of the gyroscope.

The Challenges of MEMS Gyroscope Design

From conceptual design, to optimization and performance enhancement, CoventorMP® can simulate a wide range of key issues related to successful MEMS gyroscope design. These include:

  • Proof of concept studies, to explore different device configurations, mode frequencies and drive/sensing physics (electrostatic/piezoelectric)
  • Electrostatic mode softening, to tune and match drive and sense modes
  • Pull-in and hysteresis
  • Sensitivity, bandwidth, linear acceleration effect
  • Quadrature, due to suspension sidewall-angles and comb levitation forces
  • Electrostatic compensation electrodes, to reduce quadrature
  • Over load contact-stopper design, to improve shock performance and reliability
  • Gas damping, thermoelastic damping and anchor loss, to predict Q factor
  • Response with temperature, including influence of package deformation
  • Parasitic capacitance of tracks, pads and package
MEMS Gyroscope Design

MEMS Gyroscope Design Example: Murata 3-axis gyroscope modeled in the MEMS+ module of CoventorMP with overlay of  measured and simulated data for static capacitance and X-axis sense mode shift with X-axis sense bias variation [1,2]

ROMs for Co-Simulation with Circuit and System Simulators

Readout circuitry and systems built around a gyroscope have their own design cycles, and normally have a gyroscope model included. To address this need, CoventorMP generates multi-physics ROMs that capture the inertial non-linearities of the gyroscope. The models are generated automatically so avoiding a manual build process, which can take many iterations and weeks of design effort. The models are optimized for speed, to allow for fast design iterations of typically no more than 30 minutes CPU time. CoventorMP models are provided in a VerilogA format, or as an S-function to run with Mathworks SIMULINK®.

Circuit and System Level Design - MEMS Gyroscope

Circuit and System Level Design – MEMS Gyroscope: Cadence Virtuoso® schematic with ROM generated automatically and exported in Verilog-A format. The ports on the gyroscope symbol represent: the sense electrodes (top), drive electrodes and angular velocity inputs (left) and optional capacitance outputs (right). The upper transient simulation plot show the drive pilot signal. The lower plot shows the differential Y-axis sensing capacitance response to Y-axis rate and cross-axis sensitivity to X-axis rate [1,2]

Characterization of Package-Induced Performance

An important consideration for any MEMS device is thermal stability and its robustness to deformation from its package. Gyroscopes are no exception. CoventorMP allows package models to be easily coupled to the gyroscope model. Parametric analyses can then be run to determine the response of the gyroscope over temperature, allowing designers to produce predictive models for rate offset. The package-induced performance is also included in exported ROMs.

(a) MEMS+ gyroscope model encapsulation in FEA die level package & (b) X-axis sense capacitance offset due to temperature-deformed wafer-level package, measured vs simulated [3]

As a conclusion, CoventorMP enables the designer to simulate key issues that are specific to MEMS gyroscopes, ranging from mode frequency design through to electrostatic spring softening, sidewall angle induced quadrature error and co-simulation with the package. Automated ROM export allows the user to immediately generate portable, fast, models for use in Verilog-A compatible simulations and Mathworks SIMULINK for circuit and system design.


  1. A Novel Model Order Reduction Approach for Generating Efficient Non-linear Verilog A models of MEMS Gyroscopess, ,Arnaud Parent1, Arnaud Krust1, Gunar Lorenz1, and Tommi Piirainen2 1Coventor sarl., France and 2Murata Electronics Oy, Finland, IEEE International Symposium on Inertial Sensors and Systems 2015.
  2. Efficient nonlinear simulink models of MEMS gyroscopes generated with a novel model order reduction method, Arnaud Parent1, Arnaud Krust1, Gunar Lorenz1, I. Favorskiy1 and Tommi Piirainen2 1Coventor sarl., France and 2Murata Electronics Oy, Finland, Transducers 2015.
  3. Thermo-mechanical simulation of die-level packaged 3-axis MEMS gyroscope performance, Arnaud Parent1, C. J. Welham1, T. Piirainen2 Blomqvist2 Coventor sarl., France and 2Murata Electronics Oy, Finland, DGON Inertial Sensors and Systems (ISS), 2017.

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