The capacitance versus displacement response of a MEMS device such as a comb drive resonator or pressure transducer diaphragm can be extracted from a full simulation of a MEMS device. This response "table" can be associated with the ANSYS electromechanical transducer element (TRANS126). This element can be considered a "black box" with a user defined response and can be connected to other "black box" elements to provide a representation of a more complex system. These black box elements are often refered to as lumped elements or reduced order macro model elements. The lumped elements are extremely efficient because the many thousands degrees of freedom of the full simulation are represented by perhaps 2 degrees of freedom in the "black box." When simulating a system that may be composed of dozens of functional elements it is far more efficient to use the reduced order model concept, rather than performing a fully detailed finite element analysis of the entire system which could comprise of several million degrees of freedom. However, it is important to remember that the accuracy of a lumped element system simulation is only as a good as the accuracy of the functions used in building the lumped elements. Hence, care must be taken in deriving these functions from the full analysis of each separate"component" in the system. Although the reduced approach has its limitations, it is extremely useful in performing"what if" design studies without having to invest the time involved to put together a finite element analysis of full system.
ANSYS provides a full compliment of associated mechanical lumped elements as follows:
The TRANS126 element can be coupled to spring, mass, damper, and circuit elements to effectively simulate a complex MEMS system. ANSYS Multiphysics provides the following circuit elements:
The lumped circuit elements are for simulating linear circuits, and solve for unknown nodal voltages (and currents, in some instances).
The following is an example of how the reduced order macro model approach can be used to compute the frequency response of a linear comb drive bandpass filter. The frequency response was extracted in as fraction of the time that a full Finite element simulation would take, i.e. a few minutes instead of hours. The full finite element model is shown in the following image:
This can be reduced down to the following Reduced Order Model:
Here's what the reduced order model looks like in the ANSYS GUI:
The system is actuated by applying a voltage (static or time transient) to the ends of the TRANS126 elements. By applying a harmonic voltage and sweeping the frequency a spectrum response for the system is easily constructed.
Reduced order model transfer function over the frequency range 60 kHz to 125 kHz.