Do you have a model and/or input file demonstrating a procedure to model a hypothetical dual beam MEMS filter such as the one described below?



BACKGROUND/SYSTEM DESCRIPTION:

Two fixed-fixed MEMS beams are lightly tethered by a spring. A time varying signal applied to an electrode under the first causes it to oscillate up and down. The spring transmits a mechanical 'signal' from this first beam to second one. When the second one vibrates, it induces an electrical signal in an electrode beneath it because it is maintained at a constant DC potential (the oscillation of the second beam varies the capacitance between it and the electrode, so the constant voltage applied to one of the plates of what is in effect a time varying capacitor generates an output signal).

Since the signal is efficiently passed in this manner only at resonance (beam natural frequency), the device functions as a filter (other frequencies aren't passed).

Both beams have a DC potential (bias voltage) applied to them during operation. This serves to partially pull them down. The resulting prestressed condition alters beam natural frequency. The DC bias is adjustable, so the frequency that the filter passes is adjustable as well ' by design.

A significant aspect of the operation of this device is the fact that the amplitude of the output signal is significantly affected by the electrical load (RLC) that the output electrode under the second beam drives. Circuit coupling is desired to account for this bi-directional coupling in a simulation.



OBJECTIVE:

I want to simulate operation (frequency response) of this device including the effects of all aforementioned features. First and foremost, an xy plot of output voltage versus frequency is desired. ROM144 approach is somewhat preferred due to its ability to account for field fringing, but TRANS126 is entirely acceptable.


Please inspect the attached presentation and review the procedure embodied inthe attached parameterized input files. TRANS126 is used between a section of each of the beams at midspan and the electrodes that reside beneath them. The model runs in about 5 minutes (includes modeling, a static prestress calculation, a prestressed modal analysis, and a prestressed harmonic response `sine sweep` analysis).






POSSIBLE CONCERNS:

It is natural to question the validity of certain aspects of this procedure. Although a critical assessment of this solution procedure is still pending, it appears to work correctly and is believed to be a valid approach. Concerns that user may raise follow.


CONCERN #1: Shouldn't you be applying only the AC voltage (the input signal) on the input electrode in the harmonic response calculation?

RESPONSE TO CONCERN #1: I was pleased (relieved) to discover that it doesn`t matter which way the problem is solved. Supporting evidence is provided in the attached input files:

a. V_input_electrode = V_AC + V_bias & V_input_beam = V_bias (bb10h.inp)
b. V_input_electrode = V_AC & V_input_beam = 0 (bb10i.inp)

This finding lends more credibility to the logic (lame rationalization?) I used to come up with voltage assignment on the output beam and the constraint equation between the output electrode and the node that feeds the `circuit` (single resistor). The validity of using a constraint equation in this manner is not yet fully established. Its use was the only way to get the output electrode to drive the circuit (a simulation requirement) in a harmonic response analysis. If it is later shown to be invalid, the only other recourse will be to use a series of transient analyses (one for each frequency) to determine frequency response (much less computationally efficient).


CONCERN #2: How do we account for the change in the gap due to the DC bias? Does the trans126 do this somehow?

RESPONSE TO CONCERN #2: I tried doing NLGEOM in the static prestress followed by UPCOORD in the subsequent prestressed modal analysis. This procedure is described in section 3.11 in the Structures Guide. I found that the calculated shift in natural frequency was unaffected when compared to what I got using the standard PSTRES,ON procedure without NLGEOM. Despite this, I still wanted to use NLGEOM in the static prestress run as a basis for the prestressed harmonic sweep, but when I tried this I got error trapped (apparently it isn`t allowed). My hope and hunch is that for this particular application, the change in geometry (air gap between beams and electrodes) due to the DC bias is negligible, and the dominant factor responsible for changes in AC response (i.e., the frequency shift and changes in response amplitude) is the prestress. This would justify using what I found to be my only option for the prestressed harmonic response calculation (i.e., one based on a "PSTRES,ON" static run without NLGEOM,ON).





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