Nonlinear Dynamics of Resonant Microelectromechanical System (MEMS): A Review
75
c. Sensing devices
Nonlinearity can be useful in many sensing devices. Some examples are given
below:
(i) The pull-in phenomena of electrostatically driven MEMS, which is due to
nonlinear nature of the interacting force, is desirable in MEMS switches for
reducing switching voltage [6].
(ii) Jump phenomena (Bifurcation) in a nonlinear system have been advantageously used in mass sensing. In a linear system, sweeping of excitation
frequency is carried out to detect resonant frequency. Performance of the
sensor depends on the quality factor or damping. Further, the minimum
detectable mass is also limited by noise. The strategy of exploiting bifurcation phenomena has been found giving better results. It has been found to
be applied in different ways.
(a) One way is exciting microresonator at set point A
(shown in Fig. 7a),
close to the critical point, so that an addition of mass will cause a shift
in the resonance frequency and also in the bifurcation frequency. If
the change in bifurcation frequency is large enough, then it will cause
saddle node bifurcation (jump to A) [10]. From the difference between
set point and bifurcation frequency, minimum possible value of mass
detected can be calculated. Such device has been used for switch-type
operation, whether the minimum value of measurand is detected (1) or
not (0).
(b) Another way found in literature is bifurcation tracking through sweeping a parameter [37]. Parametrically excited systems contain stable and
unstable regimes. As shown in Fig. 7b, excitation frequency is swept
towards the separating boundary of these regions. At critical point,
amplitude of oscillations goes up. On mass detection, boundary will
shift towards lower frequency and finding the shift, amount of mass
detected can be calculated. Noise will be a dominating factor for uncertainty in sensing. Rate of frequency sweeping is an important factor
for getting results with maximum precision [38]. If the rate is too fast,
then bifurcation will happen after critical point, and, if it is too low,
then noise activated jump can occur. Even influenced by noise, sensor
based on bifurcation tracking has been found giving better results than
resonant sensing.
(c) For continuous sensing, resonator has to be reset at low amplitudes,
and again sensing can be carried out, which can be time-consuming.
One technique was found very useful, which works on the phenomena
of noise squeezing [39]. While approaching critical point, just before
bifurcation, phase noise gets squeezed to a very small value. Considering
it as sign of bifurcation gas sensing has been done with faster rate.
(iii) Nonlinear parametric resonance with broad driving range is useful in
increasing the sensitivity of MEMS gyrosensor [40]. In a study, it has been
demonstrated that by adjusting the electromagnetic and mechanical nonlin-
75
c. Sensing devices
Nonlinearity can be useful in many sensing devices. Some examples are given
below:
(i) The pull-in phenomena of electrostatically driven MEMS, which is due to
nonlinear nature of the interacting force, is desirable in MEMS switches for
reducing switching voltage [6].
(ii) Jump phenomena (Bifurcation) in a nonlinear system have been advantageously used in mass sensing. In a linear system, sweeping of excitation
frequency is carried out to detect resonant frequency. Performance of the
sensor depends on the quality factor or damping. Further, the minimum
detectable mass is also limited by noise. The strategy of exploiting bifurcation phenomena has been found giving better results. It has been found to
be applied in different ways.
(a) One way is exciting microresonator at set point A
(shown in Fig. 7a),
close to the critical point, so that an addition of mass will cause a shift
in the resonance frequency and also in the bifurcation frequency. If
the change in bifurcation frequency is large enough, then it will cause
saddle node bifurcation (jump to A) [10]. From the difference between
set point and bifurcation frequency, minimum possible value of mass
detected can be calculated. Such device has been used for switch-type
operation, whether the minimum value of measurand is detected (1) or
not (0).
(b) Another way found in literature is bifurcation tracking through sweeping a parameter [37]. Parametrically excited systems contain stable and
unstable regimes. As shown in Fig. 7b, excitation frequency is swept
towards the separating boundary of these regions. At critical point,
amplitude of oscillations goes up. On mass detection, boundary will
shift towards lower frequency and finding the shift, amount of mass
detected can be calculated. Noise will be a dominating factor for uncertainty in sensing. Rate of frequency sweeping is an important factor
for getting results with maximum precision [38]. If the rate is too fast,
then bifurcation will happen after critical point, and, if it is too low,
then noise activated jump can occur. Even influenced by noise, sensor
based on bifurcation tracking has been found giving better results than
resonant sensing.
(c) For continuous sensing, resonator has to be reset at low amplitudes,
and again sensing can be carried out, which can be time-consuming.
One technique was found very useful, which works on the phenomena
of noise squeezing [39]. While approaching critical point, just before
bifurcation, phase noise gets squeezed to a very small value. Considering
it as sign of bifurcation gas sensing has been done with faster rate.
(iii) Nonlinear parametric resonance with broad driving range is useful in
increasing the sensitivity of MEMS gyrosensor [40]. In a study, it has been
demonstrated that by adjusting the electromagnetic and mechanical nonlin-