Online proceedings - EDA Publishing Association

11-13
May 2011, Aix-en-Provence, France
Fig. 3: Actuation principle
the electrostatics, magnetics, [9; 10], magnetostriction [11],
piezoelectricity [12-14] and thermal actuation. The mesoscaled
dimensions have the required surface-to-air gap ratio
to enable moderate electrostatic pull forces and allow the
use of permanent magnets with sufficient field densities to
compensate for the poor scaling of magnetic forces in
MEMS (scaling L 2 [10], compared to L 4 for pure electromagnetic
actuation, where L is the critical dimension). Both
forces are contact-less and allow in reverse capacitive/inductive
feedback measurements using frequencies
much higher than the resonant frequency of the seismic
mass. An approach of combining electrostatic and magnetic
actuation is reported in [15].
Neglecting fringing field effects, the pull force, F z , of one
extended coil (active area 4.1mm x 5mm, gap 25!m) can be
derived from the expression of the potential energy U stored
in a capacitor with the surface A, the gap d, the total charge
Q, the permittivity " 0 " r and the applied voltage V using
equations (1-2).
U =
∫ Q
0
∫ Q
q
V dq =
0 C dq = 1 Q 2
2 C = 1 2 CV 2 = 1 ɛ 0 ɛ r A
V 2 (1)
2 d
The pull force is obtained from the partial derivative in z.
F z = − ∂U
∂z = ɛ 0ɛ r A V 2
2 d 2
A voltage of 200V would generate a pull force of 5.8mN
(deflection=0) for one coil. The maximum applicable voltage
can be obtained from absolute minimum of the Paschen
curve, which describes the breakdown voltage between two
conductors as function of the product of pressure and electrode
distance [16; 17]. According to [18], the curve minimum
for air yields a breakdown voltage of 315V. Hence, a
maximum voltage of 200V can be considered to be safe for
all deflections.
Considering [19] and neglecting the stator field distortions
from the comparatively small rotor fields, the lateral
forces can be calculated from the flux density of the permanent
magnets in the air gap and the current through the six-
(2)
Fig. 4a: y-z cross-section view of the magnetic flux density (B) generated
by the four permanent magnets (5mm x 1.5mm x 1mm, 1.3 T) using the
simulation software package COMSOL TM . The graphic shows a highly
homogeneous field between the magnet pairs in the areas A and B, where
the windings of the coils are placed.
Fig. 4b: Z-component of the magnetic flux density of four permanent magnets
along the x-y plane, determined by a 3D magnetostatic simulation
using the software package COMSOL TM .
112