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Analog Front End
V s
N 1
0V
C 1
V out
0V
N 2
C 2
-V s
Figure 10-3. Dividers N 1 and N 2
When N 1 and N 2 switch from zero volts to V s and -V s , respectively, V out is determined by the capacitor
ratios as follows:
V out = -V s + [ 2 V s C 1 / (C 1 + C 2 ) ]
V out = [ - (C 1 + C 2 ) V s + 2 V s C 1 ] / (C 1 + C 2 )
V out = [ - V s C 2 + V s C 1 ] / (C 1 + C 2 )
V out = V s (C 1 - C 2 ) / (C 1 + C 2 )
Eqn. 10-1
Eqn. 10-2
Eqn. 10-3
Eqn. 10-4
Capacitance theory
This can be converted an expression of V out as a function of displacement by considering capacitance
theory. If C 1 + C 2 is modelled as standard, parallel-plate capacitors and ignore fringing capacitance, we
begin by noting:
K=NA ?
C 1 = K / (d + x)
C 2 = K / (d - x)
C 0 = K / d
Where:
? N = The number of beams in the g-cell (unitless)
? A = The area of the facing side of the beam in meters 2
Eqn. 10-5
Eqn. 10-6
Eqn. 10-7
Eqn. 10-8
?
?? = The dielectric constant in farads per meter (1 farad = 1 coulomb per volt)
? K = A constant used to simplify the equations
? d = The nominal distance between the beams in meters
? x = The beam displacement in meters
? C 1 and C 2 = Measured capacitances
? C 0 = Nominal value of C 1 and C 2
V out = V s (C 1 - C 2 ) / (C 1 + C 2 )
MMA955xL Intelligent, Motion-Sensing Platform Hardware Reference Manual, Rev. 1.0
Freescale Semiconductor, Inc.
Eqn. 10-9
185
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