handbook of modern sensors

310 8 Velocity and Acceleration
(A)
(B)
Fig. 8.7. Thermal accelerometer: (A) cross section of the heated part; (B) an accelerometer
design (shown without the roof) (adapted from [5])
The temperature at any point in the cantilever beam supporting the seismic mass 3
depends on its distance from the support x and the gaps at the heat sinks. It can be
found from
d 2 T
dx 2 − λ2 T = 0, (8.11)
where
√
K g (M 1 + M 2 )
λ =
, (8.12)
L si DM 1 M 2
where K g and K si are thermal conductivities of gas and silicon, respectively, and D
is the thickness of a cantilever beam. For a boundary conditions, where the heat sink
temperature is zero, a solution of Eq. (8.11) is
P sinh(λx)
T(x)=
WDK si λ cosh(λL) , (8.13)
where W and L is the width and length of the beam, respectively, and P is the thermal
power. To measure that temperature, a temperature sensor can be deposited on the
beam. It can be done by integrating silicone diodes into the beam, 4 or by forming
serially connected thermocouples (a thermopile) on the beam surface. Eventually, the
measured beam temperature in the form of an electrical signal is a measure of acceleration.
The sensitivity of a thermal accelerometer (about 1% of change in the output
signal per g) is somewhat smaller than that of the capacitive or piezoelectric types;
however, it is much less susceptible to such interferences as ambient temperature or
electromagnetic and electrostatic noise.
8.5.2 Heated-Gas Accelerometer
Another interesting accelerometer uses gas as a seismic mass. The heated-gas accelerometer
(HGA) was developed by MEMSIC Corporation (www.memsic.com). It
is fabricated on a micromachined CMOS chip and is a complete biaxial motion measurement
system. The principle of operation of the device is based on heat transfer by
3 Here, we assume steady-state conditions and neglect radiative and convective heat transfers.
4 See Chapter 16 for a description of a Si diode as a temperature sensor.