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Fig. 1

a Direct measurement, pressure-dependent resistor (3) b Measurement using

a force sensor (1) c Measuring the

dia-phragm deformation/

DMS (2)

d Capacitive measure-ment using the deformation of a diaphragm cell

a

c

b

d

2

4 1

p

p 3

p

p

Pressure measurement

1

æ

Diaphragm-type sensors

The most common method used for pres-sure meapres-surement (also in automotive ap-plications) uses a thin diaphragm as the intermediate stage. The pressure to be mea-sured is first of all applied to one side of this diaphragm so that this bends to a greater or lesser degreee as a function of the pressure.

Within a very wide range, its diameter and thickness can be adapted to the particular pressure range. Low-pressure measuring ranges lead to large diaphragms which can easily deform by as much as 1...0.1 mm.

Higher pressures though demand thicker, low-diameter diaphrams which only deform very slightly by a few µm. In case (capaci-tive) pick-offs for spacing or distance mea-surements are also required, voltage-mea-suring methods dominate in the medium-pressure to high-medium-pressure ranges. Here, practically only DMS techniques are used.

Capacitive pick-off

In contrast to their application in inertia sensors (see acceleration/yaw-rate sensors), capacitive pressure sensors are still only rarely encountered even though they could possibly provide similar advantages (par-ticularly with respect to their accuracy). This is more than likely the result of one impor-tant difference compared to the other sen-sors dealt with above:

Pressure sensors need direct contact with the pressure medium, whose dieelectric characteristics practically always affect the calibration of such capacitive pressure sen-sors. This means that the calibration would then not only be dependent upon the medium in question, but would also be impossible without it (that is, in the "dry"

state). Clear separation of the sensor from the pressure medium has up to now only been achieved at the cost of considerable technical outlay.

DMS¹) pick-off

Table 1 presents a systematic overview of the proven pressure-measurement techniques which to a great extent have already been

used in automotive applications. The list is arranged according to the type of di-aphragm material and the applied DMS technology. Those combinations are marked which will be dealt with in the following as examples (x) or whose manufacture or pur-chase have been considered more closely (fields marked in blue):

With regard to the particular measuring effect’s magnitude and type, the DMS tech-niques listed above have widely varying characteristics. The gauge factor (K)defines the magnitude of the measuring effect of deformation resistors. It gives the relative change in such a resistor’s resistance R re-ferred to the relative change in its length l an (Equation 1):

∆R/R d
/

K= = 1 + 2 · υ +

∆l/l ε

Here, the symbol ε (expansion) is often in-serted for the relationship ∆l/l, and in multi-ples of 10^–6(ppm) as "micron" or "micro strain".

υis the material’s "transversal-contraction factor", and
is its electrical conductivity.

υcharacterises the reduction of cross-sec-tion area of the material upon elongacross-sec-tion.

Pressure sensors Measuring principles 79

Table 1 DMS pick-off and diaphragm material

1

DMS pick-off Diaphragm material Ceramic Metal Silicon

(steel)

Foils ¹) (glued) Thick-film Metal

thin-film X

Silicon

thin-film X

Diffusion

resistances X

1) Unsuitable for large-batch production, x) Present-day examples Under consideration

1) DMS = Strain gauge or strain-gauge resistor

In the ideal case of constant volume, υ = 0.5 (in reality, υ = 0.3...0.4).

Whereas the conductivity term in Equation 1 is of hardly any importance in the case of

metallic resistors, with regard to Si resistors it plays a dominant role.

One refers, incidentally, to a longitudinal gauge factor when the resistor is expanded in the direction of current and to a trans-verse gauge factor when it is expanded cross-wise to the current direction (Fig. 2). Table 2 provides an overview of typical values for the most important gauge factors.

"Creep" (slight mechanical give under the effects of long-term unidirectional loading) is a highly-feared phenomenon which, when it occurs at all, is only encountered on glued foil-DMS. The other DMS techniques all apply non-glued techniques and are not affected by this phenomena.

To be precise, a diaphragm’s deformation depends upon the difference in the pressure applied to its top and bottom sides. This means that there are four different basic pressure-sensor types (Table 3):

Absolute pressure,

Reference pressure,

Barometric pressure, and

Differential pressure.

Transfer to a force sensor

Instead of directly using the force taken up by their diaphram, a number of sensors transfer it to a force sensor whose measuring range can remain constant due to the fact that the purely mechanical diaphragm has already performed the adaptation to the pressure-measuring range. Perfect linkage from measuring diaphragm to force sensor (for instance by a tappet) must be ensured though.

Examples of application

Thick-film pressure sensors,

Micromechanical pressure sensors,

Si combustion-chamber pressure sensors,

Metal-diaphragm high-pressure sensors.and

80 Pressure sensors Measuring principles

Fig. 2

a Longitudinal b Transverse F Force I Current R Resistance l Length w Width ε Elongation K Gauge factor

R

Gauge factor, physical quantities

2

æ

Gauge factors for different materials

2

Material Gauge factors

Longitudinal Transverse

Foil DMS 1.6 ... 2.0 ≈ 0

Thick film 12 ... 15 12 ... 15

Metal thin film 1.4 ... 2.0 –0.5 ... 0 Si thin film 25 ... 40 –25 ... –40 Si monocrystalline 100 ... 150 –100 ... –150

Basic sensor types for pressure measurement

3

Pressure on diaphragm bottom side p_U

Pressure on diaphragm top side p₀

Measuring Ambient Vacuum pressure pressure

Measuring Difference Reference Absolute pressure pressure pressure pressure

Ambient Reference – Barometric

pressure pressure pressure

Vacuum Absolute Barometric – pressure pressure Table 2

Table 3