Surface acoustic wave pressure transducers and accelerometers

Prog. Aerospace Sci. Vol 21, pp. 1-31, 1984

0376-0421/84 $0.00 + .50

Printed in Great Britain. All rights reserved.

Copyright © 1984 Pergamon Press Ltd.

SURFACE ACOUSTIC WAVE PRESSURE TRANSDUCERS AND ACCELEROMETERS S. I. R o k h l i n , * L. K o r n b l i t * and G. G o r o d e t s k y * *

*Materials Engineering Department, and **Physics Department, Ben-Gurion University of the Negev, Beer Sheva, P.O. Box 653, Israel

ABSTRACT

This study analyzes a new class of force sensors (accelerometers and pressure sensors), based on miniature surface acoustic wave (SAW) resonators. The expected performance of SAW accelerometers and pressure transducers is estimated and compared with published data. It is shown that an ideal SAW accelerometer has a performance comparable with high-quality force-balanced servo aecelerometers. However, the attainment of the required dynamic range and resolution may hinder the design of a prototype. The performance of the best laboratory SAW pressure sensors is already comparable in precision with the digital-pressure transducers employing an intricately-shaped quartz resonator.

CONTENTS

1.

INTRODUCTION

2.

THE MEASURING CONCEPT 2.1.

3.

4.

The effect of strain on sound wave propagation

2.2.

Excitation of SAW

2.3.

Delay-line-SAW oscillator

2.4.

A SAW resonator-based oscillator

2.5.

Points of importance for a sensor performance

TEMPERATURE STABILITY OF SAW OSCILLATORS

8

3.1.

Short term stability

9

3.2.

Medium term stability

10

3.3.

Long term stability

12

DYNAMIC RANGE AND SENSITIVITY OF AN IDEAL SAW SENSOR

12

4.1.

Evaluation of the maximum strain

13

4.2.

Dynamic range and resolution

14

4.3.

Sensitivity to pressure and acceleration

14

JPAS 21~I-A

1

2

5.

S.I. Rokhlin, L. Kornblit and C. Corodetsky

DESICN OF A FORCE SENSOR

16

5.1.

Differential sensor

16

5.2.

Frequency measurements

]6

5.3.

Sensitivity to lateral accelerations

17

5.4.

Effect of deformation and random fabrication errors on the resonator performance

19

Materials and fabrication

19

5.5.

6.

7.

ANALYSIS OF PUBLISHED DATA AND DISCUSSION

20

6. l .

20

Practical SAW pressure sensors

6.2.

SAW accelerometers

27

6.3.

Comparison with an ideal sensor

28

CONCLUSION

29

REFERENCES

30

1.

INTRODUCTION

The extensive use of force sensors, in particular for pressure and acceleration measurement, has resulted in the use of a variety of instruments employing different measuring principles.

However, in the final count, all the methods for measuring pressure

or acceleration reduce to the simple equivalent circuit shown in Figs ]a and lb. respectively.

Modern aviation navigation systems require high-precision pressure transducers and accelerometers for two principal functions: a vertical reference and measurement of vehicle accelerations.

Several forms of accelerometers are used in navigation platforms:

(I) Pendulous accelerometers, extensively used because of their excellent performance.

They

are usually constructed in the form of a force-balance device, i.e. a mass is held in a zero position by a servo feedback loop and the magnitude of the acceleration is determined by the required compensating force (see Fig. 2).

However, they are expensive due to difficulties in

AF=KAU F

I 1 Fig. 1.

SUPPORT (a)

I

SUPPORT (b)

Circuit equivalent of (a) pressure transducer and (b) accelerometer. Here, K is the spring stiffness, M is the mass, ~ is the viscosity, F is the applied force and Au denotes the displacement.

SAW pressure transducers and accelerometers

Fig. 2.

3

An equivalent circuit for a force-balance pendulous aeeelerometer. Here F denotes the inertial force acting on mass M. K 1 and K 2 are the feedback counterbalance forces.

constructing the electrodynamic or electrostatic transducers which produce the mass-restoring forces.

(2) Pendulous integrating gyroscope accelerometers with unbalanced gyro mass; these

measure the velocity.

(3) Vibrating-string accelerometers.

vibrating wires with a mass in their middle.

These consist of two stretched

The acceleration imparted to the mass along the

axes of the wires increases the tension in one and decreases it in the other. in a corresponding change in the vibration frequency of the wires.

This results

The difference in the

frequency is proportional to the acceleration.

One of the best digital pressure transducers used in navigation systems has been developed by the Kearfott Division of the Singer Company.

The transducer consists of a high-

Q quartz resonator which responds to an applied force by shifting its resonance frequency. This instrument was initially developed as a digital accelerometer for Singer Inertial Navigation Systems, and is presently produced by Paroscientific Inc. in a modernized form of digital pressure transducer.

It has a shortcoming in that a quartz resonator of a highly

intricate shape must be fabricated.

This is needed to provide mechanical isolation of the

vibrating quartz rod from its mounting.

The present paper provides a study of the potential use of surface acoustic wave (SAW) oscillators for precise measurements of pressure and acceleration.

The application of

mechanical forces to a piezoelectric substrate on which a surface-wave resonator is fabricated results in a shift of the natural frequency of the resonator, and consequently the operating frequency of the oscillator.

The oscillator frequency is therefore proportional

to the magnitude of the force (or acceleration or pressure) acting on the sensor.

It is

possible to localize the SAW resonator on a relatively small area of the piezoelectric crystal.

The main advantage of SAW devices is simplicity, low cost and high sensitivity.

One might regard them as the next generation of digital pressure transducers and accelerometers.

The following assumptions provide the framework used in describing the performance of SAW sensors:

The shift in the resonance frequency of the resonator is linearly proportional

to the externally applied pressure, or acceleration.

The magnitude of the strain in the

sensing element (piezoelectric crystal) is a function of both the applied force, and the crystal design, e.g. its geometry and the mounting.

On the other hand, the relation between

the strain in the crystal and the resonance frequency shift depends

only

on the material.

Hence, the upper limit of the dynamic range is determined by the mechanical strength of the crystal, whereas the lower limit of the dynamic range and the resolution are determined by the thermal stability of the device.

In the case of an ideal sensor, the effect of

4

S.I. Rokhlin,

hysteresis

and temperature-induced

Our analysis

L.

Kornblit and G. Gorodetsky

stresses caused by the sensor mounting will be neglected.

of a real device is based essentially

available data for the different then obtains

instruments

the same value of sensitivity.

upper limit of the sensitivity

on published

It is believed

THE MEASURING

The operating principle of the sensors

2.1.

and one

that this value represents

the

CONCEPT

is based on the relation between

applied to the SAW substrate and its elastic constants. in turn, changes

It is shown that the

that is achievable by present technology.

2.

oscillator

data.

can be scaled to a common geometry,

the forces

A change in the elastic constants,

the velocity of the surface wave and the resulting

shifts of the

frequency.

The Effect of Strain on Sound Wave Propagation

The velocity V 0 of a bulk elastic wave is given by 2 v 0 = M/~

(j)

where M is the elastic modulus related,

and p is the density.

to a first order approximation, o

by Hooke's

The stress o and strain c are linearly law,

= Mc.

(2)

When higher order terms are included one writes a = Ms + CE

2

+ ... = M e + ...

(3)

v

where

M

= M + Cc.

This means

that the relation between the stress and the strain,

approximation,

can be formally written in the form of Eq.

factor is a linear function of strain.

in the anharmonic

(3), where the new proportionality

In a tensorial notation Eq.

(3) can be written in the

form °ik = Mijkl ~kl + ½Cijklmn Ekl emn and

(4) f

l

M ijkl = Mijkl + ~Cijklmn Here, Cijklmn are third-order materials was calculated

~mn"

elastic constants.

The velocity of SAW in a number of deformed

from their elastic constants,

(1976) and Sinha and Tiersten

(1976).

for quartz are shown in Fig. 3.

The calculated

The disagreement

M' ijkl'

by Nalamwar and Epstein

and the experimental

between

results observed

the calculations

and experiment

is

attributed by Nalamar and Epstein to the inaccuracy of the published data for Cijklmn in quartz.

Figure 4 presents of strain.

experimental

and theoretical values of SAW velocity

The SAW here is propagating

very good agreement

is found

quartz is more sensitive

shift as a function

on fused quartz with a piezoelectric

between theory and experiment.

to stress than the quartz single crystal.

velocity shift is found to be linearly proportional

ZnO overlay.

It should be noted that fused

to the strain.

In all cases the SAW

A

SAW pressure transducers and accelerometers

15£

I

J

.....

IO.O . . . . .

5.0

I

I

Initial

stress

/

..I

t

Combined effect , ~ . / Experiment. / i /

I

~

i

Change in elastic conslonts / Change in density / / /

I 1

--

/f

/f

f

....,..----""

...,..,.'-""

q z

-5.0

\.

klJ £'3 Z

z

-I0.0

\

_1

z_o

-15.0

I-n~

u_

-20.0

-25.0 -

I

I

I

2D

4.0

6.0

"~ "I

8.0

d 10.0

STRAIN IN THE DIRECTION OF PROPAGATION (10 4 )

Fig. 3.

Computed and experimental SAW velocity changes vs strain, for YX-cut quartz. The strain is in the direction of propagation. (Adapted from Nalamwar and Epstein, 1976.)

28.0

I

I

I

i

_._Chancje inelastic constants ,q-

0i

24.0

-_ . . . . Change in density

J ~

_ _ _ Initial stress

20.0 _

o, hi >

_

~

Combinedeffect

F

"

/

•

16.0

z I.s.I LO Z 1-

12D &O-

J,,¢[ ~.) <[ I1: U_

0

2D

4.0

C::K)

8.0

I0.0

STRAIN IN THE DIRECTION OF PROPAGATION (x 104 )

Fig. 4.

Computed and experimental SAW velocity changes vs strain, for Zno/fused quartz. The strain is in the direction of propagation. (Adapted from Nalamwar and Epstein, 1976.)

5

6

2.2.

S.I. Rokhlin, L. Kornblit and G. Gorodetsky

Excitation of SAW

The SAW sensor usually employs a high-frequency

(more than 100 MHz) SAW.

generation and receiving high-frequency SAW have been extensively investigated.

Methods of Interdigital

(I.D.) transducers, deposited on the piezoelectric substrate, are the most con~non for the excitation and reception of these waves, techniques.

They are usually produced by photolithographic

A schematic description of an I.D. transducer is shown in Fig. 5.

When RF

electric voltage is applied to the input I.D. transducer, charges of opposite sign appear on adjoining electrodes, separated by a half wavelength from each other.

This produces

oppositely-phased forces with a half-wavelength spatial period and results in a surface wave, propagating in both directions from the I.D. transducer.

The surface wave produces

elastic stresses of opposite sign beneath adjoining electrodes of the receiving transducer. As a result of the piezoelectric effect, an electric charge appears on these electrodes, and an alternating signal with frequency equal to the frequency of the elastic wave appears at the transducer output.

The SAW sensing elements for both pressure and acceleration can be constructed in different ways, usually either as a SAW oscillator or as a SAW resonator.

The principles of

operation are described briefly below.

2.3.

Delay-line-SAW Oscillator

A block diagram of a SAW oscillator with a delay line in the feedback loop is shown in Fig. 5. 2~n.

Oscillations occur when the total phase shift for the entire circuit is equal to

The angular frequency is given by mL V

--

+

~E = 2 ~ n

(5)

where V is the surface-wave velocity, L is the distance between the transducer centers, CE is the phase shift associated with the transducers and amplifier, and n is the number of the

FILTER

AMPLIFIER

I

I--~ PHASE L~SHIFTER _-h

PIEZOELECTR CRYSTAL

;orber yTERDIGITALTRANSDUCER

4

Fig. 5.

SAW delay line oscillator.

SAW pressure transducers and accelerometers

wavelengths along the acoustic path.

f = ~ (n -

7

From Eq. (5) the oscillator frequency is

).

(6)

In order to eliminate the higher harmonics the dimensions of the delay path and the geometry of the transducers must be carefully designed (Lewis, 1974).

Equation (6) shows

that the change in surface-wave velocity V, associated with elastic stress, results in a shifting of the oscillator frequency Af f

AV v

AL L

(7)

or alternatively, Af T

=

(61

-

I)~

(8)

where 61 is a coefficient that can be found experimentally.

For two-dimensional strains,

for example in the case of a circular diaphragm, Af "~'- = (61 -

(9)

l ) E I + 82E2

where the coefficients 61 and 6 2 have been obtained experimentally by Cullen and Reeder (1975) for ST-cut quartz.

2.4.

A SAW Resonator-Based Oscillator

A SAW resonator consists of interdigital transducers, and reflecting gratings (Fig. 6). The region L between the reflecting gratings is defined as the resonance cavity and within the gratings forms a high quality resonator.

The quality factor Q is affected by the

scattering of the SAW at the reflective array and the transducers and by elastic losses.

To

allow for the penetration of elastic energy into the grating region, an effective cavity length is introduced, where Lef f = L + 2L and L P

(I0)

P

is the penetration depth.

The change in frequency of the strained resonator occurs due to change in cavity length, and change in the SAW velocity.

2.5.

Af=

AV

f

V

Again, as in Eq. (7), we have

ALeff

(11)

Lef f

Points of Importance for Sensor Performance

As already mentioned, the sensing element consists of a SAW quartz resonator or a delay line.

In order to operate as a force transducer, at least one edge of the quartz

plate should be rigidly attached to a support.

When used as an accelerometer, an

additional mass must be attached to the free edge.

8

I. Kornblit and G. (;orodetsky

S.I. Rokhlin,

/ ~Ref[ectors

Cavity

/_

,/,-

/

"_,/

Ref[ectors Z -7~-.~ ~ /I

~

,,,. ~

,,

//

gglZ:5 g// {

Transducer

/

(a)

Recessed aluminum transducer

Etched groove reflectors

Etched groove refl.ectors

(b)

Metat[ic strip reftectors

Metallic strip reflectors

Transducer

(c)

Fig. 6.

(a) SAW resonator with: (b) etched groove reflectors and recessed transducer, and (c) metallic strip reflectors.

The sensor performance (1)

The performance

may be analyzed

in two stages:

of an ideal sensor is determined by the properties

substrate and the resonator

fabricated on it.

shall take into account the temperature

of the quartz

For the estimation of this performance

stability of the SAW oscillator

we

(see Section 3)

and the material properties. (2)

In the analysis of the performance

included,

in particular,

hysteresis,

of a real sensor the mounting effects should be

temperature mismatch of the expansion

(see Section 6) and the effect of residual

3.

A distinction

sources or oscillators:

(I) Short-term stability,

fluctuations.

from several minutes

associated with temperature techniques.

STABILITY OF SAW OSCILLATORS

stability for the frequency

in a time period of the order of I sec.

is controlled by the noise of the electronics

temperature

time intervals

stresses.

is made between three kinds of temperature

This type of stability by short-term

TEMPERATURE

(2) Medium-term

to several hours.

stability,

Usually

drift and can be significantly

(3) Long-term stability,

aging of the sensing element,

coefficients

and the sensor, and also which corresponds

this type of instability

reduced by various

over a period of months and years,

the mounting

system,

etc.

to is

correction

associated with the

SAW pressure transducers and accelerometers

3.1.

9

Short-term Stability

Short-term stability of a sensor defines its threshold and resolution. a very important characteristic of the sensor. resonators and oscillators.

It is therefore

Tables 1 and 2 list data for surface-wave

It is seen that surface-wave resonators have a Q factor which

is an order of magnitude smaller than that of bulk resonators.

However the SAW resonators

have higher Q factors and better short-term stability than SAW delay-line oscillators.

The

reasons for this are: (I)

The noise in delay-line SAW oscillators is associated both with the electronics and

interdigital transducers (Parker, 1979), whereas in SAW resonators it is associated only with the electronics (Penavaire et el., 1980). (2)

The amplification level needed in a resonator is significantly lower than that

required in SAW-delay-line oscillators.

This reduces the noise and simplifies the

requirements put to the amplifier.

Table I.

Comparison of surface-acoustic-wave resonators (SAWRs) and bulk-acoustic-wave resonators (BAWRs)* BAWR Frequency

Parameter Low f (MHz)

One-Port SAWR Frequency

Medium

High

Low

Medium

High

1

10

50

50

500

1000

Q

2 to20xl05

1 to 10xl05

8 t o 20x104

8 to 15x10 g

12 to 20x103

8 to 10xl03

A g i n g (ppm y e a r )

0.01

Maximum P o w e r / dissipation (dBm)

to 5

~10

AfAT for O ° to 55°C (ppm)

1 to 10 -15

-20

3¶

± 5T 1

Size (cm)

+ 15 ~

1

<1

5

1

i

<1

From Cross and Elliot (1981). AT-cut quartz. ¶ST-cut quartz. maximum power dissipation is closely related to long-term stability so this value may have to be reduced to approach the very low aging rates of BAWRs. Table 2.

Short-term stabilities of SAW delay lines, SAW resonators, and conventional bulk crystal resonators (BAWR) used as oscillators*

Device

Time stability T

SAW delay line

=

1

3x10 -I0

SAW resonator SAW delay line

QF 10-13

sec

3xlO -9

Center Frequency

(MHz) 0.12

401

0.24

311

0.06

300 300

SAW resonator

2xlO -I0

0.15-0.30

SAW resonator

5x10 -II

0.77

160

SAW delay llne

5x10 -I0

0.28

1400

BAWR I0 MHz mult to 300 MHz

IxlO -12

*From Colvin (1980).

300

I0

S.I. Rokhlin,

L. Kornblit and G. Gorodetsky

It would seem to be sensible to choose, as the lower limit of the short-term stability, a value of IO-I0.

At a frequency of lO0 MHz this provides a stability of 0.0] Hz.

We

believe that such a stability can be obtained only by attaining a very high level of fabrication

technology.

Stability of the order of 10-9 to lO-8 (i.e. stability of 0.] to I Hz

at lO0 MHz) can, apparently, of SAW-force sensors. Weirauch et al.

be obtained easily.

No published data exist as to the stability

An indirect conclusion can be drawn only from the results of

(]979), where data on the frequency deviation under pressure are presented

(see Section 6.2).

3.2.

Medium-term Stability

Medium-term temperature stability of quartz oscillators can be achieved by using appropriate quartz cuts.

The temperature dependence of the elastic constants of quartz,

for these cuts, is described by a parabola.

If the operating temperature is near the

extremum, known as the turnover temperature,

the frequency shifts due to temperature changes

are minimal,

Figure 7 exhibits the frequency shifts as a function of temperature,

quartz SAW resonators and for AT and BT-cuts of quartz bulk wave resonators. 42°-rotated Y-cut quartz. zero.

for ST-cut

The ST-cut is a

The temperature coefficient at 20°C for these cuts is close to

In most inertial platforms the temperature is stabilized at 60-80°C and the ST-cut

quartz is not suitable.

Figure 8 shows the turnover temperature for a Y-rotated-cut as a

function of the cut rotation angle.

It can be seen that the turnover temperature for a

36°-rotated Y-cut quartz is in the required temperature range. use a new temperature-compensated Tiersten

(1979).

Another possibility is to

SST (super ST) cut, recently proposed by Sinha and

In this cut, the SAW propagates at an angle ~ = 23 ° relative to the X-axis.

Figure 9(a,b) shows the temperature shift of an oscillator frequency at ~ = 23 ° and 22 °. is seen that a cut of 22 ° has almost a zero temperature coefficient at temperatures of 50-90°C.

This cut exhibits lower acoustic losses, and a 23% higher electromechanical

coupling K 2 in comparison with a ST-cut.

However,

at present nothing is known about the

sensitivity of this cut to elastic stresses.

40 E

o. Ld L.9 < "lID >(D Z W (31 I..iJ IT" LL

Y

20 0 -20 -40 -60 -80

ST///B/T

~BT i

I

I

-60 -40 -20

J

0

I

20

J

40

I

60

|

80

I

I00 120

TEMPERATURE (°C) Fig. 7.

Temperature-frequency characteristics of various quartz crystal resonators. AT and BT refer to bulk wave resonators, ST to SAW resonators. (After Lewis, ]974, with the permission of Ultrasonics.)

It

SAW pressure

transducers

and accelerometers

]]

48I 46

44

4z 40-

38L o

36 I.

_.~ 3 4 :

32: 30

I

,

-20

I

,

0

I

,

I

20

,

I

40

,

60

I

80

,

I

I00

,

120

TURNOVER TEMPERATURE (°C) Fig.

8.

Turnover temperature vs crystal cut angle of rotation Y-cut quartz. (Adapted from Dias, 1981.)

E QO..

÷100_

Z

0

0I

-I00

7

-2O0

I,I

0W -300 rr LL -40

for

(Y XI[t] ) 49.2 o/[ 23 o]

(a)

I -20

I 0

I +20

I +40

I +60

I -~BO ",100

T E M P E R A T U R E (°C)

E o.

CL

,100

~

0

~

-I00

_

(YX{It]) 492"/[22°]

(b)

-200 0 w

-30C

I:1:

LL

-40

I

I

I

-20

0

+20

I

,40

I

I

+60

*80

+100

T E M E R A T U R E (°C)

Fig.

9.

Temperature behavior of (a) SST Cut ~=23 °, (b) SST Cut ~=22 °. (After Lukaszek and Bullato, 1980, with permission of IEEE.)

i~!

Rokhlin,

5.[.

3.3.

L. Kornblit

a[~d G. Gorodetsky

Long-term Stability

The aginR of a quartz crystal defects, which are introduced Hence,

it is obvious

by the production

process,

that aging effects are pronounced

can be reduced by special of a quartz oscillator magnitude.

is associated with changes

surface-polishing

increases

It has been shown by Warner

is around 350°C.

surface treatment and therefore devices

(see Table

1).

of SAW oscillators, year.

of bulk quartz resonators

Apparently,

Bulk quartz resonators

the optimal

are less affected by

10.

as bulk resonators,

Montress et al.

is about

data listed in Table

I.

Recently,

12.

I ppm/

(|979) and Gildin et al. shown in Fig.

that the aging is probably due to the mounting of the quartz plates.

aging frequency shift of this device can be seen in Fig.

SAW

(1980) that the aging rate

(]980) observed an aging of 5 ppm/year for a mounted quartz resonator

the Hewlett-Packard

On the

their aging rate is lower than that of the equivalent

mounted under the same conditions

reported on the observation

temperature

the quartz properties.

It was pointed out by Lukazek and Ballato

An example of aging is shown in Fig.

is suggested

etc.

Aging of quartz

the aging rate and can be used to stabilize

(]960) that annealing

other hand, annealing at 500°C causes cracks of the order of ]pm. temperature

polishing,

changes by I to 2 orders of

(at 300°C and a vacuum of ]0-9 torr) for a month stabilizes

heat treatment

stresses and

A raising of the operating

frequency

Vacuum annealing of quartz enhances

resonators.

e.g. cutting,

in surface layers.

methods.

irreversible

in the residual

II.

It

A typical

The above results agree with

Bulst and Willibald

of an aging rate of 0. l ppm/year

(1982) have

in quartz SAW resonators.

This

very low aging was achieved by careful selecting of natural quartz plates and by using deposited A1 reflector strips.

4.

DYNAMIC RANGE AND SENSITIVITY OF AN IDEAL SAW SENSOR

We first consider the permissible strain. threshold

strain before evaluating

The maximum strain determines strain determines

latter characteristics quartz resonators

its lower limit and resolution.

It should be emphasized

are governed by the short term stability.

~AW OSCILLATOR-STCUT DEVICE FREQUENCY-310MHz

LLI LO Z

4

I

2

>-

0

("r"

I

0

I

2

I

I

4

I

I

I

6

MONTHS ]0.

I

8

I

I

I0

l

I

12

I

1

14

I

that the

We shall refer mainly to

as these are the most cormnon.

v

Fig.

the threshold of measurable

the upper limit of the dynamic range, and the

I

16

I

l

I

18

AGING

Long term SAW aging. (After Lukaszek and Ballato, with permission of IEEE.)

]980,

SAW pressure transducers and accelerometers

13

NICKEL TUBING

38°R01 Y-CUTQUA

38°ROTATEI Y-CUTQUART SPACER

SAW-DELA~ TRANSDUCE

Fig. II.

An all-quartz SAW delay line oscillator package. Gilden et al., 1980, with permission of IEEE.)

(After

E

2 W

z

~,

I

>-

65°C

o Z ILl

-I

D

FREQUENCY1393MHz

0

Ill

rr 1.1_

-2 , , , 220

=

I

I

270

i

i

i

I

,

520

i

i

i

I

,

570

,

,

,

I

,

,

,

420

,

470

TIME(deys) Fig. 12.

4.1.

Long term aging of the all-quartz delay line oscillator package, described in Fig. ]]. (After Gilden et al., 1980, with permission of IEEE.)

Evaluation of the Maximum Strain

Data on the machanical properties of quartz are very limited and pertain primarily to static testing.

It is known that at room temperature quartz exhibits brittle fracture.

Baeta and Ashbee (1967) found that plastic strains in quartz start to be observed only at about 500°C.

Bechmann and Parsons (1952) cite a value of o = 5000 N/cm 2 for the safe

maximum loading (one half of the average tensile strength) of quartz.

Using this value and

the value of Young's modulus for ST-quartz, E = 0.87 x 107 N/cm 2, we find, using Eq. (2), that the maximum safe strain is es = 6 x 10-4 . which the quality of machining is not reported.

These data were obtained for quartz for It is known that the strength of quartz is

very sensitive to the quality of surface preparation.

Vig et al.

(1977) have shown that its

14

S.I. Rokh]in,

strength can be significantly

L. Kornblit

and C. Corodetsky

improved by chemical polishing.

loading indicated above with results obtained

for a practical

A comparison of the maximum SAW pressure

sensor is made

as follows: R2 The maximum stress occurring

in a diaphragm can be evaluated

(where P is the applied pressure,

R is the radius of diaphragm,

and the values of the maximum applied pressures,

o=~

P

and h is the thickness)

F

P = ] Atm and 3.5 Atm, are those reported

(]976) and by Weirauch et al.

by Reeder and Cullen

from the expression

(1979), respectively.

Using these

values one finds o

~ 5×I03 N/cm 2 and c ~ 6x]0 -4. These results are found to be in max s agreement with our previous estimates. In the following analysis we shall reduce our requirements

and assume that the maximum allowed strain for quartz is c = lO -4.

we know, no data are available on the mechanical

hysteresis

As far as

of quartz and its fatigue

characteristics.

According

to Peterson

(1982), single crystals of Si have excellent mechanical

and they are most attractive

candidates

for force sensing devices.

Si is 7.0 × ]05 N/cm 2 and its Young's modulus strain for Si according in our laboratory

4.2.

is ].9 × 107 N/cm 2.

properties

The tensile strength of

Therefore,

the maximum safe

to this data is c

prove that c

max

~ 10-z. However, some results obtained recently s is about I0- for both ST-cut quartz and (ll])-Si.

Dynamic Range and Resolution

The threshold

sensitivity

strain which produces

and the resolution of the sensor is determined

a measurable

the short-term stability,

resonance

given in Table 2.

shift vs an applied uniaxial

frequency

shift.

From measurements

strain in ST-cut quartz

by the minimum

This shift is determined by of SAW resonator

(Das et al.,

frequency

1976) and Si (Martin et al.,

1982) one finds that Af

Ac

.

(]2)

f 13) A = I and for quartz, A = 1.4 (Das et al.,

For Si (see Fig.

]976).

It will be shown in

Section 6 that similar values are obtained from analysis of the experimental

data of various

investigators. conservative

As mentioned above in Section 3.], we will use in the following analysis a Af = I0-i0 . From Eq. (12) we therefore conclude value of short term stability, -~-

that the value of the threshold strain is ~I0 -I0.

Using these values for an ideal sensor,

one obtains: A.

dynamic range

B.

threshold

106 (c ~ 10-I0 - 10-4) for quartz.

sensitivity

and frequency resolution

10-2 Hz for a resonance

frequency of

108 Hz.

4.3.

Sensitivity

The crystal

to Pressure

and Acceleration

geometry governs

strains and the applied forces. respect

the relationship

between

If the strain sensitivity

to applied force can be calculated.

the magnitude is known,

and distribution

the sensitivity with

of

SAW pressure

transducers

and accelerometers

15

>L) Z w 0 W C~ it Z w L9 Z -I"~D

-8 -:/-6-5-~, -3 -2-iJm'..ll

2 3 4 5 6 7 8 (xlO"4)

"-4

<~ Z ¢D <~ n+ U_

-8

STRAIN IN THE DIRECTION OF PROPAGATION

Fig.

13.

Variation in resonant frequency vs strain. The strain is in the direction of the SAW propagation. (After Martin et al., 1982.)

We will refer here to a simple cantilever in an accelerometer.

A concentrated

that it may be regarded

application than

transducer

mass will be attached

as simply loaded

and w i d t h b = I cm, thickness

element

(Fig.

h = 0.25 mm.

14).

to the end of the cantilever

The dimensions

Quartz crystal

1976).

For the mean strain,

assumed are:

is anisotropic

of simple b e a m theory assuming an isotropic material

I0% (Nalamar and Epstein,

employed hypothetically

but the

introduces

at X = 0.5L

so

length L

an error less

(see Fig.

14) we

have E =

3 PL

(13)

bh2E w h e r e P is the force and E is Young's modulus. strain e = 10 -10 , we find the threshold

From Eq.

(13) and the value of the threshold

force to be

P = 2 x 10 -5 gram. This force produces resolution.

(14)

a frequency

The sensitivity

shift of

expected

10 -2 Hz and so gives also the value of the force

for the cantilever

shape transducer

S = 500 Hz/gram.

is therefore (15)

Z

Y P, | X

Fig.

14.

A cantilever beam.

~ 2h

16

S.I. Rokhlin,

As will be seen later,

L. Kornblit

and G. Gorodetsky

this value of sensitivity is in satisfactory agreement with

experiments.

From Eq. acceleration,

(14) one immediately sees that a resolution of I ~g (g = 9.81 m/sec 2) in can be obtained with a mass of m = P/a = 20 grams.

106, the upper limit of this sensor is 1 g. to 20 ~g - 20 g.

Since the dynamic range is

A mass of 1 gram will shift the dynamic range

The resolution in this case will then be 20 ~g (when the inertial mass

used is small it will of course be necessary to take account of the distributed mass of the crystal cantilever).

5.

5.1.

DESIGN OF A FORCE SENSOR

Differential Sensor

There is often an advantage in using a differential mode of operation. differential

sensor is shown in Fig.

15(a).

oscillators are mixed and result in a differential

frequency output Af.

are fabricated on both surfaces of the quartz plate. surfaces is opposite,

The delay lines

The sign of flexure stresses on these

hence the change in the difference frequency is twice as large as the

frequency change of each of the oscillators by itself. .5 m~ in thickness,

An example of a

Here, RF signals of the SAW delay-line

Dias

(1981) used a quartz crystal of

and hence a low sensitivity to force was observed

(see Fig.

15(b)).

A differential design allows a reduction in the effect of temperature change, an increase in the sensitivity and a reduction in the effect of lateral acceleration. possible to specify the operating frequencies fl and f2 of the oscillators difference frequency between

5.2.

It is

so that the

(fl-f2) would lie in a frequency range that is easily measured,

e.g.

1 and 100 kHz.

Frequency Measurements

We may arrange that the frequency difference between the two channels at zero force is, say,

I0 kHz.

106 × 0 . 0 1 H z

The previous section then sets the upper limit of the frequency shift, as = I0 kHz (dynamic range × threshold sensitivity).

To measure a frequency of 10 kHz with resolution of about 0.0! Hz one needs to count the overall number of vibration periods during alternative way is precise measurement, oscillation period. clock.

For example,

]00sec.

resolution + 1 H z

An

the I00 MHz SAW resonator can provide a very convenient

According to this technique one must count the number of clock periods (usual

accuracy is + I count) in the measured interval.

example,

This is of course too long.

using a high stable frequency clock of one

with time of counts about

For the frequency

I msec.

10 kHz we have a

With an average period of, for

I sec we have a resolution better than 0 . 0 1 H z °

SAW pressure transducers and accelerometers

First SAW delay line oscillator D

Amp. I

!

_ . . , '

17

T__ens,'°nm

IAf=f,_fz

m

~

-

I Mixer

:-

Second

Amp. 2

SAW delay Line oscilio~or (a)

2 --

o

~

~

~o~°~ '''''~

~

g

~Otor

-2.

0

I

40

I

80 Force (grams)

I

020

160

(b) Fig. 15.

5.3.

(a) Differential arrangement of SAW delay-line based oscillator; (b) frequency shifts as a function of the applied force. (Adapted from Dias, 1981.)

Sensitivity to Lateral Accelerations

The sensor frequency may be affected by lateral acceleration.

In principle the device

is measuring acceleration in the Z d£rection (Fig. ]4). The acousto-elastic sensitivity for ST-cut quartz in the Y direction is approximately four times lower than in the Z direction (see Table 3 and Fig.

16). The magnitude of the strain in this direction decreases in

proportion to (B/h) 2, here about ]600.

(B is the width and h is the thickness of the plate.)

Due to both factors, the sensitivity in the lateral direction is therefore 1.5 × ;0-4 of the sensitivity in the Z direction.

;8

S.]. Rokhlin, L. Kornblit and C. Gorodetsky Table 3.

Sensitivity of ST-cut quartz SAW resonator for different loadings*

Test

Measured Results (Hz/gram)

]. Cantilever axis: x*

-]]2

force in z-direction 2. Cantilever axis: x* force in x-direction

-14.8

3. Cantilever axis: y'* force in z direction

+34.9

4. Cantilever axis: y,t force in y' direction

+0.3

5. Diaphragm uniformly loaded*

+]3.4

*From Staples

et al.

(1979).

#The SAW is propagating along the x-axis of the ST-cut quartz. The test arrangement is described in Fig. 16.

X

y'~

I I

z

Ip

x or y' - ~ axis

///~///

(a) (b) U t

i

/I~/I/I/ I/I/~II (c)

Fig. 16.

Uniform Loading

xory' axis

Measurements of static sensitivity for (a) cantilever bending, (b) tension, and (c) uniformly loaded diaphragm. (Adapted from Staples et al., 1979, see also Table 3.)

SAW pressure transducers and accelerometers

19

An additional reduction in the sensitivity to lateral acceleration can be obtained by using a differential configuration.

Figure 15 shows that when a lateral force is applied,

the strain for both delay lines or resonators is essentially the same, and the shift in the differential frequency from this cause vanishes.

The sensitivity to acceleration in the X direction is significantly higher.

In the

case of a cantilever it is only I0 times smaller than in the Z direction (see Table 3).

A

reduction in sensitivity to acceleration in this direction could be also attained by differential configuration.

5.4.

But, in this case it requires a high precision in fabrication.

Effect of Deformation and Random Fabrication Errors on the Resonator Performance

Errors in fabrication of ID transducers and gratings may affect the sensor quality and reproducibility.

A non-uniform distribution of deformations in the sensor affects the

regularity of the gratings and, therefore, the sensor performance.

A phase mismatch resulting from imperfection of the grating will reduce the Q factor of the resonator. strips.

This is particularly important for arrays with a large number of reflecting

Field and Chen (1981) employed the Monte Carlo method to estimate the effect of

errors in positioning of metal-strip reflectors on LiNbO 3.

Calculations for shorted-strip

reflectors show that the location of the input and output transducers has a decisive effect on the Q values.

Two different configurations were analyzed:

(I) a transmission cavity with

transducers outside the cavity, and (2) intercavity transducers (see Fig. 6).

In the first

case a standard deviation of 2.5% in the array periodicity decreases the Q factor and therefore the frequency stability by only 12% (Field and Chen,

1981).

For intercavity

transducers with the same reflector arrays, the Q factor decreases by almost 50%.

Tansky

(1979) has shown that intercavity recessed type transducers (see Fig. 6) do not affect the resonance properties of the cavity.

It is therefore probable that intercavity recessed

transducers are the best choice for resonator operation.

As for the effect of deformation,

the maximum magnitude allowed in quartz has been taken as 10-4 , and the change in Q associated with this is negligible.

Calculations (Field and Chen,

1976, 1981) show that fabrication errors have little

effect on the insertion losses of a SAW delay line.

We therefore presume that fabrication

errors and deformations do not affect the properties of a sensor with a SAW delay line in the feedback loop.

5.5.

Materials and Fabrication

High-quality quartz crystals and ZnO coated Si are found to be most suitable for the fabrication of SAW force sensors. (I)

This is a consequence of:

The possibility of temperature compensation at the required temperatures, e.g. in the range 70-80°C the 36 ° rotated Y-cut quartz has a turnover temperature.

In the case of

ZnO/SiO2/Si layered medium a proper choice of SiO 2 thickness results in a temperature stability at the required temperature (Martin et a~., 1980). (2)

Favorable aging characteristics of quartz and Si.

(3)

The large volume of information on quartz and Si devices.

20

S.[. Rokhlin,

(4)

Relatively

L. Kornblit

and C. Corodetsky

low cost.

Other materials

such as ZnO/Saphire

a serious investigation

or ZnO/fused

of their properties

It has been pointed out previously

quartz may well also be used.

that resonators with grooved reflectors

higher Q factor than those with evaporated

However,

is required.

strip reflectors.

have a

On the other hand, etched

grooves may reduce the strength of the substrate and as a result the dynamic range of the sensor.

Bulst and Willibald

strip reflectors

(1982) have shown that quartz resonators with evaporated AI

are advantageous

in regard of their aging rate.

It will be shown in Section 6.3 that the threshold of practical determined by the mounting rather than their Q-factor. higher dynamic range,

Therefore,

SAW force sensors is

in the trade off for a

the designer may prefer higher strength and set the Q-factor only as a

second priority.

6.

6.1.

Practical

ANALYSIS OF PUBLISHED

SAW Pressure

Sensors

A variety of SAW force sensors are described Cullen,

1976; Dias et al.,

1979; Cullen et al., Staples et al., shown in Fig.

17.

]976; Das et al.,

1980; Tiersten et al.,

1981). Here,

An interesting

in the published

literature

]976; Staples et al., 1980; Dias,

sensor

(Weirauch et al.,

thickness

transducer exhibits

is that located on the thinner

the best SAW pressure-sensor

~

performance

a frequency

yet known.

1 ~ SENSOR

TOR

17.

Construction

of pressure

et al., 1979.)

operated.

sensor.

reference.

(0.25 m~n thick) plate.

SAW RESONATOR

Fig.

1979) is

Since the thicker plate is virtually not

the frequency of a resonator placed on this plate provides sensing resonator

1981;

are sealed with a

fabricated on the inner surfaces are differentially

The volume between the plates is evacuated.

The pressure

(Reeder and

1979; Weirauch et al.,

1981; Hartemann and Meunier,

design of a pressure

two ST-cut quartz plates of different

frit ring, and the resonators

deformed,

DATA AND DISCUSSION

(Adapted from Weirauch

This

SAW pressure transducers and accelerometers

Cullen and Montress Y-cut quartz diaphragm.

21

(1980) have suggested a somewhat different arrangement, with a In their configuration, one SAW resonator is placed at the center

of the diaphragm, whereas the other is placed near the edge (see Fig. ]8).

Figure ]9 shows

the pressure sensitivity of the sensor as a function of the distance of the resonator from the center towards the edge. towards the edge.

It is seen that the sensitivity changes sign from the center

This fact is being used to increase the sensitivity of a sensor which

operates in a differential mode.

There is a further advantage in this configuration; both

resonators are on the same side of the crystal and can be fabricated simultaneously.

The

short-comings of this configuration are: (]) One resonator is located near the edge where thermal and residual stresses could be significant; compensated.

(2) Y-cut quartz is not temperature

It is difficult to eliminate the effect of temperature solely by a

differential arrangement,

According to the authors a better performance may be obtained

by increasing the resonator frequency to 260 MHz.

At this frequency it is possible to

reduce the size of the second resonator and move it away from the frit seal region. Figures 20 and 2] show the variation in the difference frequency as a function of pressure. The frequency shift observed by Collen and Montress by Weirauch et al.

(]979) is 43 kHz/atm.

(]980) is 35 kHz/atm, and that observed

The sensor nonlinearity is shown in Figs. 22(a) and

22(b), and it is of the order of 0.2 and 0.4%, respectively.

Note that the departure from

linearity is well described by a parabola and, therefore, can be corrected for. nonlinearity is inherent to the bending of a diaphragm.

The

It should be noted that the plate

used by Weirauch et al. is thinner and hence the nonlinearity is greater.

Figure 23 shows data on the frequency fluctuation at low pressure for this sensor. The threshold limit, determined by the rms deviation, is of the order of 0.2 Hz. and 25 show the sensor hysteresis and temperature sensitivity.

Figures 24

The performance with respect

to these parameters is satisfactory.

In Table 4 are listed data for a number of pressure sensors.

To allow proper

comparison we have scaled the sensitivity results to correspond to the disc dimensions and material used by Weirauch et al.

(]979).

These scaled values are shown in column 9.

scaling procedure is briefly described in the footnotes to Table 4. sensitivity is about 50 Hz/mm Hg.

The

It is seen that the

Thus, as expected, the sensitivity of the sensors scaled

to an identical geometry, is determined solely by the sensor material.

Comparison of the experimental data for pressure sensors shows that the performance of the laboratory SAW sensor designed by Welrauch et al.

(]979) (Texas Instruments) is almost

equivalent to that of the pressure sensors of Paroscientific Inc. employing a bulk quartz resonator (see Table 4).

The SAW sensor is somewhat inferior in respect of the temperature

sensitivity to the bulk resonator.

SAW Delay Line United Technologies Research Center

SAW Resonator Reasselaer Polyt. Inst.

SAW Resonator Rockwell International

SAW Resonator Texas

2

3

4

5

SAW Resonator Paroscientific

7

40 KHz

130 MHz

194 MHz I port

62 MHz

77 MHz I port

82 MHz

160 MHz I port

Frequency

2

Quartz

Y-cut Quartz

ST Quartz

ST Quartz

ST Quartz

Y-cut 0=35o84 ' Quartz

ST Quartz

Material

3

4 KHz (; atm)

120 KHz (3.5 atm) 34 KHz/atm

43 KHz (! atm)

-

-

I0 KHz

.

.

40×103

lOxl03

15×I03

25×103

25×103

Q

Af Full Scale

.

5

4

Comparison 6

of various

-

-

I/°C

0.05% F.S.

0.06% F.S.

0.004% F.S.

-

Hysteresis

7

5.2 H z _ _ ~ mm Hg

Hz 46 -m m- Hg

Hz 6 0 rmn - - Hg

Hz 13.4 mm H------~

13 n z _ ~ gram

Hz 18.5 -mm- Hg

Hz 9 mm H-----g

Sensitivity

8

#The sensitivity of the two edge supported beam, measured by Das e~ a~. (1976) results of Table 3 (lines I and 5), to a diaphragm of the required thickness.

0.004% F.S.

+0.005% F.S.

-

of a cantilever,

and then,

was also made

at

24

7

36

30

8

27

9

Ref.

13

using the experimental

A correction

7×10 ~

1.5x10 ~

Dynamic Range

12

of the stress

Resolution

11

Here o is the magnitude

-

0.18% F.S.

0.5% F.S.

0.16% F.S.

0.1% F.S.

Nonlinearity

I0

of Y-cut and ST-cut quartz. to the geometry

sensitivities is scaled

#The data given by C u l l e n a n d Montress (1960) were adjusted to allow the differing for the different positioning of the resonators on the diaphragm surface.

-

Hz *t 45 -m m- Hg

60 n~n H z Hg

Hz * 54 -rmm- Hg

45 n z _ _ ~ rm~ Hg

Recalculated Sensitivity

9

sensors

applicable.

SAW and bulk wave pressure

o = (3/4) P (R2/h), is universally and P is the pressure.

0.005% F.S.

0.13% I/°C F.S. I atm New 260 MHz 0.005% I/°c

F.S.

0.06% ]/°C

.

Temperature Sensitivity

*The diaphragm dimensions were scaled assuming that the relation, the center of the disk; R is the disk radius, h is its thickness

SAW Resonator United Technologies Research Center

6

Instruments

SAW Resonator Hewlett-Packard

1

No. Type of Oscillator

1

Table 4.

©

~t

el"

o ~t

u~

o ~:~

SAW pressure transducers and accelerometers

~' -tB

Area of flitseal

spacer

~

/

passingthrough fritsealarea

/ - - Evacuated

~_. chamber ./I--T .//I -'rIF-I--Au-Sn vacuum

A-A

Cap. . . . .

L

IF-t- ~

At ,.,,~_. I

Spacer ~

Base

~

I/"

i-.

/

F

I

~ I~ I

[IA /

"=\

~.~--Glassfrit seals

B - B / Pressure p o r t L-O.4 / z--Pressure sensitive diaphragm

x

~

solder seal

in.

Cap

~fw,-"~,~ ~J'~,,~- Sensitive ,S#,W. ~ I .~1 Diaphragm s u o s t r a t e ~ B ase

x-

Fig. ]8.

~'",..,~"". | inch

(a) Cross-section view of an all-quartz pressure sensor package, (b) exploded view of the package. (After Cullen and Montress, 1980, with permission of IEEE.)

23

24

S.I. Rokhlin,

L. Kornblit

I0--

.............

0.50 in.dia x 0.015in.thick G O M H z resonator(X = 2 4 ~ m ) 260 k effectivecavitylength

Q.

E

l

Diaphragm

O9

o. e~

and G. Gorodetsky

5~

50ko

)erture

>-

0

Z w o9

~ I

, /'~,

0

x°/°

-5--

w n-" co o9 w nc}_

-15

Fig.

19.

Pressure sensitivity as a function of the distance of the resonator from the center of the diaphragm. (After Cullen and Montress, 1980, with permission of IEEE.)

160 -r-

,./

140

oz

120

o

I00

u_

80

>-

Y-cut quartz

w

w or" w Z w rr w LL LL

6O

- ~ ~ ~ ; ~ / s . T ° r r

40 2C

I 0

I

600

1

I

1200

PRESSURE Fig. 20.

~

1

I

1800

1

I

2400

( Torr )

Pressure sensitivity of an all-quartz SAW pressure sensor. (Adapted from Cullen and Montress, 1980, with permission of IEEE.)

SAW pressure transducers and accelerometers

I

"~ "i- 4 0

ST

I

I

I

I

25

I

f

- ~ T ~

>-

°7

3c

0 w rr t.L UJ

20

w

Z W n~ W ULL

/SEN!ITIVIT¥=57I-Iz/Torr

IG

J DEVIATION f FROM LINEARIT~ 03 °/oFS 1 I I I I I 0~ I

~

200 400 600 800 (Torr)

PRESSURE

Fig. 21.

Pressure sensitivity of a frit bonded quartz sensor (see Fig. ]7). (After Weirauch et al., 1979.)

OA

>-

•

(a)

DATA POINTS --FIT PARAB

or

0.2

W Z __/

Y- CUT

QUARTZ

TEMP.56°C /~o..

0

cr Ix. t

Z

-0.2

Q >

-0.4

W

0

I

I

600

I

I

1200

I

I

i

2800

I

2400

PRESSURE (Torr) ,...,..

~

O Lg n-h~

i

~

I

I

i

0.81-

ST- CUT QUARTZ

0.4~-. " ~

" DATA POINTS --BEST FIT I~RAB.

0

200

b

>_

I

o '"

,,, _.q r--,

-0.4 400

I

I (b)

/~ ./

X.., I 600

I ~00

PRESSURE (Torr) Fig. 22.

Deviation of measured pressure from linearity (a) adapted from Cullen and Montress (1980), and (b) from Weirauch et al. (]979), with permission of IEEE.

26

S.I. Rokhlin, L. Kornblit and (]. Gorodetsky

5

I >(..P Z LLI

I -RMS

I

r

I

I

I

i

I

'

DEVIATION OI2HZ

4 - MAX DEVIATION 0.5Hz

3

-

e/O •

--

2I -~4"-/;f*l -ll

0

n

I

, i

_

(:3 LLJ rY LL LLI CP Z LLI 13! LIJ LL

I ~

Oi

• O0

0.02

I

0.04

I

J

0.06

I

I

0.08

I

I

0 . 1 0 0.12

PRESSURE (Torr) Fig. 23.

Response of pressure sensor to small pressure changes at 6]8 Torr. (After Weirauch et al., ]979, with permission of IEEE.)

o9 Ii I I

Z

'

_o

ls'Tdd

'

I i

I

443 TORR

'

I I 1

178 TORR

0008

> b3

0.004

>(..) -0004 Z D.J

,.,...-,

0

-0008

0 w oi Lc

I 0

I I I I I I 12 0 4 8

I

I

I 8

L

4

I 0

1 I 4

I 8

TIME(rain) Fig. 24.

Deviation from setpoint with decreasing and increasing pressure. (After Wierauch et al., ]979, with permission of IEEE.)

_1 #r

T

b z

I-- 0 0 4 _ _ uJ =

_

..

;

_

(D

D E O' UJ m 0 LI_

Fig. 25.

:

-O.08J

I I I I ; I I i I i I I I I I i I I I i I

-50

0

50

I00

150

TEMPERATURE (°C)

Pressure sensor thermal sensitivity. ]979, with permission of IEEE).

(After Weirauch et al.,

SAW pressure transducers and accelerometers

6.2.

27

SAW Accelerometers

A number of papers describing prototype SAW accelerometers have been published recently. Figure 26 shows the basic configuration of the first laboratory accelerometer Meunier,

(Hartmann and

1981) in which an inertial mass is clamped between two parallel quartz diaphragms.

Two delay-line-oscillators differential mode. and Montress

(1980).

are fabricated on the upper diaphragm and operated in a

The location of these delay lines is similar to that examined by Cullen This transducer shows a high deviation from linearity (2 × 10-3 of

full scale) and hysteresis of ]0-3 g, in our opinion, inherent to the design.

A possible

source of trouble is the dry-friction contact between the inertial mass and the diaphragms, which usually involves nonlinearity and hysteresis.

Figure 27 shows a different design of an acceleration sensor (Staples et aZo,

]98]).

Here, the two resonators L I and L 2 are located in regions A and B and coupled through a semitransparent grating R 2.

When a force is applied, the quartz deforms only in region B.

Hence the frequency of the first resonator (region A) is constant, whereas that of the second changes with the load.

This results in a change in the interference conditions and

the oscillation amplitude.

The experimental data on SAW accelerometers is very limited and therefore their performance could be evaluated only by inference from that of SAW pressure sensors.

Since

both SAW accelerometers and SAW pre3sule sensors are, in principle, SAW force sensors (operating as a form of strain gauge), data for pressure sensors are applicable to the analysis of SAW accelerometers.

The possible performance of a SAW aceelerometer based in

Section 4 and the observed performance of pressure sensors are given in Table 5.

Table 5.

Possible performance of practical SAW accelerometers

I.

dynamic range *(a)

10 5

2.

resolution and (a) threshold

10-S of F.S.

3.

lateral sensitivity (b)

less than 0.001 g/g referred to the true sensitive axis

4.

nonlinearity (a),(c)

probably similar to that of pressure SAW device < 0.5% F.S.

5.

hysteresis (a)

< 0.05% F.S.

6.

temperature coefficient (d) 60Oc - 80Oc

< 0.06% F.S./°C

*The dynamic range of the accelerometer could be extended by using two sensing elements in a single packaged device. (a)evaluated from the data on pressure transducers (Table 4). (b)using differential operation mode (see Section 5.3). (C)before any parabolic corrections (see Figs 22,23). (d)ST-cut quartz differential operation mode.

28

S. [. llokhlin, k. Kornblit

and G. Corodetsky

Signaloutput P filter

__~

Suspensiogri n ds~

~'~\\~, /

Quartz

Ring ~ Dowel Inertialmass Fig. 26.

Basic configuration of a SAW accelerometer. and Meunier, 1981, with permission of IEEE.)

(After Hartmann

J S Fig. 27.

6.3.

......

SAW accelerometer with two coupled SAW resonators placed on a cantilever beam. (After Staples et al., 1981, with permission of IEEE.)

Comparison with an Ideal Sensor

We have distinguished case of an ideal sensor, the sensor mounting

previously between an ideal and a practical the effects of hysteresis

are neglected.

and temperature

On the other hand,

based on the results of the various existing laboratory

A comparison "ideal" sensor

of the experimental

force sensor.

induced stresses caused by

the analysis of a real device is sensors.

data above with the calculated performance

(see Section 4) is given in Table 6.

In the

of an

SAW pressure transducers

Table 6.

Performance

of force sensors:

Experimental Sensitivity

S*

experimental

Data

500 Hz/gram

0.2 Hz

Dynamic range

vs ideal

"Ideal" quartz sensor

450 Hz/gram

Frequency threshold and resolution

29

and accelerometers

0.01Hz

105

106

*The sensitivity was calculated for a 0.25 m~ cantilever concentrated force at the free edge.

It is seen that the sensitivities

are about the same, whereas

and dynamic range of possible practical threshold value obtained

the threshold,

devices are an order of magnitude

limits the dynamic range.

resolution here are not limited by the resonator frit sealing).

loaded by a

It is at present unclear

The magnitudes

resolution

poorer.

The high

of threshold and

stability but by the mounting problems

to us to what extent it will be possible

(e.g.

to mitigate

the mounting problems and approach the threshold of an ideal instrument.

7.

CONCLUSIONS

In this study we analyze a new class of high precision pressure accelerometers.

The highlight of these devices

of a miniature,

high quality SAW resonator

We found that the performance hysteresis

is their force sensing element.

"ideal"

SAW force sensor,

in inertial navigation

satisfies

systems,

and threshold of I ~g in an operational

accelerations

in a differential

than the sensitivity

mode of operation

"practical" According

of prototype

The sensitivity

is several orders of magnitude

to lateral smaller

experimental

data they reduce the dynamic

It should he noted that the results

By virtue of its simplicity

The main problem of the

to a minimum.

SAW pressure

the best available BAW digital pressure Inc.

placed on

i.e. a dynamic range of 106-10 ? with

range 0-I g.

device depend upon the specific design.

is to reduce the mounting effects

The performance

for which effects of

the requirements

SAW sensors we include also the effects of hysteresis

to the published

range and the resolution by an order of magnitude. observed for a practical designer

dependence

on the main axis.

In our analysis of and thermal stresses.

It consists

that exhibits a linear frequency-strain

and parasitic stresses are neglected,

precise accelerometers resolution

of an

sensors and

transducers

transducer

are found to be similar to that of

such as that produced by Paroscientific

the SAW pressure sensor should be superior when cost is

taken into account.

ACKNOWLEDGEMENT S

The authors would like to thank the Israel Academy of Science for partial support of this study, and the many colleagues with whom we have had helpful discussions. also like to thank Dr. A. Ballato and Professor mechanical

properties

of quartz.

S. Lang for providing valuable

We are particularly

grateful

to Professor

We would data on the

S. Shtrikman

from

30

S.]. Rokhlin, L. Kornblit and G. Corodetsky

the Weizmann Institute of Science for numerous stimulating and fruitful discussions am~1 to Dr. P.J. Finley from Imperial College of Science and Technology for his helpful comments and suggestions regarding the manuscript.

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