Distributed Architecture for Interfacing
Quartz Dual Mode Sensors
Abstract  This paper presents a microprocessorbased distributed system
architecture designed to interconnect piezoelectric resonant sensors to a
measurement and control unit. Previously, a temperature compensated force
sensor was designed and prototyped, featuring thicknessshear dual mode
operation driven by several pairs of electrodes, as seen in published article [1].
The starting idea to design the resonator was to optimize a particular
electrodes shape that could allow dual mode excitation by electrically isolated
electronic oscillators. This approach greatly simplified the electronics,
knowing that dual mode operation with classical electrodes requires elaborate
schematics for signal mixing and filtering to finally discriminate the
vibrating mode frequencies. In our case, since the signals are already
separated, only a minimal attention was paid to design of electronic
oscillators, the rest of the work being devoted to frequency counting and
information processing. The present paper continues the work and focuses on the
electronic schematic necessary for extracting the useful output data from raw
frequency values.
1 INTRODUCTION ON RESONATOR FEATURES
The force sensitive element is a planoconvex
diskshaped thicknessshear resonator manufactured in quartz. The diameter of
the plate is 13.2 mm, the curvature radius of the convex side is 300mm while
the thickness of the plate is 0.7 mm. The quartz crystal had an SCcut
[2]. Electrodes were made by vacuum
deposition of gold over a chrome layer followed by photolithography. Resulted
plates were tested extensively [1] under different force and temperature
conditions. The design of electrodes is not a subject of the paper, although it
should be stressed out that a good concordance was found between analytical
simulation of vibrating amplitude distribution and experimental Xrays
topographies [1,6] performed on the real samples.
One vibrating mode (socalled Cmode) is mainly
sensitive both to a compressional diametral force and to the temperature, while
the other mode (Bmode) is about fifty times more sensitive to the temperature
and almost insensitive to the applied force.
Figure 12 explains the geometry of the resonator
plate while figures 3.a,b,c shows several pictures of the first series of
prototypes.
Figure 1. SCCut in quartz. (XYZ) represents
crystalline system of axis and (X_{1}X_{2}X_{3}) is the
cut coordinates system
Figure 2. SCCut resonator geometry. (X_{1}’X_{2}’X_{3}’)
is the local mode system of axis turned by the angle y_{n} w.r.t. (X_{1}X_{2}X_{3}). The
external force F is applied at y_{a} azimuth angle.
The mark in Figure 3 is made during manufacturing of
plate for orientation purposes and represents the projection of the
crystallographic axis –X over the (X_{1}X_{3}) plane of the
cut. The value of the turning angle is 13^{0}.
Figure 3.a) Plate completely metalized by vacuum
deposition
b) Plate after UV photolithography
c) Resonator with electrical connections under
compressional force setup.
2 TRANSFER EQUATIONS SET
This part discusses electrical equivalent schematic
and motional parameters values necessary to design the electronic oscillators.
Afterwards it presents experimental results from testing the first prototypes
and establishes the method to compute the force and temperature based on the
two resonant frequencies of B and C modes.
2.1
Equivalent electrical schematic
The first series
of samples were tested in a passive PI network, in order to calculate the
equivalent electrical parameters, according to the schematic shown in figure 4.
Quality factors Q of the resonators were found
to be equal with 211037 and 120800 respectively. Motional resistances R_{1}
range around 20…30 kW, inductances L_{1} around 55…90 H, and equivalent
dynamic capacitances C_{1} equal about 0,005 fF as seen in the
table below.
Pairs of
electrodes are named according to paper [1] notation. Static parallel
capacitance Co of the pair P2+P4 intended to work for the Cmode is 3,1 pF and
the value of static capacitance of the Bmode pair P1+P3 is equal to 2,7 pF.
Obs.

fs [Hz]

R1 [ohm]

L1 [H]

C1 [F]

C0 [pF]

Mod (C,3,0,1)
Electr. P2+P4 in antiparallel

7294798

20619

87,1

4,6 E18

3,1

Mod (B,3,0,1)
Electr. P2+P4 in antiparallel

7955660

22523

70,2

6,8 E18

3,1

Mod (C,3,1,0)
Electr. P1+P3 in antiparallel

7291262

38749

58,2

8,2 E18

2,7

Mod (B,3,1,0)
Electr. P1+P3 in antiparallel

7972292

28324

68,3

5,8 E18

2,7

Figure 4.
Electrical equivalent schematic – electrodes pair P2+P4 [1].
Figure 4. Frequency analysis simulation.
Figure 5. Experimental frequency spectrum
The operating frequency for this pair of electrodes
(P2+P4) is marked by a circle in figure 5. The rest of the modes are unwanted
ones and can be further suppressed by the electronic oscillator.
2.2
Frequency to temperature experimental characteristics
Frequencies – temperature curves of the resonators
were investigated under a controlled oven between –15 ^{0}C and +90 ^{0}C.
However, experiments can be performed over a wider temperature range. As known,
mode B offers large temperature sensitivity, with a fairly linear slope. The
Cmode is temperature compensated, exhibiting a cubic frequency to temperature
curve. We fitted the experimental data under different polynomials of various orders, and finally we
came to the conclusion that for the interval –10^{0}C …+80^{0}C
the optimum fit of the B mode is made with by a 2^{nd} order
polynomial, while the Cmode is described by a 3^{rd} order polynomial.
Larger polynomial orders do not improve significantly the correlation
coefficient SD, but only complicate the formulas by adding extra terms
difficult to handle by 8bit microcontroller systems for example.
Figure 6. Frequency – temperature characteristic f_{B} = f (t) of
Bmode.
Mode
(B,3,1,0). Polynomial Regression for CFTM2B:
Y = A + B1*X + B2*X^2
Parameter Value Error

A 7,97756E6 7,137
B1 203,1257 0,48741
B2 0,22721 0,00663

RSquare(COD) SD N P

0,99997 36,17484 81 <0.0001

The curves are expressed by the following equations:
and
,
where t is the temperature and: _{}
Figure 6. Frequency – temperature characteristic f_{C} = f (t) of the
Cmode.
Mode
(B,3,1,0). Polynomial Regression for CFTM2B:
Y = A + B1*X + B2*X^2
Parameter Value Error

A 7,97756E6 7,137
B1 203,1257 0,48741
B2 0,22721 0,00663

RSquare(COD) SD N P

0,99997 36,17484 81 <0.0001

2.3
Force to frequency experimental characteristic
Diametral force sensitivity was previously
investigated [4],[5] and is known to depend of the azimuth angle (figure 1).
For a given direction the forcefrequency dependence is linear up to 95% of the
crushing load.
Figure 8. Linear frequency to force characteristic of
Cmode f_{C} = f (F) at y_{a} = 75
^{0}azymouth angle.
As seen in figure 3.c, we tested the resonant
structure under compressional diametral force by adding calibrated weights on
the mobile superior blade. Nonlinearities of frequency response in figure 8 are
not caused by the sensor, but especially by the bearing frictions.
It has been experimentally investigated the frequency
coefficient of force sensitivity for different force orientations [1]. Finally,
it has been recorded that for an azimuth angley_{a} = 75
^{0} the force sensitivity of the C mode is almost maximum while the
force sensitivity of the B mode is insignificant.
Linear
Fit for FrequencyForce Characteristic:
Y
= A + B * X
Parameter Value Error

A 7294794,04 0,84218
B 14,94751 0,08037

For the azimuth angley_{a} = 75 ^{0}
the experimental sensitivity coefficients of the C and B modes are: _{}
_{}
2.4
Transfer equations of force and temperature and related errors formulae
Finally we get the set of equations relying the
frequencies to nonelectric quantities temperature and force.
_{} (x)
_{}
From equation
(x) we get the temperature value
based on f_{B} frequency
and S_{FB}F factor.
_{}
Ignoring _{} factor the set of
equations become:
_{}
_{}
With the solution:
_{}, and
_{}
Figure 9. Temperature to frequency transfer function
where _{} factor is neglected.
We computed the _{} relative error:
_{}where _{}
Force relative error is then given by formula:
_{}
Figure 10. Temperature absolute error caused by
neglecting _{} factor
3.
Distributed electronic architecture
Main components of the electronic system of
measurement are based on a masterslaves architecture. Precise time base is
obtained from a 20 MHz reference
temperature compensated oscillator (TCXO). This component is critical, since
the accuracy of the system is dependant on the stability of the frequency
reference; two types of connections are possible. In figure 11 the reference
serves all slave microcontroller where three counters are enabled. The
alternative to use two counters is to connect the TCXO to the master
microcontroller which generates precise delay hardware interrupts for all
slaves (figure 12).
Figure 11. Architecture of measurement system where
precise delay interrupts are generated by the master microcontroller connected
to a TCXO.
Figure 12. Architecture of measurement system where
the reference TCXO signal is connected to the bus.
3.1
Slave microcontroller schematic
Slave microcontroller schematic contains the following
components:
·
Two independent
oscillators connected to the multielectrode resonator
·
A microcontroller
with three 16 bit integrated counters (PIC18F1320)
·
A EEPROM memory
designed to store conversion parameters and recorded data
·
A synchronous
serial interface bus to communicate with the master controller (for adjusting
the registers and for delivering the data).
·
An in circuit
debug (ICD2) interface for programming and debugging the microcontroller.
Figure 13. Slave microcontroller schematic connected
to TCXO.
3.1
Master microcontroller schematic and interface
Master microcontroller (18F4550) schematic has the
following features as seen in figure 14:
·
A synchronous
serial interface bus to communicate with the slave controllers.
·
An LCD display
and a keypad port
·
Four signaling
state LEDs
·
Four channels
8bit analogtodigital inputs to
connect to TC1047A temperature sensors, HIH3610 humidity sensor and MPX4115
pressure sensor.
Figure 14. Master microcontroller schematic
The microcontroller is able to handle USB
communication. The computer interface was done by USBHID protocol.
Figure 15. Labview block diagram interface
4 CONCLUSIONS
Frequency output resonators intended for
nonelectrical quantities offer a better noise immunity than classical voltage
output sensors, being suitable for remote or distributed systems, especially on
harsh environments.
Nowadays, since microcontrollers and compilators [8]
are very accessible and powerful, containing for instance integrated counters
and bus interfaces, the design of high precision measurement systems for
resonant sensors is straightforward, as seen in this paper. Further
developments consist to improve the microcontrollerdistributed algorithm and
to realize a performing virtual instrumentation interface under National
Instruments LabView [9].
Acknowledgments
Main author would like to acknowledge the EU project
QxSens  Multichannel measurement and control system based on resonant
piezoelectric crystal sensors (G6RDCT200200648) for allowing research
funding as well as the prolific collaboration with professors Roger Bourquin
and Bernard Dulmet from FEMTOST Department LCEP/ENSMM, Besançon, France.
REFERENCES
[1] Ivan, R. Bourquin, B. Dulmet, Dual mode, multiple electrodes
quartz sensor, Proc. IEEE –
Int. Ultrasonics Symposium (2005)
[2] J. Zelenka, Piezoelectric Resonators and their Applications,
Czechoslovak Academy of Sciences, Prague
(1986)
[3] R. Bourquin, J.J. Boy, B. Dulmet, SCcut resonator with
reduction of Bmode electrical response, Proc. IEEE Int. Frequency Control
Symp. (1997)
[4] R. Bourquin, B.Dulmet, Force Sensitivity
of trapped energy vibrations in a contoured resonator, 41st
Ann.Freq.Cont.Symp. p. 289294 (1987)
[5] B.Dulmet, R.Bourquin, N.Shibanova, Frequencyoutput force
sensor using a multimode doubly rotated quartz sensor, Sensors and
Actuators, A 48, p.109116 (1995)
[6] G. Genestier, Application de la topographie par rayons X a
l’etude des modes de vibration dans un resonateur a onde de volume, These
de doctorat l’Université de FrancheComté (1982)
[7] ***, PIC18F4550 Data Sheet, Microchip Technology Inc.,
(2004)
[8] ***, MikroBasic 2.0 Users Manual, MikroElektronika (2005)
[9] ***, Labview 6 Users Manual, National Instruments, (2002)