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BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates
generally to transducers, and more particularly to the design and construction of transducer
systems designed to provide optimum performance in terms of linearity and sensitivity.
BACKGROUND OF THE INVENTION Many types of transducers have been proposed which
convert various physical effects (acceleration, force, pressure etc.) into the corresponding
movement of the transducer member relative to one or more other fixed members. There is. The
relative position of the transducer movement member is a measure of physical effect. One
common way of determining the position of a motion transducer member is to measure the
electrical capacitance between the transducer member and one or more stationary members.
FIG. 1 is a cross-sectional view of an idealized transducer with a moveable plate positioned
between a pair of stationary plates. Each plate is flat, conductive and equal in area, and other
points are symmetrical. The capacitance between the movable plate and any fixed plate is
inversely proportional to the separation distance. That is, the position of the movable plate can
be determined by measuring the capacitance.
The performance characteristics of such a converter can be represented by its capacitance.
However, practical converter systems include some form of electronic device to convert
capacitance changes into more useful forms of information, such as voltages. The conversion
itself also affects the performance characteristics of this combination.
The total "sensitivity" of the transducer system used in this case means the change in electrical
output caused by the change in physical input. The change in output is linearly related to the
change in input. It is important to ensure that the introduction of a scaling factor such as gain
into the system does not affect the linearity.
The sensitivity of a capacitive transducer system is considered to be the synergy of three
independent factors. That is, FIG. 1 shows the change (displacement) of the position of the
movable member with respect to the change of the physical input. FIG. 2 is a change in
capacitance with respect to a change in position (displacement). FIG. 3 is a change in electrical
output with respect to a change in capacitance.
The first two factors relate to the characteristics of the converter and the third relates to the
characteristics of the electronic device.
It is desirable to increase the sensitivity of the transducer and to minimize the effects of
mechanical and electrical inaccuracies.
This can be done by increasing the displacement of the movable member to a given change of
factor 1 or physical input (e.g. by reducing the internal force which constrains the displacement)
or the change of capacitance to a factor 2 given displacement. It is obtained by increasing (for
example, by reducing the separation distance between the movable member and the fixed plates)
or by both of them. Each of these effects causes the displacement to become a relatively large
part of the separation distance for a given change in physical input. That is, it is desirable to
maximize the quantity (displacement / separation distance).
The effect of each of the three factors can be evaluated by referring again to the ideal converter
of FIG. It is assumed that the displacement of the movable member from the center position, that
is, the zero position is proportional to the physical input (factor 1). The distance (D1-D2) is
proportional to this displacement. The capacitance C1 is inversely proportional to D1 and the
capacitance C2 is inversely proportional to D2 (factor 2), since by definition the capacitance
between two mutually parallel plates is inversely proportional to the separation of these plates. If
the change of the electrical output is proportional to (1 / C1-1 / C2) (factor 3), this change is
proportional to the physical input. That is, the electrical output is zero when the physical input is
zero (no displacement) and increases in direct proportion to the increase of the physical input.
The change in sensitivity, ie the change in electrical output with respect to changes in physical
input, is constant and independent of the value of physical input. That is, the non-linearity is zero.
This sensitivity can be increased by increasing the quantity (displacement / separation) without
introducing non-linearity. In this idealized system, each of the three factors that affect the
linearity of the system is itself linear.
The ideal case of high sensitivity and zero non-linearity can not be obtained with practical
converter systems. There are fundamental limitations that reduce sensitivity and increase
nonlinearity. Furthermore, sensitivity and non-linearity are interrelated, with one improvement
leading to the other.
Each of the above three factors affecting sensitivity and linearity are affected by different
limitations. Each example in this case is described below.
A limitation affecting factor 2 or changes in capacitance to changes in position is introduced by
the unavoidable external capacitance between the movable member and the fixed capacitor plate.
This occurs in the converter itself and in the external connection to the measuring electronics.
The external capacitance is in parallel with the transducer capacitances C1 and C2 to produce an
effective transducer capacitance equal to the sum of these two capacitances. The electronic
device can not react to this effective capacitance and isolate the effects of transducer capacitance
and external capacitance. Since the external capacitance does not change in response to the
position of the movable member, the relationship between the effective transducer capacitance
and position of the movable member and the corresponding physical input is changed.
The effect of external capacitance on overall system sensitivity and linearity depends on the
electronics algorithm used for factor three. Even if the change in electrical output with respect to
the change in capacitance is made proportional to (1 / C1-1 / C2) as the best choice for the
lowest non-linearity, the external capacitance still reduces the sensitivity and increases the nonlinearity. Produce Detection of non-linearity results in increased sensitivity to increasing inputs
as shown in FIG. As the sensitivity is further increased by increasing the quantity (displacement /
separation distance) non-linearity increases.
This effect of the external capacitance becomes increasingly important as the capacitance of the
converter is reduced by miniaturization as the external capacitance increases relative to the
converter capacitance.
The external capacitance functions as part of the transducer capacitance not responding to
physical inputs.
In general, limitations on ideal performance always exist when all parts of the transducer
capacitance do not respond equally to the physical input.
This limitation can affect the change of the position of the movable member (displacement) with
respect to the factor 1, ie the change of the physical input, when the displacement of the whole
area of the movable member is not the same for the change of the physical input. This nonuniform displacement causes the sensitivity to be non-linear, and the non-linear direction also
causes the sensitivity to increase with increasing input.
An example of this limitation is the introduction of a suspension member that mechanically
positions the movable member relative to the fixed member. The displacement of the suspension
member varies from total displacement at the connection to the movable member to no
displacement at the connection to the fixed member. To the extent that the suspension members
are included as part of the sensor's capacitance, the effect is to add non-linearity. The direction of
this non-linearity is the direction in which the sensitivity increases with increasing input.
A more complicated example of this limitation is when the movable member and its suspension
member merge into a clamped diaphragm as shown in FIG. A circular flexible diaphragm is
mounted on its periphery in a fixed structure. Two capacitor plates are positioned relative to the
fixed structure on each side of the diaphragm at an equal distance for each purpose. A pressure
differential is applied across the diaphragm to bend the diaphragm towards one of the fixed
capacitor plates and away from the other plate.
Even though the displacement of each region of the diaphragm is directly proportional to the
pressure input, the entire region of the diaphragm does not produce equal deflection. The curved
diaphragm itself exhibits non-uniform displacement resulting in non-linearity. Since all areas
operate in this manner, it is practically impossible to eliminate the inconvenient area of the
diaphragm from the transducer capacitance. The sensitivity is thus non-linear, and the direction
of this non-linearity is also the direction in which the sensitivity increases with increasing input.
As in the previous example, as the sensitivity is increased by increasing the quantity
(displacement / separation), nonlinearity increases.
Factor 3, a limitation that affects the change in electrical output relative to a change in
capacitance, is introduced by the choice of algorithm that defines the conversion of the
transducer capacitance to an electrical output.
As noted above, making the output proportional to (1 / C1-1 / C2) results in a linear output for
the ideal converter and thus is the best choice. For example, if the output of the ideal transducer
system is made proportional to (C1-C2), the sensitivity becomes very non-linear for significant
displacements and approaches infinity as the movable plate approaches one of the stationary
plates. That is, the choice of the electronic device conversion algorithm has a significant effect on
the non-linearity. As in the previous case, the direction of this non-linearity is such that the
sensitivity increases with increasing input. Also, as in the previous case, the sensitivity is
increased by increasing the quantity (displacement / separation), which increases the nonlinearity.
All these practical limitations of the performance of practical capacitance converter systems
function to reduce sensitivity and increase non-linearity. The direction of non-linearity is always
the direction in which the sensitivity increases with increasing input.
The usual way of reducing this non-linearity is to use relatively low value quantities
(displacement / separation), ie to limit the displacement of the movable member to a small part
of the separation between the members. However, in this case, the sensitivity also decreases.
Since non-linearity approaches zero only when the displacement approaches zero, an acceptable
compromise must be obtained between non-linearity and sensitivity. With decreasing sensitivity,
mechanical stability and accuracy become increasingly critical as displacement for a given input
decreases. Also, the stability and noise of electronic devices becomes increasingly critical as the
signal level for a given physical input is reduced. These problems are all the more critical as the
dimensions of the transducer are reduced.
Primarily, linearity is improved by compensating for non-linearity in factor 3, ie, converting the
change in capacitance to a change in electrical output. However, the linear homogeneous
function of the transducer capacitance, or the ratio of such functions, cancels out the
aforementioned non-linearity without reducing the sensitivity to increasing inputs. In this case,
the use of non-linear functions is forced, which adds cost and complexity. The complexity of the
required circuitry increases significantly with the increasing accuracy of the correction, and this
variant is only practical for medium performance or high cost converters.
U.S. Pat. Nos. 4,542,436 and 4,858,097 illustrate means for reducing the non-linearity of
capacitive sensors. In the specifications of U.S. Pat. Nos. 4,054,833, 4,295,376 and 4,386,312,
the non-linearity inherent in the sensor circuit is generally reduced or occurs within the circuit
itself. A circuit design method for compensating for non-linearity has been proposed.
As is apparent from the foregoing, there is a need for a solution that results in high sensitivity
and low non-linearity without adding additional cost or complexity.
There is also a need for a method of obtaining substantially zero non-linearity over the
performance range of the converter without unduly compromising the degree of sensitivity.
There is also a need for a method that results in substantially zero non-linearity when using nonideal electronic device conversion algorithms.
There is also a need for a method that can increase the quantity (displacement / distance)
without unduly compromising the degree of non-linearity.
In addition, one direction of nonlinearity is introduced into the transducer device manufacturing
to offset the inherent nonlinearities in the opposite direction due to the effects of external
capacitance, uneven displacement and non-ideal electronic device conversion algorithms. We
need a way to do that.
SUMMARY OF THE INVENTION In accordance with the present invention, a method and
corresponding apparatus are described for constructing transducers and cooperating systems
that can make nonlinearity substantially independent of sensitivity.
In practice, the parameters to achieve this can be changed to increase or adjust the sensitivity of
the system as well as to maintain the non-linear control states introduced into the system.
According to the present invention the well-known increase in sensitivity with increasing input
can be eliminated by introducing equally opposite non-linearities so as to offset the conventional
upward curve shown in FIG.
By using the present invention, there is no need to sacrifice sensitivity or use complex electronic
correction to improve the linearity of the transducer system.
Rather, the sensitivity can be increased and the linearity can be reduced or adjusted by changing
the correction parameter that exhibits the property of decreasing sensitivity with increasing
input, as shown by the downward curve in FIG.
FIG. 4 shows the required correction that results in a decrease in sensitivity with increasing
This effect can be adjusted to match the transducer's usually inherent non-linearity sensitivity.
With correct correction, the sensitivity of the system increases substantially with non-linearity
substantially zero. The method of obtaining this result will be described later.
Materials It is well known that stretching the diaphragm material in the preferred embodiment
increases its resistance to stiffness or even further displacement. As the displacement increases,
the rate of increase of the displacement relative to the increase of the applied rate decreases.
Although this non-linearity in the conversion of input to displacement is negligible for small
displacements relative to the thickness of the material, such non-linearity increases rapidly with
increasing displacement with respect to thickness.
In this region of motion of the material, the displacement anywhere in the material is a constant
part of the maximum displacement. That is, the "shape" of the material in the mechanical sense
does not change substantially upon the change of displacement. In the preferred embodiment,
the material at each location of the diaphragm is displaced to some extent proportionally to each
other location.
As the displacement further increases, additional effects are introduced and the "shape" of the
material changes. The advantages of the invention are considered to be less significant in this
operating area of the material.
If the material controlling the displacement of the moveable member of the transducer is
manipulated to introduce such non-linearity in conversion of the input to displacement, the
sensitivity to the input sensitivity is reduced due to the effect on the transducer sensitivity But
this is a totally desirable offsetting effect. Non-linear parameters are included in the suspension
system for the movable member, or this parameter cooperates with all the movable members, for
example as in the case of a clamped diaphragm.
In the preferred embodiment of the present invention, the method of adjusting this displacement
non-linearity to compensate for the normal non-linear performance of the transducer system
includes various choices of diaphragm thickness and clamping diaphragms and fixed capacitor
plates. And the choice between the separation distance between.
The effect of these two parameters is opposite to increasing nonlinearity in the direction of
increasing sensitivity to increasing input by increasing quantity (displacement / separation
distance) and increasing quantity (displacement / diaphragm thickness) It is clear if you know
that you increase the non-linearity in the direction.
The displacement is common to both of these quantities. For a given displacement, in this case
the separation distance and diaphragm thickness control the non-linearity in the opposite
direction, and these two parameters are adjusted to produce zero non-linearity regardless of the
degree of sensitivity can do.
Preferred embodiments of the present invention will now be described in detail with reference to
the attached drawings.
An experimental way of implementing the principles and concepts of the present invention is to
construct multiple transducers with various parameter values and evaluate the results.
Due to the large number of variables involved in the actual converter and the complexity of the
influence, this experimental method is extremely time-consuming and expensive and generally
provides little knowledge that the parameters can be adjusted to obtain the desired result.
A preferred solution produces a mathematical model of the transducer system and quantitatively
determines the effect that can be obtained. The parameters of this model are then adjusted to
obtain the desired performance. In particular, the parameters affecting the non-linear
displacement of the movable member are adjusted to correct the normally non-linear sensitivity
of the transducer system. Several actual transducer structures and tests can be used to confirm
the prediction of the model.
The model must accurately predict the relationship between electrical output and physical input.
The model consists of a set of sub-models, each depicting a specific contribution to the result.
The preferred solution is as follows. A) Define a sub-model to determine the position of the
moveable member of the transducer according to the physical input. B) Define another sub-model
to define the composite capacitance of the transducer according to the position of the movable
member. C) Define yet another sub-model to define the combined electrical output according to
the combined capacitance.
The predetermined model is the synergy of these submodels.
This model is used to predict the performance of the proposed converter structure.
The physical inputs are incremented to find the sensitivity and linearity of the structure, and the
appropriate parameters are adjusted to obtain the desired performance. Particularly suitable
parameters are such that the non-linearity introduced by factors such as extra capacitance and
non-uniform displacement is compensated by the non-linearity introduced by the non-linear
displacement effect of the material controlling the displacement of the movable member To
is given in the case of a pressure transducer having a circular silicon diaphragm nominally
centered between two circular condenser plates having a uniform thickness as shown in FIG. It
will be described below. This case is an extreme example of non-uniform displacement. Those
skilled in the art given this description can easily develop other models for other types of
transducer systems.
The first step A) defines a sub-model that indicates the displacement of the diaphragm according
to the applied pressure. The need to define diaphragm displacement is common to many fields
and many models are being developed. The model used in the present invention is L. E. Andreva
(L. E. L. E., et al.) Translated from Russian by the Israel Program for Scientific Translations,
published in 1966. It is derived from the paper "Elastic Elements of Instruments", authored by
The displacement of the diaphragm is determined by first determining the maximum (central)
displacement of the diaphragm caused by the applied pressure, and then the displacement of
each region of the diaphragm and the like for the same applied pressure.
The maximum (central) displacement Wp is derived from the following equation.
The coefficients a, b and c in this equation are as follows.
And each parameter and the corresponding unit of measurement are as follows.
The pressure / displacement equation described above represents the displacement of the center
of the diaphragm as a function of applied pressure and the diaphragm method.
The displacement of each other area of the diaphragm is defined by representing the
displacement of a series of arbitrarily narrow concentric areas or rings of the diaphragm.
This displacement is part of the central displacement which varies from 1 at the center to zero at
the clamping edge.
That is, the displacement Wr at a certain radius is as follows.
In this equation, SF is a "shape factor" that changes with the radius.
The shape factor is derived from the following equation:
In this equation
"Z" is an experimentally determined coefficient.
For the working area of the material considered in this case, the "shape" does not change
substantially due to changes in displacement.
Therefore "Z" is constant.
A value of about Z = 3 has been found to be appropriate for thin silicon materials.
The shape factor equation described above represents the displacement of each region of the
diaphragm as a relationship of central displacement. That is, the displacement of each region of
the diaphragm is known as a function of applied pressure and diaphragm dimensions.
The second step B) defines a sub-model to define the transducer composite capacitance as a
function of diaphragm displacement as described above.
The general equation for the capacitance between two parallel plates is:
In this equation
In this case, the calculation is carried out by considering the diaphragm as a series of optionally
narrow concentric rings each parallel to the capacitor plate as shown in FIG.
The distance between each ring and the capacitor plate is the above-mentioned displacement
without displacement minus the displacement of the ring.
The total capacitance is the sum of the capacitances for all rings contributing to this capacitance.
This summation is respectively limited at the center by the holes of the capacitor plate with
radius R1 and on the outside by the capacitor plate with radius Ro. すなわち
In this equation
This equation is applicable to both capacitances C1 and C2 for proper use with the algebraic sign
of the displacement.
The extra capacitance in parallel with the transducer capacitance adds these values to obtain the
total effective transducer capacitance.
The third step C) defines the sub-model to define the combined electrical output as a function of
the combined capacitance.
This sub-model is simply an expression of the chosen algorithm that defines the conversion of
capacitance to electrical output.
For example, in the above example of the ideal converter, the submodel is
In this equation
The combination of the submodels represents the desired model of the transducer system.
This model is an example of how to apply to a particular transducer system structure.
Other models of this structure are also possible, and different transducer system structures
require different models.
The model includes the property of producing non-linearity in both directions that balances to
obtain zero non-linearity for the system.
If the displacement is determined by solving the equation that relates the center displacement of
the diaphragm to pressure, the displacement rises to the first power and depends on the pressure
that represents the expected linear relationship, and by the stiffness that increases with the
increase of the input Depends on the pressure rising to higher power, which represents the nonlinear displacement that occurs.
The effect of uneven displacement of the diaphragm is introduced by the "shape factor" equation.
The effect of the extra capacitance is introduced by including in the conversion of the diaphragm
position to the capacitance.
Also, the effect of non-ideal electronic conversion on the output of capacitance is introduced into
the electronics sub-model.
These three factors introduce higher order terms that relate the output to the pressure input.
These terms produce a non-linearity in the opposite direction to that introduced by the nonlinear displacement described above.
It has been found that the non-linearity of the converter system, the extra capacitance and the
non-ideal electronic conversion algorithm caused by the unequal displacements are mainly
caused by the third order term.
The coefficients of these terms can be adjusted to provide near complete cancellation.
That is, non-linearity is eliminated by selection of transducer structural members corresponding
to the terms of each equation that define non-linear displacement in the opposite direction to
that produced by non-uniform displacement, extra capacitance and non-ideal electronic
conversion algorithms. Can.
Depending on the complexity of the model, the preferred solution for the application of the
model allows all transducer system parameters to be input into the model to determine the
electrical output for incremental input pressure and to report the sensitivity and non-linearities
obtained. To create a computer program. This is repeated for a range of parameter values and an
optimum determined for the desired performance.
It contains many parameters. Methods of organizing data in a meaningful way can help to obtain
real results quickly. The preferred solution is to change the two parameters while keeping all
other parameters constant. The two variable parameters are chosen such that they have a strong
influence on the two non-linearities which must finally be balanced and can be changed relatively
easily during the production of the actual transducer.
It is clear from the above pressure / displacement equation that displacement and displacement
non-linearity strongly depend on the thickness, diameter and reverse strain of the diaphragm.
Any and all of these parameters can be adjusted to affect non-linearity. However, in typical
constructions the diameter is relatively limited by factors such as cost and ease of manufacture.
Also, diameter changes are difficult to implement quickly, as many members of the transducer
are affected by diameter changes. The value of reverse strain is also limited by factors such as
assembly technology and material properties.
However, the thickness of the diaphragm is easily adjusted during manufacture and does not
affect other parameters. Also, the non-linearity of the displacement can be controlled relatively
large. Thus, this is the preferred variable to use for adjusting the non-linearity of the
A preferred parameter for controlling the non-linearity caused by the extra capacitance and
uneven displacement is the separation between the non-displaceable diaphragm and the fixed
capacitor plate. Because distance separation and diaphragm thickness are both controlled by the
dimensions of one member of the transducer, diaphragm structure, sensitivity and non-linearity
can be controlled by adjusting the parameters of a single transducer member it can.
The preferred solution is to use diaphragm thickness and separation distance as design variables
to define a range of performance results for a given transducer structure. These results indicate
the value of one of the parameters for a given value of the other parameter to obtain the desired
level of non-linearity and synthetic sensitivity. The sensitivity has been found to increase while
maintaining zero non-linearity. However, the required accuracy of the dimensions obtained is
more exacting and limits the sensitivity obtained in the actual construction.
In the preferred construction of the invention, a clamped silicon diaphragm is made. A silicon
wafer 10 with thinned areas is made and sandwiched between opposing supporting glass
substrates 12, 14 on which the capacitor plates 16, 18 are respectively disposed or formed. FIG.
6 shows such a converter structure. The diaphragm is made of silicon using silicon processing
which allows both the diaphragm thickness and capacitor clearance parameters to be defined
independently in a single set of processing steps. More particularly, the converter structure
shown in FIG. 6 is shown with layers separated from one another for clarity, and comprises a
silicon wafer 10 sandwiched between an upper glass substrate 12 and a lower glass substrate 14.
The silicon wafer 10 is etched on both sides to form a step-shaped recess that separates the gap
22 between the thin silicon diaphragm 24 and the capacitor plates 16 and 18 formed on the
upper and lower glass substrates together with the diaphragm thickness shown as dimension 20.
Do. The semiconductor material itself is mixed with impurities so that it has sufficient
conductivity to form a flexible conductive capacitor plate common to both fixed capacitor plates
16 and 18. Thus, due to the movement of the silicon diaphragm 24, the differential capacitance
between the first capacitance C1 between the silicon diaphragm 24 and the upper capacitor plate
16 and the second capacitance C2 between the silicon diaphragm 24 and the lower capacitor
plate 18 is Generate When pressure is applied to the thin silicon diaphragm plate 24, the
diaphragm 24 flexes one or the other according to the differential pressure back and forth, the
capacitance of one increases and the capacitance of the other decreases. In such a configuration,
the total capacitance C1 + C2 remains substantially constant.
The upper and lower glass support substrates 12 and 14 are Pyrex glass structures that are
covered on both sides by metal deposition to form two conductive biases 26 and 28 that perform
two functions with the capacitor plates 16 and 18 . First, external fluid is applied to the
diaphragm 24 by the biases 26, 28 to create and deflect a differential pressure across it. Second,
the conductive biases 26, 28 form an electrical path from the capacitor plates 16, 18 to the
conductors 30, 32 on opposite sides of the glass substrate. An electrical connection is made to
the silicon material 10 with both leads 30, 32 and changes in capacitance are detected in
response to changes in pressure applied to the transducer. By using large diameter silicon wafers
and corresponding large diameter glass substrates, such multiple transducers are made
simultaneously. The glass and silicon materials are made as shown and then electrically sealed to
one another so that such layers adhere to one another. Such a seal seals the glass support
substrates 13 and 14 circumferentially around the diaphragms 24.
With respect to the processing of the silicon 10, the wafer covers each side of the wafer and
defines a plurality of certified circular areas each having a diameter corresponding to the
diameter of the diaphragm. The wafer is then silicon etched on both sides to etch the silicon
material to a desired depth corresponding to the desired capacitor gap 22. Many etchants are
used to etch the coated silicon. In describing the structure of the glass-silicon glass capacitive
transducer in more detail, reference is made to the above-mentioned U.S. patent application
entitled Sensitive Small Pressure Transducer. The etch mask is then removed and the entire
unmasked silicon wafer is again etched, and then the silicon is evenly removed on both sides of
the wafer until the desired diaphragm thickness is achieved. The silicon material can be removed
in known proportions and the desired diaphragm thickness 20 can be obtained without affecting
the stepped recess dimension 22 by time etching the wafer. In practice a diaphragm thickness 20
of 2 to 3 microns is possible. One skilled in the art, having reference to the prior art, can readily
contemplate other methods of making a diaphragm with suitable diaphragm thickness and offset
It is clear that the capacitor gap 22 is related to the output capacitance of the transducer, as the
output capacitance becomes larger with smaller gaps and also with a considered range of
diaphragm deflection. The reason is that the distance between the fixed capacitor plate and the
diaphragm is smaller and the capacitance is increased. Also, by adjusting the diaphragm
thickness, non-linearity can be introduced into the transducer to the extent that it offsets
inherent non-linearities in opposite directions due to extra capacitance etc. That is, as the
deflection of the diaphragm is increased due to the increase of the input fluid, the diaphragm
material itself causes a pairwise non-linearity with an increased resistance to the deflection.
The reverse radial strain of the silicon diaphragm also affects the deflection, and this parameter
can also be used to linearize its output. Radial back strain of the diaphragm can be generated
while electrically sealing the silicon diaphragm material to the glass support substrates 12, 14.
By appropriately selecting the thermal expansion coefficient of the glass substrates 12 and 14 as
compared to the thermal expansion coefficient of the silicon wafer 10, desired reverse strain can
be introduced into the diaphragm 24. The thermal expansion of the bulky glass substrates 12, 14
is less than that of the thin silicon material 10 at sealing concentration. That is, when the
composite sandwich-like glass-silicon-glass structure is heated to a predetermined sealing
temperature, secured together by electrical sealing, and subsequently cooled, the diaphragm 24
retains reverse strain. This means that the silicon diaphragm 24 shrinks more than the glass
during the cooling process when it is fixed to the glass support substrates 12 and 14 at high
temperature. Depending on the difference in thermal expansion coefficient time and the choice of
the temperature at which the electrical seal occurs, different reverse strains can be produced in
the diaphragm 24.
The output of the capacitive displacement transducer includes a capacitance that changes in
response to a physical input, such as pressure. The capacitance is generally converted to a
corresponding electrical signal to produce an output that can be used in a typical control system.
Many circuits are conceivable for performing electrical conversion on this capacitance. However,
such circuits generally require extremely complex circuits to introduce further non-linearity into
the system or to produce adequate linearity, adding substantial cost to the system. FIG. 7 shows
an electrical circuit adapted to perform electrical conversion of capacitance while being well
adapted for use in the converter of the present invention and maintaining linearity at low or
reasonable cost.
In order to maintain the full linearity of the transducer system, measurement of the displacement
of the movable member must be performed using the reciprocal capacitance difference, ie 1 / C11 / C2. The transducer capacitances C1 and C2 are switched to the input of the differentiator to
produce an output representation of the reciprocal of the capacitance, as will be described in
more detail below. A difference circuit is used to produce the difference in capacitance indication,
but a feedback of the sum of the capacitance reciprocals is sent to a ramp generator which drives
the transducer capacitance. The effect of the extra capacitance is eliminated by the feed current
flowing only through the converter capacitance and the measuring voltage being based solely on
the feed current.
Although direct measurement of the capacitance reciprocal can be easily implemented, circuit
simplification can be achieved by measuring the capacitance itself rather than the reciprocal.
This is apparent by the following relationship.
FIGS. 7 and 8 illustrate circuit diagrams and waveforms of the conversion circuit of the preferred
embodiment of the present invention. The converter capacitances C 1 and C 2 are alternately
switched to the differentiating circuit 40 and alternatively driven by the ramp generator 42.
Deriving circuit 40 produces an output signal having an amplitude proportional to the transducer
capacitance, and demodulation circuit 44 transfers this signal to a ground reference. The
difference circuit 50 derives the sum (C1 + C2). This sum is held by the holding circuit 52. This
sum is held constant by the integration circuit 54, eliminating the need to perform the actual
division. Alternatively, a division method may be used in which the ratio of difference and sum is
generated by a dividing circuit.
The ramp generator 42 is of conventional construction and produces an output having a
triangular waveform 58 with positive and negative voltage gradients alternately at node 56. A
complete measurement cycle consists of two alternating half cycles. The switches 60, 62
actuated by the waveform 64 during the first half cycle are in the position shown. Such a switch
connects plate 16 of transducer capacitance C1 to the output of the ramp generator and plate 18
of capacitance C2 to ground. The differentiating circuit 40 comprises converter capacitances C 1
and C 2, a resistor 66, a capacitor 68 and a differential amplifier 70. The non-inverting input of
amplifier 70 is connected to ground, and feedback through resistor 66 applies the inverting input
to node 72 at the actual ground potential. A common conductor 74 of the transducer connects
the movable member 24 to the connection point 72.
During phase 1 of the first portion of the first half cycle, the output of the ramp generator, i.e.
portion 76 of waveform 58, maintains a constant positive slope. The resulting constant fraction
of the voltage change across C1 induces a constant current through C1 and thus through the
resistor 66 to the output of the amplifier 70. After a short settling time, the output of amplifier
70 at node 78 settles to a negative voltage level representing the value of transducer capacitance
C1, as shown by portion 80 of waveform 82. Frequency compensation of amplifier 70 is required
for large values of resistor 66 or transducer capacitance and is caused by capacitor 68.
The capacitance between the input connection point 72 and the circuit ground consists of stray
capacitances cooperating with the transducer movable member 24, capacitances cooperating
with the circuitry itself, and a transducer capacitance C2 grounded by the switch 62. Because this
junction is in fact at ground potential, the voltage across this capacitance can not change, and
substantially no current can flow through this junction, and the conversion of the ramp signal
current Prevent conversion from the device capacitance C1. Furthermore, the current required to
deliver the extra capacitance to the ground associated with the C1 plate 16 does not affect the
signal current produced by the output of the ramp generator 42 and through the transducer
capacitor C1.
That is, the output with waveform 82 of differentiating circuit 40 is not affected by the extra
capacitance from the converter element to the environment and circuit input capacitance.
During phase 2 of the first half cycle, the slope of the ramp generator output is reversed as
shown in portion 84 of waveform 58.
In this manner, the polarity of the output of the differentiating circuit 40 is reversed as shown in
portion 86 of waveform 82.
Ideally, the level of the portions 80, 86 of the waveform 82, with appropriate clearance for
polarity, is proportional to C1 between both phase 1 and phase 2 of the first half cycle. However,
in practice the input current of the amplifier 70 is not negligible compared to the signal current
generated via C1. This is in fact the case for very small values of transducer capacitance
associated with miniature transducer structures. However, the amplifier input currents flow
through resistor 66 equally between phase 1 and phase 2 and in the same direction. The effect in
this case is to simply add a voltage offset to the derivative circuit output waveform 82. The peakto-peak amplitude of this signal is not affected by this amplifier input current and gives an
accurate indication of C1. An additional advantage of the use of peak-to-peak values is that the
signal level effectively doubles the value obtained by opening phase 1 or phase 2. Further, as a
function of the unequal ramp generator slope, waveform 58 is not important during Phase 1 and
Phase 2 as this effect does not affect peak-to-peak output.
The peak-to-peak output voltage value generated for C1 by the differentiating circuit 40 is
converted to a ground standard value by a demodulation circuit 44 comprising a coupling
capacitor 88, a switch 90 and a differential amplifier 92. During the latter part of phase 1, switch
90 is closed by waveform 94 and capacitor 88 is charged to the negative voltage level of portion
80 of waveform 82. Switch 90 is open for the remainder of the first half cycle. The input to
amplifier 92 during this time period is simply waveform 82 which is reduced by the negative
voltage across capacitor 88. The whole effect is addition. A waveform 96 of this signal appears at
the output of amplifier 92 which functions as a unity gain buffer. During the latter part of phase
1, the level of this signal, part 98, is approximately zero volts. During the latter part of phase 2 of
the first half cycle, the level of this signal, 100, is the peak-to-peak output of the differentiating
circuit 40 and is proportional to the transducer capacitance C1, referred to herein as ground
potential. This level is sampled by difference circuit 46 and summing circuit 50 as shown by
waveform 102.
A comparator (not shown) in switch control circuit 104 completes the first half cycle when ramp
generator output waveform 58 is approximately zero volts. In this case, zero charge is stored in
C1 to prevent circuit transitions when C1 and C2 are switched for the next half cycle.
During the second half cycle, switches 60 and 62 reverse the position shown as shown by
waveform 64 to connect transducer capacitance C2 to the ramp generator output and ground C1.
Repeating this measurement process, during the latter part of phase 2, the level of the part 106
of the waveform 96 is proportional to the transducer capacitance C2. This level is sampled by the
difference circuit 46 and the summing circuit 50 as indicated by the waveform 108. Thus, the
measurement cycle is completed. The output of the system is characterized by the following
That is, this output is the desired ratio of the difference and sum of C1 and C2 multiplied by the
reference voltage. The scaling of the circuit gain and transducer capacitance does not
substantially affect the output. Changes in non-critical parameters, such as the dielectric constant
of the transducer capacitance, change the output of the feedback integrator circuit 54, resulting
in a different ramp slope which returns the output of the system to a pre-existing value. Changes
in non-critical parameters are therefore ignored, i.e. the output of the stem causes the movement
of the transducer member 24 to respond to the parameters in question in the preferred
FIG. 9 shows a diagram of the linear performance of a transducer using the concepts and
principles of the present invention as compared to previously known transducers. The vertical
axis of this diagram shows the% of non-linearity including both positive and negative values. The
horizontal axis of this diagram shows the relative gap dimension between the movable member
or diaphragm 24 and the fixed capacitor plate. The lower curve 120 generally indicates nonlinearity in the case of the known transducer. When stretched, this line becomes asymptotic to
both the horizontal and vertical axes. That is, if the gap is reduced as in the general case, the nonlinearity increases sharply to an unacceptable degree. Also, the linearity improves as the gap
increases. By increasing the gap spacing, the non-linearity is somewhat improved until the
transducer output capacitance is significantly reduced. This is evident because the capacitance is
inversely proportional to the gap spacing, so in the past converter manufacturers try to improve
linearity to the extent that wide gap spacing is acceptable, and then by means of complex and
expensive electronic circuits Improved further.
The upper line 122 in FIG. 9 illustrates the linearity obtained when using diaphragm stiffness as
a non-linear parameter to offset other inherent non-linearities such as extra capacitance. As
shown, these lines pass through zero non-linearity to indicate that optimum linearity is obtained
using the proper choice of transducer structural parameters. While these lines are characteristic
of transducers having a defined diaphragm thickness, a group of such lines, all passing through
zero, can be utilized for transducers having different diaphragm thicknesses. Also, the slopes of
these lines correspond to the output of the transducer system. Thus, a larger output of the
transducer system is obtained and zero non-linearity is obtained, but the constraints on the
tolerance of the capacitor gap are correspondingly limited.
FIG. 10 shows the predicted non-linearity (vertical axis) versus gap dimensions in microns
(horizontal axis) for the indicated diaphragm thickness T. The predicted relative output is
represented numerically to the right of each curve.
For each diaphragm thickness, there is a range of gaps that produce a range of non-linearities
that cross through zero. The desired value of non-linearity can be selected by choosing a gap of
appropriate value. The output amplitude can be increased by choosing a thinner diaphragm and
maintaining the non-linearity at the desired value. In this case, the range of the gap satisfying the
non-linearity requirement is further reduced.
This choice of the parameter to be adjusted and the way in which this result is provided is merely
exemplary. The power gain and non-linearity correction made available by this method can be
implemented in various other ways using different transducer structures.
Furthermore, the operating results of the clamping diaphragm transducer are shown
diagrammatically, in particular using the introduction to the non-linearity caused by the stiffness
of the diaphragm 24. This diagram shows the results of a typical transducer with a diameter of
about 0.250 in and a reverse strain of about 40 microstrain. This transducer is designed for a
pressure input of about 3 inches head. Fig. 6 shows a group of curves in which diaphragms 24 of
different thicknesses cooperate. The output V of the full size converter system is shown
numerically adjacent to each line. Importantly, each line of this group passes through zero nonlinearity, in which case the corresponding capacitance gap and diaphragm thickness values are
within the practical range of use and manufacture of the transducer device. For example, by
constructing a silicon diaphragm thickness of T = 6 microns, a non-linearity of zero at a deviation
or gap of about 12.5 microns is obtained. In particular, the transducer system remains linear
over the entire operating range, not within a certain band. A converter system output of about
2.94V is available for such converter structures. The upper line 124 has a slope that is much
steeper than the other lines and includes a corresponding larger output of 6.11V. Transducers
that produce such output and have zero non-linearity have a transducer diaphragm thickness of
about 3 microns and a gap of about 12.8 microns. It is apparent that thinner diaphragms
produce more deflection for a given pressure resulting in increased output capacitance and thus
higher system output voltage. Each line between the lines described above defines a transducer
having an intermediate diaphragm thickness and producing an intermediate output voltage.
Importantly, the output voltages associated with the lines of the diagram are relative and
irrelevant to the particular type of circuit utilized to convert the capacitance to a voltage output.
As is apparent from this diagram, the output is doubled by halving the thickness of the
diaphragm and zero or minimum non-linearity is obtained. Nothing has changed in the circuit to
get this result. The important technical advantages of the present invention are thus obtained, in
which the linearity and power of the converter system can be influenced without modifying or
changing the electrical converter circuitry. The circuit used to produce the characteristics of the
diagram of FIG. 10 was of the type described above for FIG.
When making some transducer diaphragms from wafers of silicon material, it is often difficult to
obtain uniform dimensional characteristics of the diaphragms over the entire wafer area. For
example, the etch rate varies from batch to batch of silicon wafers and from its central area to its
periphery. Thus all diaphragms do not have exactly the same thickness and do not have the same
offset or capacitive gap. That is, it is practical to allow the transducer to be within the range of
such tolerance, which defines the range of acceptable non-linearity.
The two dashed lines 126 and 128 shown in FIG. 10 indicate the range of acceptable nonlinearity of ± 0.2%. Such ranges are optional and depend on the particular application of the
transducer. For example, at a diaphragm thickness of 6 microns, the gap spacing varies from
about 11 microns to about 15 microns and is in the range of ± 0.2% non-linearity. Thus, a
substantial tolerance of the gap spacing is obtained without sacrificing substantial linearity. Also,
gap clearance tolerances are reduced when higher powers are desired with such relatively thin
diaphragms. Also, as shown in FIG. 10, with a diaphragm thickness of 3 microns, the gap spacing
needs to be maintained at about 12.8 ± 0.03 microns. The same frustration is performed in the
tolerance range of the diaphragm to obtain transducer operation that falls within a particular
non-linearity range.
Many other diagrams and groups of lines showing the operation of transducers with different
diaphragm diameters are derived and other sets of diagrams have different diaphragm reverse
strains. For the first group of curves, the pressure / deflection equation described above can be
used to define various diaphragm deflections based on a given pressure and a given diaphragm
thickness. Different groups of curves can be used using the same iterative method for different
parameter values of diaphragm thickness. Other iterations can be performed by changing the full
scale pressure with the reverse strain. Once the deflection of the diaphragm is found for each
example, the corresponding capacitance range can be calculated using the equations described
above as well. The output voltage using the feedback using circuit can again be derived using the
algorithm described above. Finally, the linearity of the circuit can be ascertained by determining
what the electrical output is under ideal conditions as compared to the actual system constructed
in accordance with the principles and concepts of the present invention.
The attached table as a chart shows the computer printout after several iterations of the
calculations which define the linearity obtained on the basis of the change of the predefined
converter parameters. This data shows a typical transducer in which the full scale deflection of
the diaphragm responds to a pressure corresponding to 3 inches of water. The condenser
diaphragm diameter is 200 mils, but its fluid communication hole is a comatic mill in diameter.
The stray capacitance associated with such a structure is about 1.7 pf. Importantly, unlike the
text display, the Young's modulus value of silicon is 14 for thin diaphragms. This is in contrast to
the reported value of 26.2284 x 106 psi for thick shirin. The displayed results give the output
voltage with feedback (Vowfb) and the% linearity of the system using circuit feedback (Lwfb).
As evident by this illustrated iteration, the diaphragm thickness is held constant at 10 microns
and the gap is increased from 12 microns to 28 microns for three iterations of the diaphragm
inverse strain. The increased strain values increase upward from 60 microstrain to 100
microstrain in 20 microstrain increments. As expected, as the radial microstrain increases, the
deflection decreases. The first two lines of the table show the display results for a transducer
with 60 diaphragms inverse strain and are shown to be invalid data as the deflection is
substantially equal to the gap. Although not shown, the 2 micron deposition of material on the
glass substrate forms a fixed capacitor plate and reduces the number of gap parameters shown
by a corresponding amount. A non-linearity range of ± 0.2% for the same part of this table
creates very strict requirements for the capacitor gap. For example, a gap change of 18 to 19
microns results in a non-linear change of -0.59 to +0.43 or a total non-linearity of 1.02% through
zero. Since this is far outside the 0.2% range, very tight tolerances for the gap parameters have to
be kept. However, if such tolerances can be maintained, a voltage output of 0.584 to 0.539 V can
be obtained. By refraining from such a large voltage output, the restriction on capacitance gap
tolerances is relaxed and the operation can be kept within a defined non-linearity range. By
increasing the reverse strain to 100 microstrain, the non-linearity passes through zero with a gap
tolerance of 19 to 20 microns. The non-linearity range at this operating limit is about 0.2%.
However, although the voltage output decreases, it is still sufficient to output an electrical
indication of the change in input pressure. The output voltage in this example is 0.336 to 0.315
for a full scale diaphragm deflection of about 8.12 microns. Although this example shows how to
vary the inverse strain to obtain acceptable nonlinearity and output voltage, perform the same
analysis for other similar calculations of different diaphragm thicknesses while keeping the
inverse strain constant. it can.
As mentioned above, the calculation results are calculated from the above equation, which
provides an easy way to identify the various parameters of the converter to obtain the desired
output. In practice, the calculated numbers are very highly relevant to the actual transducer
system. By actually selecting the various structural parameters of the converter, the total linearity
of the converter system can be corrected even when the feedback of the circuit is not normally
used. Thus, the operation and interaction of the capacitive displacement transducer and the
method of improving its linearity by using the present invention will be apparent to those skilled
in the art.
Although the details of the clamping diaphragm type transducer have been described above, the
principles and concepts of the present invention can be applied to many other types of
transducers that use movable members in response to physical input stimuli. As an example, a
flat diaphragm is used and fixed to a support structure by a suspension member. In response to
the pressure, the flat member itself does not deform and moves due to the deflection or
deformation of the suspension member. Suspension member transducers are made using models
other than those described above, taking into account material stiffness, and introduce nonlinearity in the desired direction and amount to account for other non-linearities caused by
external capacitance etc. cancel.
The foregoing has described a converter system that produces a linear output without abnormal,
complex or high precision circuits. An important technical advantage of the present invention is
that by selecting various structural parameters of the transducer, a more linear output can be
obtained. A more particular technical advantage of the present invention is that inherent
nonlinearities, such as due to external capacitance, can be offset by introducing nonlinearities in
the other direction. A significant technical advantage of the present invention is that the thirdorder non-linearities caused by intrinsic stray capacitances can be offset just as well by
introducing third-order non-linearities in different directions. A cooperating technical advantage
obtained by the present invention is that the overall linearity of the transducer arrangement can
be improved by using the stiffness factor that the movable transducer element can flex. Yet
another technical advantage of the present invention is that, based on the foregoing, various
structural parameters of the transducer can be mechanically selected to produce the ideal result.
Another technical advantage provided by the present invention is the ability to obtain ideal
linearity or at least non-acceptable non-linearity while maximizing transducer output. Yet another
technical advantage of the present invention is that the entire transducer system, including the
electrical circuitry, as well as the sensor itself produces optimum performance.
Related Application The present invention relates to "High-sensitivity small pressure transducer",
U.S. Pat. No. 304,344, Jan. 30, 1989, and U.S. Pat. No. 304,359, Jan. 30, 1989. Application for
continuation of "Precision converter circuit and linearization method" and continuation of prior
United States Patent Application No. 462 448, "Precision Capacitive Transducer", dated January
18, 1990 The respective patent applications, etc. are referred to in the present description.
While the preferred embodiment of the present invention has been described with reference to
particular converter devices and circuit configurations, it will be appreciated that the present
invention is capable of various variations and modifications without departing from the spirit
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