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Claims  |
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What is claimed is:
1. A method of calibrating and linearizing the output of an instrument that
includes a particular transducer having an output that is a non-linear
function of a concentration of a component of interest in a fluid,
comprising:
(a) producing a first equation which is characteristic of the output of a
typical transducer of the type to be used in the instrument as a function
of the concentration of the component of interest,
(b) producing a second equation which gives the concentration of the
component of interest as a function of the output of said typical
transducer,
(c) applying a first fluid having a known non-zero concentration of the
component of interest to the particular transducer to be used in the
instrument and measuring the actual output thereof,
(d) substituting a value corresponding to said known concentration into the
first equation and evaluating the first equation to determine the
estimated output of said typical transducer,
(e) using said actual and estimated outputs to determine the relative
sensitivity of the particular transducer,
(f) applying a second fluid having a known nonzero concentration of the
component of interest to the particular transducer and measuring the
actual output thereof,
(g) correcting the measured output of step (f) for said relative
sensitivity and using the result and the second equation to produce the
linearized concentration value corresponding to the concentration of said
second fluid,
(h) applying a sample fluid having an unknown concentration of the
component of interest to the particular transducer and measuring the
actual output thereof,
(i) correcting the measured output of step (h) for said relative
sensitivity and using the result and the second equation to produce the
linearized concentration value corresponding to the concentration of said
sample fluid, and
(j) referencing the concentration value of step (i) to that of step (g) and
displaying the result as the concentration of the component of interest in
the sample fluid.
2. The method of claim 1 in which step (j) is performed by multiplying the
ratio of said linearized concentration values by the concentration of the
component of interest in the second fluid.
3. The method of claim 1 in which the first and second linearized
concentration values are produced by substituting the corrected measured
outputs produced in steps (g) and (i) into the second equation and then
evaluating that equation.
4. The method of claim 1 in which the first and second linearized
concentration values are produced by utilizing the second equation to
construct a look-up table and then addressing said look-up table with the
corrected measured outputs produced in steps (g) and (i).
5. The method of claim 1 in which said first and second fluids have the
same concentration of the component of interest.
6. The method of claim 1 in which step (e) comprises taking the ratio K of
said estimated output to said measured output.
7. The method of claim 6 in which the correcting steps of steps (g) and (i)
comprise the multiplication of the measured output by ratio K.
8. The method of claim 1 in which at least one of the first and second
equations is produced by:
(i) performing a pluraity of measurements on each of a plurality of
transducers of the type to be used in the instrument,
(ii) selecting an equation of the type that is to be used in representing
the response of a typical one of said transducer, said equation including
at least one term with an unknown coefficient, and
(iii) determining the values of said coefficients which most closely fit
said equation to the results of said plurality of measurements.
9. A method of calibrating and linearizing the output of an instrument that
includes a particular transducer having an output that is a non-linear
function of the concentration of a gas of interest, comprising:
(a) producing a first polynomial equation which is characteristic of the
output of a typical transducer of the type to be used in the measurement
as a function of the concentration of the gas of interest,
(b) producing a second polynomial equation which gives the concentation of
the gas of interest as a function of the output of said typical
transducer,
(c) applying a gas having substantially none of the gas of interest to the
particular transducer to be used in the instrument, measuring the
resulting output thereof, and storing that output for use as a zero
correction value,
(d) applying a first gas having a first known nonzero concentration of the
gas of interest to the particular transducer and measuring the actual
output thereof,
(e) substituting a value corresponding to said first concentration into
said first equation and evaluating the first equation to determine the
estimated output of the typical transducer,
(f) subtracting the zero correction value from the actual output of the
particular transducer to produce a zerocorrected actual output,
(g) using said estimated output and the zerocorrected actual output to
determine the relative sensitivity of the actual transducer,
(h) applying a second gas having a second known non-zero concentration of
the gas of interest to the particular transducer and measuring the actual
output thereof,
(i) correcting the measured output of step (h) for the zero correction
value and said relative sensitivity, and using the result and the second
equation to produce the linearized concentration value corresponding to
said second concentration,
(j) applying a sample gas having an unknown concentration of the gas of
interest to the particular transducer and measuring the actual output
thereof,
(k) correcting the measured output of step (j) for the zero correction
value and said relative sensitivity, and using the result and the second
equation to produce the linearized concentration value corresponding to
said unknown concentration, and
(l) producing an output signal that is indicative of the ratio of said
linearized concentration values and said second concentration.
10. The method of claim 9 in which the first and second linearized
concentration values of steps (i) and (k) are produced by substituting the
zero-corrected measured output values into the second equation and then
evaluating the same.
11. The method of claim 9 in which the linearized concentration values of
steps (i) and (k) are produced with reference to a look-up table
constructed by evaluating the second equation for a plurality of assumed
output values.
12. The method of claim 9 in which the first and second gases are the same
gas.
13. The method of claim 9 in which the second equation is multiplied by a
scaling factor prior to its use in steps (i) and (k), said scaling factor
being a number which assures that the signal processing capacity of the
instrument is not exceeded when the transducer produces its maximum
output.
14. A method of calibrating and linearizing the output of an instrument
that includes a particular transducer having an output V that is a
non-linear function of the magnitude C of a property of interest of a
fluid, comprising:
(a) performing a series of measurements on each of a plurality of
transducers of the type to be used in the instrument,
(b) selecting a first equation V=f.sub.1 (C) of a type that is suitable for
use in representing the response of a typical one of said transducers,
where f.sub.1 is a first function having at least one unknown coefficient,
(c) selecting a second equation C=f.sub.2 (V) of a type that is suitable
for use in representing the inverse response of the typical one of said
transducers, where f.sub.2 is a second function having at least one
unknown coefficient,
(d) determining the values of the unknown coefficients of the first
function to adapt said first equation to represent the response of the
typical transducer,
(e) determining the values of the unknown coefficients of the second
function to adapt said second equation to represent the inverse response
of the typical transducer,
(f) applying to the particular transducer a fluid having substantially a
zero magnitude of the property of interest and measuring the output
V.sub.o thereof,
(g) applying to the particular transducer a first fluid having a first
known magnitude C.sub.s1 of the property of interest and measuring the
actual output V.sub.sa thereof,
(h) substituting C.sub.s1 into the first equation and evaluating the first
equation to determine the estimated output V.sub.se of said particular
transducer,
(i) determining the ratio K of V.sub.se to V.sub.sa -V.sub.o,
(j) applying to the particular transducer a second fluid having a second
known magnitude C.sub.s2 of the property of interest and measuring the
actual output V.sub.c thereof,
(k) using the second equation to determine the value of C.sub.c, which
corresponds to V=K (V.sub.c -V.sub.o),
(l) applying to the particular transducer a fluid having an unknown
magnitude of the property of interest and measuring the actual output
V.sub.u thereof,
(m) using the second equation to determine the value C.sub.u which
corresponds to V=K (V.sub.u -V.sub.o) and
(n) producing as an output a signal indicative of the value C.sub.out,
where C.sub.out =C.sub.u (C.sub.s2 /C.sub.c).
15. The method of claim 14 in which the first fluid is
the same as the second fluid.
16. The method of claim 14 in which values C.sub.c and C.sub.u are
determined with reference to a look-up table constructed by evaluating the
second equation for a plurality of assumed values of V.
17. The method of claim 14 in which values C.sub.c and C.sub.u are
determined by evaluating the second equation for the values V=K (V.sub.c
-V.sub.o) and V=K (V.sub.u -V.sub.o), respectively.
18. The method of claim 14 in which the second equation is multiplied by a
scaling factor K' prior to its use in steps (j) and (l), K' being a number
which assures that the signal processing capacity of the instrument is not
exceeded when the transducer produces its maximum output.
19. A method of calibrating and linearizing the output of an instrument
that includes a particular transducer having an output V that is a
non-linear function of the magnitude C of a property of interest of a
fluid, comprising:
(a) performing a series of measurements on each of a plurality of
transducers of the type to be used in the instrument,
(b) selecting a first equation V=f.sub.1 (C) of a type that is suitable for
use in representing the response of a typical one of said transducers,
where f.sub.1 is a first function having at least one term with an unknown
coefficient,
(c) selecting a second equation C=f.sub.2 (V) of a type that is suitable
for use in representing the inverse response of the typical one of said
transducers, where f.sub.2 is a second function having at least one term
with an unknown coefficient,
(d) determining the values of the unknown coefficients of the first
function to adapt said first equation to represent the response of the
typical transducer,
(e) determining the values of the unknown coefficients of the second
function to adapt said second equation to represent the inverse response
of the typical transducer,
(f) applying a fluid for which C is substantially equal to zero to the
particular transducer and measuring and storing the resulting output
V.sub.o thereof,
(g) applying to the particular transducer a first fluid having a first
known magnitude C.sub.s1 of the property of interest and measuring the
actual output V.sub.sa thereof,
(h) substituting C.sub.s1 into the first equation and evaluating the first
equation to determine the estimated output V.sub.se of said typical
transducer,
(i) determining the ratio K=V.sub.se /(V.sub.sa -V.sub.o),
(j) evaluating the second equation for C.sub.max =f.sub.2 (KV.sub.max)
where V.sub.max is the maximum output of the typical transducer,
(k) determining the ratio
K'=0.95 (V.sub.cap)/C.sub.max
where V.sub.cap is the maximum V value which can be handled by the
instrument,
(l) reformulating the second equation as
C=K'f.sub.2 (K[V-V.sub.o ]),
(m) applying to said particular transducer a second fluid having a second
known magnitude C.sub.s2 of the property of interest and measuring the
output V.sub.c thereof,
(n) using the reformulated second equation to determine the linearized
value C.sub.c which corresponds to V=V.sub.c,
(o) applying to the particular transducer a sample fluid having an unknown
magnitude of the property of interest and measuring the output V.sub.u
thereof,
(p) using the reformulated second equation to determine the value C.sub.u
which corresponds to V=V.sub.u, and
(q) producing as an output a signal indicative of the value C.sub.out where
C.sub.out =C.sub.u (C.sub.s2 /C.sub.c).
20. The method of claim 19 in which said first and second fluids have the
same magnitude of the property of interest.
21. The method of claim 19 in which steps (n) and (p) are performed by
substituting the measured outputs into the reformulated second equation
and then evaluating the same.
22. The method of claim 19 in which steps (n) and (p) are performed by
referencing a look-up table constructed by evaluating the reformulated
second equation for a plurality of assumed values of V. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
The present invention relates to fluid measuring instruments and is
directed more particularly to a method of calibrating and linearizing the
outputs of fluid measuring instruments which utilize transducers that have
nonlinear responses.
In measuring the magnitude of a property of a fluid, such as the
concentration or partial pressure of a component of interest, it is often
necessary to utilize a transducer which has a nonlinear response. In
non-dispersive infrared analyzers, for example, the concentration of a gas
of interest is measured by means of a gas filled cell, commonly known as a
Luft detector, which is illuminated by an infrared source through a sample
cell that contains a gas of unknown composition. In such analyzers, the
output of the Luft detector is an exponential (Beer's Law) function of the
concentration of the gas of interest in the sample cell. Similar nonlinear
responses are, however, exhibited by the transducers used in many other
types of instruments, such as those which measure the temperature of a
gas, the pH of a liquid, etc.
The nonlinearity of the response of many types of transducers creates a
number of problems for the instruments in which they are used. One of
these problems is that the nonlinearity prevents the property of interest
from being determined by simply ratioing the output produced by the
transducer during exposure to a sample fluid to the output produced by
that transducer during exposure to a calibration fluid. This is because
ratioing is a linear process and cannot therefore readily be used with
nonlinear functions. Another of these problems is the loss of resolution
that results from directly displaying the outputs of nonlinear
transducers. Using a nonlinear display, for example, causes the resolution
of the instrument to be greater at one end of the display range than at
the other. Using a nonlinear display also introduces the inconvenience of
having to interpolate between scale divisions of variable spacings.
The above-described problems are often dealt with by making use of
linearization circuits. Analog linearization circuits, for example, make
use of the nonlinear response of an analog circuit to compensate for the
nonlinear response of the transducers with which they are used. Digital
linearizing circuits make use of the mathematical processing ability of
computerized instruments to solve equations which compensate for the
nonlinear response of the detectors with which they are used. Linearizing
circuits of the latter type can also operate by referencing look-up tables
which are constructed from the equations to be solved.
While the above-mentioned types of linearizing circuits can operate with a
moderate degree of accuracy, they can also introduce significant errors
into the displayed outputs of the instruments with which they are used.
These errors result from the fact that particular transducers often have
nonlinear responses which differ from that of the typical transducer for
which the linearizing circuit was designed. Such differences can, for
example, result from differences in the sensitivity (or gain) of various
transducers, or from differences in their zero responses or offsets. Such
differences can also arise in a single transducer as its response changes
with time, the accumulation of dirt deposits, etc. These differences
produce errors by causing linearizing circuits to over- or under-correct
for the response of the particular transducers with which they are used.
SUMMARY OF THE INVENTION
In accordance with the present invention there is provided an improved
method for calibrating and linearizing the outputs of an instrument that
uses nonlinear transducers which is not subject to the above-described
problems and errors.
Generally speaking, the method of the present invention contemplates the
production of two multi-term (preferably polynomial) equations which
define the nonlinear response of a typical transducer of the type to be
used in the instrument, the taking of measurements which determine the
relationship between the response of the particular transducer to be used
in the instrument and that of the typical transducer, and the utilization
of the determined relationship and the equations to calibrate and
linearize the output of the instrument. The use of this method assures the
availability, at each calibration, of a linearizing function which
accurately reflects the response of the particular transducer in its then
current condition. The utilization of this linearizing function during
both the calibration of the instrument and the making of measurements
thereby, allows measurements upon the unknown fluid to be referenced to
the result of calibration, without regard to the nonlinearity of the
transducer response. An instrument which utilizes the calibration and
linearization method of the invention is therefore able to provide
accurate measurements with any of a variety of different transducers or
with a transducer having a response which changes with time.
One particularly advantageous feature of the method of the invention is
that it utilizes equations which describe the response of the transducer
in two different ways. More particularly, the response of the transducer
is described both in terms of a first equation which gives the output of
the transducer as a function of the magnitude of the property of interest,
and in terms of a second equation which gives the magnitude of the
property of interest as a function of the output of the transducer.
Because both of these equations represent the same response, they may be
used interchangeably during the course of the calibration and
linearization process. Each stage of the latter process may therefore use
whichever equation most easily provides the information that is needed
during that stage.
The availability of two different equations which describe the response of
the transducer also makes it possible to determine the magnitude of the
property of interest from the transducer output, or vice versa, without
having to solve either equation for its roots. Since third and higher
order equations may be evaluated much more easily than they may be solved,
the practice of the invention provides its benefits without placing a high
signal processing burden on the instrument. As a result, the nonlinear
response of the transducer may be represented by equations having orders
higher than those which could be used heretofore. This, in turn, makes
possible the use of equations which more accurately represent the response
of the transducer, thereby providing a more accurate linearization.
In the preferred embodiment, the method of the present invention also
contemplates the determination and use of a scaling factor which assures
that the maximum output of the nonlinear transducer does not cause the
maximum signal processing capacity of the instrument to be exceeded. This
scaling factor assures that the instrument is able to modify its use of
the equations so as to provide the highest possible output resolution. The
use of this scaling factor therefore makes it possible to service or
replace a transducer without adversely affecting the resolution of the
instrument in which it is used.
DESCRIPTION OF THE DRAWINGS
Other objects and advantages of the present invention will be apparent from
the following description and drawingss in which:
FIG. 1 is a block diagram of one type of instrument that is suitable for
use in practicing the method of the present invention;
FIGS. 2a and 2b comprise two graphical and mathematical representations of
the response of the transducer used in the instrument of FIG. 1;
FIG. 3 is a flow chart which depicts the computer executable parts of the
method of the present invention; and
FIG. 4 is a partial flow chart which depicts an alternative computer
executable part of the method of the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to FIG. 1, there is shown a block diagram of a typical instrument
of a type which is suitable for use in practicing the method of the
invention. In FIG. 1 the instrument is of the type which measures the
concentration (or partial pressure) of one gas in another by measuring the
quantity of infrared radiation that is absorbed by the gas of interest as
it flows through a sample cell that is illuminated by an infrared source
of known intensity. Instruments of this type are commonly referred to as
non-dispersive infrared analyzers. In general, however, the method of the
invention may be applied to any instrument in which the magnitude of a
property of interest of a fluid is measured by a transducer that has a
nonlinear response to that property.
The analyzer of FIG. 1 includes a sample cell 10 for conducting a flow of
the gas upon which measurements are to be made. As the gas flows through
the sample cell, a beam of infrared radiation from a source (not shown) is
transmitted therethrough through windows which are transparent to the
portion of the infrared spectrum that is being used for the measurement.
The quantity of radiation that is not absorbed by the gas of interest
within the sample cell is measured by means of a suitable infrared
transducer 12 which may comprise a Luft detector. The output of this
detector is preferably demodulated and digitized in a signal interface
board 14 before being communicated to a suitable digital computer 16 for
further processing and/or for display on a human readable display 18.
In order to assure that the instrument accurately measures the
concentration of the gas of interest, it is necessary to calibrate the
instrument by measuring its response to the flow of a gas having none of
the gas of interest (zero gas) and a gas having a known non-zero
concentration of the gas of interest (standard or calibration gas). These
gases are applied to the sample cell through a set of valves 20 which are
controlled by computer 16 through a suitable valve driver board 22.
Computer 16 also operates through valve driver board 22 and valve set 20
to control the flow of the unknown or sample gas through sample cell 10
after the calibration process has been completed. The sequence in which
the valves of valve set 20 are operated, and the manner in which the
output of transducer is received and processed are controlled by computer
16 in accordance with its stored program. A flow chart for the program by
which computer 16 controls the operation of devices 10-22 in order to
achieve the objectives of the invention will be described later in
connection with FIGS. 3 and 4.
Computer 16 may comprise a conventional single board digital microcomputer
of any of a variety of types. This computer includes a central processing
unit or CPU 24 for performing sequencing and data processing operations, a
read-only memory or ROM 26 for storing the program to be executed by CPU
24 and a read-write memory or RAM 28 for storing intermediate results and
changeable program values and addresses. CPU 24 communicates with ROM 26,
RAM 28 and the external devices with which it operates through a
bidirectional multi-bit data/address bus 30. CPU 24 may also, however,
communicate directly with certain peripheral devices, such as an operator
keyboard 32, if it is provided with a port through which it can interface
with such external devices. Because the internal structure and operation
of a computer of the type shown in FIG. 1 is well known to those skilled
in the art, it will not be described in detail herein.
As is well known, there is a nonlinear relationship between the output of
an infrared transducer, such as Luft detector 12 of FIG. 1, and the
concentration of the gas of interest within the associated sample cell.
The nonlinearity of this response is illustrated by the curves shown in
FIGS. 2a and 2b. In FIG. 2a this response is plotted in terms of the
demodulated, digitized output voltage V of transducer 12 (expressed in
digital counts) as a function of the concentration C of the gas of
interest within the sample cell (expressed as a %). In FIG. 2b this
nonlinear response is plotted in terms of the concentration C of the gas
of interest as a function of the demodulated, digitized output voltage V
of transducer 12. For the sake of convenience, a response curve of the
type shown in FIG. 2a will be referred to as defining the direct (or
forward) response of the transducer, and a response curve of the type
shown in FIG. 2b will be referred to as defining the inverse (or reverse)
response of the transducer. As will be explained more fully presently, the
method of the present invention makes use of both of the direct and
inverse response characteristics of the transducer in calibrating the
instrument and linearizing data produced thereby.
Because of normal manufacturing variations in the dimensions and
compositions of different infrared transducers, the response of a
particular transducer may be different from the response shown in FIGS. 2a
and 2b. A particular transducer may, for example, have a sensitivity or
gain which causes its output to be greater or less than that shown in FIG.
2a for a given concentration of the gas of interest, and/or a response
which does not pass through the zero of the axis system. Because of the
broad similarity of the responses of transducers of the same type,
however, it is possible to define the response of a particular transducer
in terms of (i) the response of a typical transducer, and (ii) the
relationship between the response of a particular transducer and that of
the typical transducer. In accordance with the present invention, there is
provided a method which determines items (i) and (ii) and then uses the
same to calibrate the instrument for operation with the particular
transducer. After calibration, these items are used further to linearize
the output of the particular transducer and thereby provide an instrument
output of improved accuracy and repeatability.
In providing the above-mentioned advantages, the method of the invention
contemplates the performance of the following steps. Firstly, there is
produced a first equation which gives the direct response of a typical
transducer of the type that is to be used in the instrument. In the course
of performing this step, a series of measurements are performed on a
plurality of representative (randomly selected) transducers of a type that
are to be used in the instrument. This series of measurements is
preferably made by applying to each of the plurality of transducers a
sequence of gases having known concentrations of the gas of interest, and
measuring the output voltages (counts) that are associated with those
concentrations. After measurements have been performed on a sufficient
number of transducers, the resulting data are plotted on the axes shown in
FIG. 2a. Once this has been done, an equation that represents, or is
characteristic of, the response or output of a typical transducer may be
produced by fitting a selected type of curve to the plotted points. In the
preferred embodiment, the selected type of curve is a polynomial equation
of the type shown in FIG. 2a. The fitting of this curve is accomplished by
selecting the value of n to be used in the equation, i.e., selecting the
order of the equation, and then calculating the values of the coefficients
such as "A.sub.n " which minimize the difference between the curve
representing the equation from the plotted points. Since such curve
fitting procedures are well known to those skilled in the art, the
application thereof will not be described in detail herein.
The next step in the practice of the method of the invention comprises the
production of a second equation which gives the inverse response of a
typical transducer of the type that is to be used in the instrument. This
equation, the form of which is shown in FIG. 2b, may be produced in
generally the same manner as the equation of FIG. 2a. More particularly,
the equation may be produced by plotting the measured sets of points on
the axes of FIG. 2b, and by fitting a selected type of curve to the
plotted points using a conventional curve fitting technique. As is
suggested by the use of different subscripts n and m in the equations of
FIGS. 2a and 2b, both the coefficients and the exponents in the inverse
response equation will ordinarily be different from those of the direct
response equation. With one commonly used infrared transducer, for
example, a third order (m=3) polynomial equation has been found adequate
to represent the inverse response shown in FIG. 2b, but a fourth order
(n=4) polynomial equation has been found necessary to adequately represent
the direct response shown in FIG. 2a.
The production of equations which represent both the direct and inverse
response characteristics of a typical transducer greatly facilitates the
signal processing which is incident to the performance of the remaining
steps of the method of the invention. This is because the availability of
both equations makes it possible to determine either (a) the transducer
output which corresponds to a given concentration of the component of
interest, or (b) the concentration of the component of interest which
corresponds to a given transducer output, without having to solve either
of the two equations for its roots. Stated differently, the transducer
output which corresponds to a given concentration of the gas of interest,
or the concentration which corresponds to a given transducer output may be
determined by merely substituting the available one of these variables
into the appropriate one of the two equations, and then evaluating that
equation by multiplying out and adding together its various terms.
Moreover, since both equations represent the response of the same
transducer, they may be utilized interchangeably at vraious stages of the
calibration and linearization processes, depending upon which equation
then most conveniently provides the information that is needed from the
information that is then available. The reasons why it is desirable to use
different equations at different stages of the calibration and
linearization process will be apparent from the following description of
the manner in which the method of the invention makes use of the equations
of FIGS. 2a and 2b.
Once the equations which give the direct and inverse response
characteristics of a typical detector have been produced, they are made
available to the instrument by storing them within computer 16. If the
instrument is used with only a single type of transducer, this may be
accomplished by storing the two equations for that type of transducer in
ROM 26. If, however, the instrument is to be utilized with different types
of transducers, the equations for those types of transducers may be
entered via keyboard 32 and stored in RAM 28. Once these equations are
stored in the computer, the remainder of the method of the invention may
be practiced by causing the computer to execute the program depicted in
FIG. 3.
Upon beginning the execution of the program shown in FIG. 3, the computer
first encounters a block 40 which causes it to read the known
concentration value C.sub.s1 of the standard gas which will later be
applied to the sample cell through valve set 20. If the instrument is
always used with a standard gas of the same concentration, this
concentration may be permanently stored in ROM 26. Alternatively, if the
instrument is to be used with standard gases having a variety of different
concentration values (e.g., values which depend upon the type of
transducer being used), the concentration of the standard gas may be
entered by the operator via keyboard 32.
After completing the operation called for by block 40, the computer
proceeds to a block 42 which causes it to apply a suitable zero gas to
sample cell 10 and read the resulting output V.sub.O of transducer 12. The
result of the performance of this step is the determination of the value
of any offset or zero offest between the output of transducer 12 and the
output of a typical transducer of its type. By determining this zero
offset, the computer makes available to itself one of the two quantities
that are needed in order to correct for differences between the actual
response of transducer 12 and the estimated response thereof that is
predicted by the two stored equations. The ability of the computer to
correct for a zero offset also makes it possible to correct for any DC
bias which is introduced by the circuitry of interface board 14. Such a DC
bias may, for example, be desirable to assure that the A/D converter need
not handle both positive and negative signal voltages.
After determining the offset of the transducer, the computer proceeds to a
block 44. Upon encountering this block, the computer is directed to apply
the standard gas to the sample cell, and to read the actual transducer
output signal V.sub.SA which is associated with the standard gas.
Thereafter, upon encountering block 46, the computer is directed to
substitute the known concentration C.sub.S1 of the standard gas into the
direct transfer function equation (FIG. 2a) and evaluate the same in order
to determine the calculated or estimated transducer output signal V.sub.SE
which is associated with the standard gas.
Once both the actual and estimated transducer output signals are available,
the computer proceeds via block 48 to determine the relative sensitivity
of the particular transducer, i.e., its sensitivity with respect to that
of the typical transducer. This is done by calculating the ratio K of the
estimated transducer output signal to the actual transducer output signal,
after the latter has been corrected for offset voltage V.sub.O. By
determining the latter ratio, the computer makes available to itself the
second of the two quantities that are needed in order to correct for
differences between the actual response of the particular transducer and
the estimated response thereof that is predicted by the two stored
equations. The manner in which sensitivity ratio K and offset voltage
V.sub.O are used in this connection will be described later.
Upon encountering blocks 50 and 52, the computer performs a series of
operations which result in a determination of the scaling factor K' which
is necessary in order to assure that the signal processing capacity of the
instrument of FIG. 1 is not exceeded when the transducer produces its
maximum output signal V.sub.MAX. The determination of this scaling factor
is desirable because it defines the amplification (or attenuation) that
may be safely provided during signal processing. Such amplification (or
attenuation) is desirable because it assures that the instrument is
operating at its highest potential resolution, thereby assuring a more
accurate output reading.
The determination of scaling factor K' begins as the computer encounters
block 50 and is directed to evaluate the inverse transfer function
equation (FIG. 2b) at maximum transducer output V.sub.MAX (as corrected
for sensitivity ratio K) to determine the maximum concentration C.sub.MAX
that is to be processed by the instrument. Note that this operation is
performed by simply evaluating the inverse transfer function equation at
the then available value of independent variable V, and is analogous to
the operation performed via block 46 using the direct transfer function
equation and the then available value of independent variable C.
The determination of scaling factor K' then continues as the computer
encounters block 52 and is directed to determine the ratio of the signal
processing capacity V.sub.cap of the instrument and maximum concentration
C.sub.MAX. (One factor that limits the processing capacity of the
instrument is the number of bits in the digital words used therein.) In
forming this ratio, the factor 0.95 is inserted to provide a margin of
safety which assures that the capacity of the instrument is not exceeded
as a result of rounding errors.
Once scaling factor K' has been determined, the computer is directed to a
block 54 which causes it to modify or reformulate the inverse transfer
function equation so as to correct for the values of offset V.sub.O,
sensitivity ratio K, and scaling factor K'. The effect of this
reformulation generates a linearizing function which allows the response
of the particular transducer to be expressed in terms of the equation for
a typical transducer.
Once this linearizing equation is available, the instrument is calibrated
by causing the computer to carry out the steps called for by blocks 56 and
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