Methods and systems for temperature compensation of physical property sensors

Embodiments generally relate to material and physical property sensors, such as fluid or solid sensors. Embodiments also relate to temperature compensation methods and systems. Embodiments additionally relate to electrical circuitry, such as Wheatstone Bridge circuits utilized in sensor applications.

A number of approaches have been devised to measure the thermal conductivity, thermal diffusivity, specific heat and fluid velocity of a fluid or solid of interest. Typically, these and other properties are detected through the use of various types of detectors including resistive bridge type sensors.

One approach for determining thermal conductivity involves the use of a heated element in one leg of a Wheatstone Bridge. The heated element can be placed or positioned in a cavity through which the sample fluid of interest is passed. The heated element is used to introduce a series of amounts of thermal energy into the fluid of interest at various levels by varying the input voltage via alternating current, voltage or power so that the changes in dissipated power caused by changes in the thermal properties of the surrounding fluid or solid (e.g. powder) can be detected as voltage, current or resistance change signals. One of the measurable fluid properties is the thermal conductivity of the fluid.

Further to the measurement of thermally induced changes in electrical resistance, as will be discussed in greater detail below, very small and very accurate “micro bridge” or “micro membrane” semiconductor chips supporting sensors have been implemented in the context of heaters and sensors. Such sensors might include, for example, a pair of thin film sensor elements around a thin film heater element for measuring flow rates. An example of a semiconductor chip sensor configuration is disclosed U.S. Pat. No. 6,361,206, “Microsensor Housing”, which issued to Ulrich Bonne on Mar. 26, 2002, and which is incorporated herein by reference. It can be appreciated that U.S. Pat. No. 6,361,206 is referenced herein for generally illustrative and background purposes only, and should not be considered a limiting feature of the present invention.

Another approach for measuring the thermal conductivity, thermal diffusivity and specific heat of a fluid involves the use of a micro bridge structure that has a heater film and at least one spaced sensor films. A pulse of electrical energy can be applied to the heater at a level and duration such that both a transient change and a substantially steady-state temperature occur at the sensor.

The thermal conductivity of the fluid of interest is determined based upon a known relation between the sensor output and the thermal conductivity at steady-state sensor temperatures. The specific heat and thermal diffusivity of the fluid of interest are determined based on a known relation among the thermal conductivity, the rate of change of the sensor output during a transient temperature change in the sensor, and the thermal diffusivity and specific heat.

A typical approach for determining the velocity of a fluid of interest is to determine the time require for a thermal wave to flow from a source heater element to a destination sensor element. By knowing the distance between the heater element and the sensor element, the velocity of the fluid can be calculated.

The thermal waves can propagate through the fluid at a rate that is dependent on the fluid velocity flowing perpendicular to the heater strip. A thermo-electric detector, spaced from one or both side of the heater, senses the thermal wave and provides a corresponding detector output signal. The velocity of the fluid is determined, at least to first order, from the time differential between the heater input signal and the detector output signal.

In many instances it may be necessary to achieve temperature compensation for fluid properties, such as thermal conductivity, viscosity, pressure, vapor concentration, and so forth. Heretofore, temperature compensation has involved digitally processing independent signals of property and temperature, preferably taken at two temperatures, and requiring a fair amount of time. Other methods, such as an orientation sensor and many of the aforementioned devices, provide no compensation at all. The ability to achieve temperature compensation properly for fluid sensors, such as the fluid sensors discussed above, and other similar sensing devices, is an important objective that has not yet been achieved. The methods and systems disclosed herein provide a solution to the lack of temperature compensation associated with current and traditional thermal property and other fluid property sensors.

The following summary of the invention is provided to facilitate an understanding of some of the innovative features unique to the present invention and is not intended to be a full description. A full appreciation of the various aspects of the invention can be gained by taking the entire specification, claims, drawings, and abstract as a whole.

It is, therefore, one aspect of the present invention to provide improved temperature compensation methods and systems for physical property sensors.

It is another aspect of the present invention to provide improved temperature compensation methods and systems for physical property (e.g., gas, liquid or solid) sensors.

The aforementioned aspects of the invention and other objectives and advantages can now be achieved as described herein. Temperature compensation methods and systems for physical property sensors are disclosed herein. An example of a physical property sensor is a fluid property sensor. A bridge circuit (e.g., a Wheatstone Bridge circuit) can be located on a physical property sensor substrate. Such a bridge circuit can include one or more heating elements and a plurality of resistors, including a plurality of compensating resistors thereof. An imbalance of the bridge circuit can be driven to a zero value while a supply voltage thereof is simultaneously driven to a level required to stabilize the heating element at a constant temperature rise above ambient temperature.

The heating element can comprise a thin-film heating material. A non-linear temperature coefficient of resistance of the thin-film heating material can then be dynamically compensated utilizing one or more compensating resistors of the bridge circuit. Temperature compensation can therefore achieved in a front-end analog circuit (i.e., the bridge circuit), which can serve eliminate the need for digital circuitry and its associated cost.

The accompanying figures, in which like reference numerals refer to identical or functionally similar elements throughout the separate views and which are incorporated in and form part of the specification, further illustrate embodiments of the present invention.

FIG. 1 illustrates a temperature compensation system for a fluid property sensor, which can be implemented in accordance with an embodiment of the present invention;

FIG. 2 illustrates a schematic electrical diagram of a micro-bridge circuit, which can be implemented in accordance with an embodiment of the present invention;

FIG. 3 a illustrates a graph of temperature dependence of a sensor prior to compensation, in accordance with an embodiment of the present invention;

FIG. 3 b illustrates a graph of temperature dependence of a sensor after compensation, in accordance with an embodiment of the present invention;

FIG. 4 a illustrates a graph of temperature signals in volts versus output in volts, in accordance with an embodiment of the present invention;

FIG. 4 b illustrates a graph of temperature sensitivity of a thermal conductivity sensor versus resistance in ohms, in accordance with an embodiment of the present invention;

FIG. 5 illustrates a graph of purge response time of a thermal conductivity sensor, in accordance with an embodiment of the present invention;

FIG. 6 illustrates a physical property sensor package holding an alumina substrate, which holds a flow sensor chip, which can be implemented in accordance with an embodiment of the present invention;

FIG. 7 illustrates an electronic circuit for a temperature compensated thermal conductivity sensor or a viscosity sensor, along with an optional temperature sensor, which can be implemented in accordance with an embodiment of the present invention;

FIG. 8 illustrates a graph indicating a ratio error resulting from measurement with a compensated thermal conductivity sensor under parametric variation, in accordance with an embodiment of the present invention;

FIG. 9 illustrates a graph indicating a ratio error resulting from measurement with a compensated thermal conductivity sensor under HC-type variations, in accordance with an embodiment of the present invention; and

FIG. 10 illustrates a graph indicating a ration error resulting from measurement with a compensated thermal conductivity sensor under pressure variations, in accordance with an embodiment of the present invention.

The particular values and configurations discussed in these non-limiting examples can be varied and are cited merely to illustrate an embodiment of the present invention and are not intended to limit the scope of the invention.

With reference now to the figures, and in particular with reference to FIG. 1 , a temperature compensation system 100 for a fluid property sensor is illustrated in accordance with an embodiment of the present invention. System 100 generally includes a substrate 112 upon which sensor portions 102 and 106 may be formed over a sensor region 110 and beside a heater portion 104 . The configuration of system 100 can be modified to include fewer or greater sensor portions, depending on desired implementations. Sensor portions 102 and 106 can, for example, can function as a single sensor or a plurality of individual sensors. System 100 can thus be implemented in the context of an integrated circuit (IC) chip.

FIG. 2 illustrates a schematic electrical diagram of a micro-bridge circuit 200 , which can be implemented in accordance with an embodiment of the present invention. Circuit 200 of FIG. 2 is associated with system 100 of FIG. 1 . Circuit 200 comprises a heater Wheatstone bridge (WB) circuit that includes at least resistors 202 , 204 , 206 , and 210 , which are respectively also labeled in FIG. 2 as resistors R A , R B , R C and R C1 . Circuit 200 can be utilized to implement heater portion 104 of FIG. 1 . An optional resistor 224 , labeled in FIG. 2 as R′ C1 can be located between resistor 204 and resistor 202 . Circuit 200 further includes an op-amp device 216 whose output is tied back between resistors 202 and 204 at a node 214 , also labeled as V Q .

In the illustrated approach of FIG. 2 , resistors R A , R B , R C and R C1 are temperature independent, but a thin-film resistance 212 (R H , on the micro-bridge) and 208 (R R , on the chip, i.e., system 100 ) are not. Resistor 210 and resistance 208 are shown parallel with each other in FIG. 2 and tied to a ground 222 , along with resistance 212 . The combined temperature dependencies of R H , its heat dissipation via thermal conductivity and that of the reference resistor system, [R R +R C +R C1 ], are configured to cancel, so that V Q becomes temperature independent, which generally requires that ΔT htr (T) is approximately equivalent to a constant value.

The temperature compensation methods and systems disclosed herein can be achieved utilizing a temperature compensation technique adapted to flow sensors for the measurement of fluid properties. Such a technique preferably involves a measurement of thermal conductance, which can then be correlated to parameters such as thermal conductivity, viscosity, pressure, vapor concentration orientation and/or other properties such as specific heat. Although the flow sensor depicted herein illustrates a preferred microstructure because of its established/proven commercial availability, stability, compactness, low cost, low power consumption and ruggedness (i.e., shock, vibration and overpressure), other structures are clearly possible. Other structures can benefit from the temperature compensation proposed here.

Achieving a temperature compensated output for a flow sensor can be achieved via a circuit, such as circuit 200 of FIG. 2 . As depicted in FIG. 2 , a configuration is presented in which the heater's Wheatstone bridge (WB) imbalance driven to zero and its supply voltage is simultaneously driven to a level needed to stabilize the heating element at the desired, constant temperature rise above ambient, ΔT htr , while compensating for the non-linear TCR (Temperature Coefficient of Resistance) of the thin-film heater material (e.g., Pt, FeNi, etc.) via a zero-TCR, compensating resistor, R c .

In order to avoid altering the intended ΔT htr at reference conditions, an additional, zero-TCR, parallel resistor 210 , which is labeled as R C1 in FIG. 2 , can be provided, which brings the total reference resistance back to its original value, after increasing R C to also compensate for the temperature dependence of thermal conductivity, k. The heater WB circuit 200 of FIG. 2 represents a preferred embodiment of a temperature compensation method and/or system for property sensors. For varying methods for the measurement of k (i.e., reflecting some of the different ways for the measurement of flow) the illustrated embodiment can be characterized by several factors, including measurement of heater power, measurement of temperature field, and extrapolation to property values at reference conditions.

The measurement of heater power can be achieved under conditions in which the heater element (e.g., heater portion 104 of FIG. 1 ) is maintained at an approximately constant temperature rise above ambient, t. The value t can be configured to vary with ambient temperature precisely enough to compensate for the combined effects of the non-linear heater-film TCR and the temperature dependence of the thermal conductance (i.e. heater thermal power dissipation) as indicated approximately by a WB input voltage, V Q 2 , such that V Q , which is the value to be correlated to the property of interest, then becomes precisely independent of ambient temperature.

Because each fluid has its individual temperature dependence of thermal conductivity (or of thermal conductance in the geometrical setting of the sensor), the exact elimination of V Q 's temperature dependence is only achieved for the one chosen fluid. Preferably, we would choose that fluid to be one serving as reference fluid, such as “normal” air, e.g. for atmospheric pressure measurements, leak detection, gasoline vapor concentration; but one would choose methane for the determination of natural gas properties, or water for aqueous solutions, or hexadecane for fuel oils. As “normal” air one would select air at T, p, RH and CO 2 concentration values corresponding to averages for the intended application.

FIG. 3 a illustrates a graph 301 of temperature dependence of a sensor prior to compensation, in accordance with an embodiment of the present invention. FIG. 3 b illustrates a graph 302 of temperature dependence of a sensor after compensation, in accordance with an embodiment of the present invention. The data plotted in FIGS. 3 a and 3 b generally illustrates values, which can be obtained for three gases near atmospheric pressure after adjustment of R C to achieve constant heater temperature rise above ambient, ΔT htr ( FIG. 3 a ), and after simulating the effect of additions to R C and of R C1 to make V Q independent of temperature for N 2 ( FIG. 3 b ).

Alternative methods and systems for this measurement approach (heater power) can include, for example, operating the heater's WB at constant current (measure WP's input voltage a input power), constant voltage (measure WP's input current a input power) or constant power (measure WP's input voltage or current) excitation. Note that none of the above makes use of the sensing elements of the sensor structure.

FIG. 4 a illustrates a graph 401 of temperature signals in volts versus output in volts, in accordance with an embodiment of the present invention. FIG. 4 b illustrates a graph 402 of temperature sensitivity of a thermal conductivity sensor versus resistance in ohms, in accordance with an embodiment of the present invention.

The measurement of a temperature field can be performed under conditions of constant ΔT htr (preferred) or by holding the other parameters constant as above, by sensing the temperature rise above ambient of the thin-film elements (preferably the average of those two elements) adjacent to the heater. For example, graphs 401 and 402 respectively illustrate a temperature rise, expressed as a sensor's WB output voltage, V S , changes as a function of the changing k value of different gases. The R c of the heater's WB is now chosen to keep ΔT htr constant and the R c of the sensors WB is chosen to eliminate the temperature dependence of V S , again, only for the chosen fluid.

Extrapolation to Property Value at Reference Conditions. This approach is based on either (a) Deriving and using a correlation between measured values of T and k (and possibly others such as c p ) and the desired value k o at reference temperature, T o ; (b) Measuring k at two (preferred) or more temperatures, realized by operating the heater at two temperatures (e.g. 60 and 120-C) in order to then enable extrapolation to k o ; this involves significant time, which may disqualify the sensor in some applications or (c) To avoid this time delay, measuring k 1 and k 2 at effective temperatures T 1 and T 2 simultaneously with two sensor chips (preferably mounted on the same alumina or TO 5 substrate), so that the extrapolation of k o at T o can be made continuously and involving minimum processing time. The extrapolation may be linear, or fitted for a set of preferred fluids to a better, non-linear correlation.

k o =k 1 −( T 1 −T o )( k 2 −k 1 )/( T 2 −T 1 )  (1)

Graph 401 therefore illustrates actual measurement results as R C was increased to the optimum value of 3680 Ω, and FIG. 4 b a plot of the overall TCR. Graphs 401 and 402 (preferred) can be implemented via digital electronics in sensors for FFCC (feed-forward combustion control) demonstrations.

FIG. 5 illustrates a graph 500 of purge response time of a thermal conductivity sensor, in accordance with an embodiment of the present invention. Graph 500 generally depicts how fast a sensor implemented in accordance with an embodiment of the present invention can respond to a change in gas property (N 2 to Argon), in spite of being held in a recessed cavity.

FIG. 6 illustrates a physical property sensor package 600 holding an alumina substrate, which holds a flow sensor chip, which can be implemented in accordance with an embodiment of the present invention. An O-Ring 610 surrounds an integrated circuit (IC) chip 617 to provide a gas-tight seal thereof. Sensor package 600 additionally includes holding screws 604 and 608 , a housing 618 that can be constructed from metal, and an alumina substrate 620 . Sensor package 600 also includes I/O (input/output) leads 602 and at least one hex nut 614 .

A protective screen 619 also serves to provide a protective barrier against fluid 608 . Note that chip 617 of FIG. 6 is analogous to the IC chip or system 100 of FIG. 1 and circuit 200 of FIG. 2 . Sensor package 600 additionally includes a package portion 622 , which seals fluid 608 via one or more O-rings 610 around the chip 617 , while ring 626 (e.g., approximately 1.5″ OD) keeps fluid 608 from leaking out of and past package portion 622 . Note that a cover portion 618 can be implemented as a part that is separate from package portion 622 and can be held together via the screws 604 and 608 , which can be located around the ceramic chip 617 and the alumina substrate 620 . Note that the chip 617 can be, for example, approximately 1.7×1.7 mm in size, on a 1×1″ ceramic substrate.

An electronic circuit diagram of the configuration depicted in FIG. 6 is presented in FIG. 7 . FIG. 7 generally illustrates an electronic circuit 700 for a temperature compensated thermal conductivity sensor or a viscosity sensor, along with an optional temperature sensor, which can be implemented in accordance with an embodiment of the present invention. Circuit 700 generally includes a resistor 702 , which is connected to a resistor 704 . Resistors 702 and 704 are generally located in parallel with a resistor 706 . Circuit 700 additionally includes an amplifier 708 , which is connected to a capacitor 709 . An output of amplifier 708 is connected to a resistor 710 and a TC or viscosity detector 712 . Circuit 700 also includes an amplifier 722 having at least one input connected to a resistor 721 .

Resistor 721 can be further connected to a resistor 718 and parallel capacitors 714 and 716 . Resistor 718 is connected in series with a POT resistor 720 , which in turn is connected to a resistor 723 and a resistor 725 . The resistor 723 is also connected to the output of amplifier 724 . Resistor 725 is also tied to an output of amplifier 724 , which is further tied to a temperature detector or sensor 726 . A resistor 728 is connected in series with a resistor 730 , which in turn can be connected to parallel capacitors 714 and 716 . Additionally, resistor 730 and capacitors 714 and 716 can be connected to a voltage reference 734 . The voltage reference 734 can be, for example, approximately +5V.

It can be appreciated, however, that this is only an illustrative example and that other voltage reference values are possible. A positive voltage (V+) input of voltage reference 734 can be tied to a capacitor 732 , while a negative voltage of voltage reference 734 can be tied to ground. A micro bridge sensor 736 can also be implemented in accordance with circuit 700 . Additionally, a header 738 (i.e., power supply input, signal voltage output) can also be implemented in association with a power supply input 740 , whose value can be, for example, approximately +10V. A common power supply 742 can additionally be implemented in accordance with circuit 700 . Common power supply 742 provides a voltage of approximately +10V.

In some applications demanding high-accuracy and well-compensated thermal conductivity output, it is necessary to eliminate also the residual influence of temperature on the sensor output signal after the analog compensation. For example, it may be necessary to eliminate a large fraction of this dependence, but doing so may limit residual TCR mismatches in the electronic components of the sensor circuit. To reduce this residual temperature effect, the addition of a temperature sensor is proposed, so that in a calibration run with the selected reference fluid (e.g. nitrogen, dry air or a stoichiometric mixture of fuel gas and air), the deviation, dV, from a constant reference output voltage, V o , can be recorded as a function of temperature, T.

At a temperature, T=T o , for example, the following deviation can occur: dV=0. During actual measurement, the values V and T can be measured, and the proper correction value, dV, can be interpolated from listed data so that the corrected sensor output, V out =V+dV(T) can be obtained and converted to thermal conductivity, k, by way of an individually derived k(V out ) function. Such a function or value can be achieved by performing a minimal number of measurements with pure gases of known k(T) values, such as CH 4 , N 2 and Argon, with k values at, for example, 1 atm and 15° C. of 79.69081, 59.58516 and 41.2435 μcal/(sKcm), respectively. Once k has been determined for a chosen reference temperature (e.g. 15° C.), regardless of the actual ambient temperature by virtue of the completed temperature compensations, other fluid properties of interest, f(k), can be determined, independently of each sensor because f(k) is universal.

If in addition to a temperature sensor, also an ambient pressure sensor signal is available, then pressure compensation can be implemented via a method very similar to the look-up table method, just described, to also minimize the pressure dependence. Calculated and measured (noise and signal levels) sensor specifications can indicate, for the example, the use of a thermal conductivity sensor as a rough butane-air stoichiometry sensor to measure directly the mass A/F ratio or its normalized λ-value. The pressure dependence, while small in terms of its influence on k(λ) or k(A/F), could be made even smaller and thus reduce the overall error of the T and p-compensated output signal.

Similarly, the availability of specific humidity and other gas property (such as gas density, specific heat and viscosity) sensor signals could be used to reduce the errors introduced by changes in ambient humidity and in the average composition of the fluid, which may have unique and detracting influences on the intended thermal conductivity measurement.

FIG. 8 illustrates a graph 800 indicating a ratio error resulting from measurement with a compensated thermal conductivity sensor under parametric variation, in accordance with an embodiment of the present invention FIG. 9 illustrates a graph 900 indicating a ratio error resulting from measurement with a compensated thermal conductivity sensor under HC-type variations, in accordance with an embodiment of the present invention. FIG. 10 illustrates a graph 1000 indicating a ration error resulting from measurement with a compensated thermal conductivity sensor under pressure variations, in accordance with an embodiment of the present invention.

Graphs 800 , 900 and 1000 illustrate the computed influence of humidity (0 and 3 vol. %) at various λ-values, of replacing butane by pentane or by a 50-50 mixture of the two, and of ambient pressure at the sensor location. If the desired maximum total uncertainty of the λ-measurement is ±10% of λ, then FIGS. 8–10 describe the merits of the simultaneous measurement of temperature (because we have measured the residual TCk (temperature coefficient of k) to be equivalent to 9% of λ), humidity and pressure. With these measurements and the resulting ability to reduce the individual effects of temperature, humidity and/or pressure, we can then reduce the total k-sensor output error.

Whether a basic analog k-measurement method is augmented by the addition of a microprocessor to process the various look-up table steps as an integral feature of the sensor functions, or to process these steps with the help of a microprocessor residing elsewhere is left to the discretion of the system designer.

An additional object and practical matter of is to (1) suggest the use of range mean values of disturbance variables such as humidity, pressure and fluid composition, as reference fluid conditions (rather than the ones shown in FIGS. 8–10 ); and (2) to reduce the cost of calibration by allowing the use of simple fluids, and not especially tightly controlled (but accurately measured!!) reference conditions for calibration, whereby the deviation from the ideal reference fluid and condition is incorporated into the ideal calibration curve via computed sensor output “deltas”.

A number of advantages can accrue from implementations of the temperature compensation embodiments described herein. For example, as indicated earlier, the use of a look-up table of dV(T) data can be implemented, such that the data is added to obtain a computed and compensated readout V out =V+dV(T)+ . . . , to further reduce the residual temperature compensation error. Additionally sensors of the fluid's humidity, pressure and/or additional properties can enable the stepwise reduction of the corresponding, undesirable influences on the sensor's output, and to thus increase its accuracy. Also, the relaxation of the calibration conditions due to the use of appropriate sensors and look-up tables can enable a cost reduction in the calibration and thus in the overall manufacturing costs.

The use of a look-up table not only can increase the accuracy of the ultimate thermal conductivity readout k(V out ), but can also relieve the accuracy requirement of the analog temperature compensation, and thus reduces the calibration and fabrication costs, by reducing the effort to match the TCRs of its circuit elements.

The ability to productive thermal conductivity sensors based on a mass air flow sensor chip, and its correlations to other properties of gases and liquids can significantly enhance with temperature-compensated sensors, as enabled via the methods and systems described herein. A number of applications are possible via implementations of embodiments of the present invention. For example, compensation for gasoline vapor concentration sensing is one application, which can result in a low-cost means for such compensation. Many designers do not want to deal with two sensor outputs, k and T, and also to work out their own temperature compensations.

Digitally; such compensation can be crucial in vapor sensing implementations because the vapor concentration induced change in k is generally smaller than that induced by temperature over the range of outdoor temperatures. On the other hand, some designers may insist on an uncompensated output, with a temperature signal thereof, when proper control of their process depends on the actual, absolute value of the property, such as for example, the viscosity of the ink in the ink-jet printer.

In general, a first temperature compensation method for physical property sensors (in a zero or low flow environment), can be implemented which is based on an adaptation of methods and systems for thermal mass air flow micro-sensors. Such methods or systems may or may not involve altering a set ΔT htr , and can generally entail, as indicated in FIG. 2 , adjusting at least one resistor, R c of the heater WB, such that (for a preferred analog circuit embodiment) the temperature dependence of V Q disappears at least for one chosen reference fluid. Adjustment of R C1 or R C1 ′ may be required to maintain the desired ΔT htr value.

A second temperature compensation method and/or system for physical property sensors, is based on at least two sequential (e.g., with one sensor or simultaneous with two sensors) measurements of V Q , but involves different micro-thermal environments of the sensor(s) by changing at least one resistor in at least one of the reference legs of the heater's WB. The two values of V Q can then be related to values of k, which are thereafter converted to the temperature-compensated value, k o , via equation (1) indicated herein or via its non-linear equivalent, or via an equivalent in which the two values of V Q is inserted directly, instead of the two k values.

Based on the foregoing, it can be appreciated that embodiments of the present invention are directed toward a physical property sensors and the temperature compensation of such physical property sensors. A physical property sensor, as indicated herein, can detect physical properties of materials such as gases, liquids, or solids (e.g., powder). Other physical properties, which can be detected in accordance with embodiments of the present invention can include, for example, thermal conductivity, specific heat, compressibility, octane number, heating value, speed of sound, viscosity, and the like. Embodiments can thus be implemented, which measure the thermal conductivity, thermal diffusivity, specific heat and/or fluid velocity of a fluid or solid

According to embodiments of the present invention, a technique is presented in which a compensating resistor is optimized in order to minimize output signal (i.e., certain bridge voltages) variations versus ambient temperature. This optimization is therefore automatically compensated for temperature dependencies (i.e., linear or non-linear) of heater, circuit components and the material to be measured. Such compensation is optimal only for the selected material, typically air or water.

The embodiments and examples set forth herein are presented to best explain the present invention and its practical application and to thereby enable those skilled in the art to make and utilize the invention. Those skilled in the art, however, will recognize that the foregoing description and examples have been presented for the purpose of illustration and example only. Other variations and modifications of the present invention will be apparent to those of skill in the art, and it is the intent of the appended claims that such variations and modifications be covered.

The description as set forth is therefore not intended to be exhaustive or to limit the scope of the invention. Many modifications and variations are possible in light of the above teaching without departing from the scope of the following claims. It is contemplated that the use of the present invention can involve components having different characteristics. It is intended that the scope of the present invention be defined by the claims appended hereto, giving full cognizance to equivalents in all respects.