A low self-heating constant temperature difference control circuit and control method for compensating process errors of thermal flowmeters

Abstract

The present invention discloses a low self-heating constant temperature difference control circuit and control method for compensating for process errors in a thermal flowmeter. The circuit comprises a heating resistor, an ambient temperature resistor, a control resistor, a starting resistor, a first potentiometer, a second potentiometer, first to sixth resistors, a transistor, a first operational amplifier, a second operational amplifier, a third operational amplifier, and a power supply. The third operational amplifier uses negative feedback to control a Wheatstone bridge circuit composed mainly of the first resistor, the second resistor, the heating resistor, and the ambient temperature resistor to maintain a balanced state. The third to sixth resistors reduce the heating power of the ambient temperature resistor through voltage division. The resistance values ​​of the first and second potentiometers are adjustable, thereby compensating for errors in the resistance and temperature coefficients of the heating and ambient temperature resistors that occur during processing. The present invention can more accurately control the overheat temperature of the heating resistor to be constant, thereby improving measurement accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of flow sensors, and in particular to a low self-heating constant temperature difference control circuit and a control method for compensating process errors of a thermal flow meter. Background Art

[0002] A complete thermal flowmeter system consists of a sensor chip and its corresponding interface circuitry. During operation, the sensor senses and responds to changes in the external fluid state, while the interface circuitry controls the sensor's optimal operating state, suppressing interference factors, particularly temperature fluctuations, to achieve accurate readings, thereby leveraging the sensor's strengths and minimizing its weaknesses.

[0003] Constant bias and constant temperature differential are the two most common operating modes for thermal flowmeters. While the interface circuitry required for constant bias mode is relatively simple, compensating for ambient temperature drift through hardware is difficult, and in complex operating environments, software compensation is often required. In contrast, the constant temperature differential operating circuit, primarily based on a bridge structure, maintains a constant difference between the average temperature of the sensor's sensitive area and the ambient temperature through negative feedback. This adaptability to diverse operating environments, coupled with high accuracy and fast response, makes it the most promising operating mode.

[0004] The classic single-bridge constant temperature difference circuit has a simple structure and is widely used, but in practice, it often suffers from a certain degree of constant temperature error. This is because the circuit structure requires that the voltages across the ambient temperature resistor and the heating resistor be essentially equal. This applies a certain amount of heating power to the ambient temperature resistor, causing it to heat up and not accurately reflect the ambient temperature. This is known as the self-heating effect of the ambient temperature resistor. Furthermore, process errors are inevitable during the sensor tape-out process. The resistance values ​​and temperature coefficients of different sensor chips within the same batch can vary by as much as 5%, which also introduces non-ideal factors into the interface circuit. These two issues are difficult for the classic single-bridge constant temperature difference circuit to address. Summary of the Invention

[0005] The purpose of the present invention is to provide a low self-heating constant temperature difference control circuit and control method for compensating for the process errors of a thermal flowmeter. By optimizing the design of the circuit, the self-heating effect of the ambient temperature resistor is effectively reduced, and the process errors in the resistance value and temperature coefficient of the heating resistor and the ambient temperature resistor can be compensated, thereby achieving high-precision constant temperature difference control.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A low self-heating constant temperature difference control circuit for compensating process errors of a thermal flow meter, comprising:

[0008] A heating resistor, an ambient temperature resistor, a control resistor, a starting resistor, a first potentiometer, a second potentiometer, first to sixth resistors, a transistor, a first operational amplifier, a second operational amplifier, a third operational amplifier and a power supply.

[0009] One end of the heating resistor is respectively connected to one end of the first resistor, one end of the first potentiometer and the positive input end of the first operational amplifier, and the other end of the heating resistor is grounded.

[0010] The negative input terminal of the first operational amplifier is connected to the output terminal of the first operational amplifier and one end of the sixth resistor respectively, the other end of the sixth resistor is connected to one end of the fifth resistor and the negative input terminal of the third operational amplifier respectively, and the other end of the fifth resistor is grounded.

[0011] One end of the third resistor is connected to one end of the fourth resistor and the positive input end of the second operational amplifier respectively, and the other end of the third resistor is grounded.

[0012] The negative input terminal of the second operational amplifier is respectively connected to the output terminal of the second operational amplifier and one end of the second resistor, the other end of the second resistor is respectively connected to one end of the control resistor, one end of the second potentiometer and the positive input terminal of the third operational amplifier, the other end of the control resistor is respectively connected to one end of the ambient temperature resistor and the other end of the second potentiometer, and the other end of the ambient temperature resistor is respectively connected to the other end of the heating resistor and is grounded.

[0013] The output end of the third operational amplifier is connected to the base of the transistor, the collector of the transistor is respectively connected to one end of the starting resistor and the power supply, and the emitter of the transistor is respectively connected to the other end of the starting resistor, the other end of the fourth resistor, the other end of the first resistor and the other end of the first potentiometer.

[0014] Furthermore, the temperature coefficients of the heating resistor and the ambient temperature resistor vary within a range of ±10%.

[0015] Furthermore, the resistance ratio of the heating resistor to the ambient temperature resistor varies within a range of ±10%.

[0016] Furthermore, the first to sixth resistors are fixed resistors without a temperature coefficient.

[0017] Furthermore, the first potentiometer and the second potentiometer are low-temperature drift potentiometers.

[0018] Furthermore, the power supply voltage is 5V.

[0019] Furthermore, the resistance of the heating resistor satisfies:

[0020] R H =R H0 (1+α H ΔT H )

[0021] Among them, R H is the heating resistance, R H0 is the resistance of the heating resistor at 0°C, α H is the temperature coefficient of the heating resistor, ΔT H is the average temperature of the heating resistor in Celsius.

[0022] Furthermore, the resistance of the ambient temperature resistor satisfies:

[0023] R S =R S0 (1+α S ΔT S )

[0024] Among them, R S is the ambient temperature resistance, R S0 is the resistance value of the resistor at the ambient temperature of 0℃, α S is the temperature coefficient of the ambient temperature resistance, ΔT S is the average temperature of the resistor in degrees Celsius relative to the ambient temperature.

[0025] Furthermore, an analog-to-digital converter is included; the two differential inputs of the analog-to-digital converter are heating resistors R H and the voltage across the first resistor R1.

[0026] Furthermore, the present invention also proposes a control method for a low self-heating constant temperature difference control circuit for compensating process errors of a thermal flowmeter, wherein a first resistor, a second resistor, a heating resistor and an ambient temperature resistor form a Wheatstone bridge.

[0027] The third and fourth resistors of the right arm of the Wheatstone bridge are divided by voltage and then buffered by the second operational amplifier, thereby reducing the bias voltage across the ambient temperature resistor and suppressing the self-heating effect of the ambient temperature resistor. One end of the heating resistor of the left arm of the Wheatstone bridge is buffered by the first operational amplifier and then divided by voltage by the fifth and sixth resistors, thereby completing the matching of the two arms of the bridge and controlling the overheat temperature of the heating resistor to remain stable.

[0028] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0029] The circuit proposed in the present invention reduces the self-heating power of the ambient temperature resistor through the voltage division of the third and fourth resistors, so that it can more accurately reflect the ambient temperature; through the fifth and sixth resistors, the responses of the resistors on both sides of the bridge to changes in ambient temperature are consistent; through the first and second potentiometers, process errors in the resistance values ​​and temperature coefficients of the heating resistor and the ambient temperature resistor are compensated, thereby achieving high-precision constant temperature difference control of the thermal flow meter. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a circuit overall structure diagram of embodiment 1 of the present invention.

[0031] Figure 2 It is a circuit overall structure diagram of the second embodiment of the present invention.

[0032] Figure 3 This is a structural diagram of a MEMS thermal flow sensor used in the test of Example 1 of the present invention.

[0033] Figure 4 It is a schematic diagram of a classic single-bridge constant temperature difference circuit.

[0034] Figure 5 Schematic diagram of the constant temperature difference control effect of the constant temperature difference control circuit in the first embodiment of the present invention.

[0035] Figure 6 Schematic diagram of the effect of suppressing the self-heating effect of the ambient temperature resistor by the constant temperature difference control circuit in the first embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention.

[0037] It will be understood that when used in this specification and the appended claims, the terms “comprises” and “comprising” indicate the presence of described features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof.

[0038] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0039] To achieve the above objectives, the present invention proposes a low self-heating constant temperature difference control circuit for compensating the process error of a thermal flow meter, such as Figure 1 FIG. 1 is an embodiment of the present invention, which specifically includes:

[0040] Heating resistor R H , Ambient temperature resistance R S , control resistance R T , starting resistor R B , the first potentiometer R p1 , the second potentiometer R p2The circuit comprises first to sixth resistors R1 to R6, a transistor Q1, a first operational amplifier A1, a second operational amplifier A2, a third operational amplifier A3, and a power supply VCC. The circuit can reduce the self-heating effect of the ambient temperature resistor and compensate for process errors in the resistance and temperature coefficient of the heating resistor and the ambient temperature resistor.

[0041] The third operational amplifier A3 controls the first resistor R1, the second resistor R2, and the heating resistor R H and ambient temperature resistance R S The Wheatstone bridge composed of the main body is in a balanced state; the third to sixth resistors R3 to R6 reduce the heating power of the ambient temperature resistor by voltage division, thereby suppressing the self-heating effect of the ambient temperature resistor; the first and second potentiometers R p1 、R p2 The resistance value is adjustable and can compensate the heating resistance R H and ambient temperature resistance R S The error in resistance and temperature coefficient caused by processing.

[0042] Heating resistor R H One end of the first resistor R1 and the first potentiometer R p1 One end is connected to the positive input terminal of the first operational amplifier A1, and the heating resistor R H The other end of the first operational amplifier A1 is connected to the negative input end of the first operational amplifier A1 and one end of the sixth resistor R6, respectively. The other end of the sixth resistor R6 is connected to one end of the fifth resistor R5 and the negative input end of the third operational amplifier A3, respectively. The other end of the fifth resistor R5 is grounded.

[0043] One end of the third resistor R3 is connected to one end of the fourth resistor R4 and the positive input terminal of the second operational amplifier A2, respectively. The other end of the third resistor R3 is grounded. The negative input terminal of the second operational amplifier A2 is connected to the output terminal of the second operational amplifier A2 and one end of the second resistor R2, respectively. The other end of the second resistor R2 is connected to the control resistor R T One end of the second potentiometer R p2 One end is connected to the positive input terminal of the third operational amplifier A3, and the control resistor R T The other end is connected to the ambient temperature resistor R S One end of the second potentiometer R p2 The other end of the ambient temperature resistor R S The other end is connected to the heating resistor R H The other end is connected to the ground. The output end of the third operational amplifier A3 is connected to the base of the transistor Q1, and the collector of the transistor Q1 is connected to the starting resistor R B One end of the transistor Q1 is connected to the power supply VCC, and the emitter of the transistor Q1 is connected to the starting resistor RB The other end of the fourth resistor R4, the other end of the first resistor R1 and the first potentiometer R p1 to the other end of the

[0044] Heating resistor R H and ambient temperature resistance R S The temperature coefficient of the heating resistor R H and ambient temperature resistance R S The resistance ratio varies within the range of ±10%.

[0045] The first to sixth resistors R1 to R6 are fixed resistors having no temperature coefficient.

[0046] The first potentiometer R p1 and the second potentiometer R p2 It is a low temperature drift potentiometer.

[0047] The voltage of the power supply VCC is 5V.

[0048] like Figure 2 As shown in the figure, this is the second embodiment of the present invention. The second embodiment adds an analog-to-digital converter ADC1 on the basis of the first embodiment. The two differential inputs of the analog-to-digital conversion circuit are heating resistors R H and the voltage across the first resistor R1.

[0049] The principle of the circuit proposed by the present invention is:

[0050] The increase of fluid velocity makes the heating resistor R H The convection heat dissipation power increases, resulting in the heating resistor R H The temperature drops, causing a voltage difference between the positive and negative inputs of the third operational amplifier A3, which causes the output of the third operational amplifier A3 to increase, and the heating resistor R H Heating to the equilibrium temperature; therefore, when the fluid flow rate is different, the heating resistance R H The corresponding heating power is also different. By measuring the heating resistance R H The fluid flow rate can be measured by the heating power. If the ambient temperature changes during this process, the ambient temperature resistance R S This change will be sensed and fed back to the positive input of the third operational amplifier A3. The third operational amplifier A3 will adjust the circuit through negative feedback to keep the balance again, thereby achieving a constant temperature difference.

[0051] In this process, in order to make the ambient temperature resistor R S Accurately reflects the ambient temperature, and reduces the voltage across the ambient temperature resistor Rs during operation through the voltage divider of the third resistor R3 and the fourth resistor R4, thereby suppressing the ambient temperature resistor R STo compensate for the self-heating effect of different sensor chips, the heating resistor R H and ambient temperature resistance R S The circuit controls the resistance R T , the first potentiometer R p1 , the second potentiometer R p2 The equivalent resistance and temperature coefficient between the positive input terminal of the third operational amplifier A3 and ground, and the equivalent resistance between the positive input terminal of the first operational amplifier A1 and the top of the bridge are adjusted in series and parallel to match the response of the two arms of the bridge to the ambient temperature.

[0052] In order to conduct system-level simulation verification of the circuit proposed in this invention, it is necessary to establish a macro model of the thermal flowmeter that is coupled with multiple physical fields and can be simulated collaboratively with the electronic circuit. Therefore, a MEMS device macro model construction method based on physical field analysis is adopted, that is, the heating resistor R is constructed using the energy analysis method. H and ambient temperature resistance R S The macro model of the device is used. At the same time, the operational amplifier, instrumentation amplifier, transistor and other devices all use the officially provided SPICE models.

[0053] The thermal flow meter used in the present invention is a MEMS thermal flow meter, such as Figure 3 As shown, its working principle is governed by King's Law. The semi-empirical formula shows that the heat dissipation power of the sensor includes the power P dissipated by the solid heat conduction of the substrate cond And the convection heat dissipation power P between the heating resistor and the air conv , the specific expression is:

[0054]

[0055] Among them, k s is the thermal conductivity of the substrate, D is the thickness of the substrate, L is the length of the sensor chip, and ΔT is the heating resistance R H The superheat temperature, k f is the thermal conductivity of the gas, α is the thermal diffusivity of the gas, γ is the dynamic viscosity of the gas, and U is the fluid flow rate.

[0056] When the thermal flowmeter is in thermal equilibrium, the heating resistor R H The heating power is equal to the heat dissipation power. The relationship between the output power and the fluid flow rate is solved. The specific expression is:

[0057]

[0058] Among them, R H0 is the resistance of the heating resistor at 0°C, α H is the temperature coefficient of the heating resistor, ΔT His the average Celsius temperature of the heating resistor, V H is the voltage across the heating resistor.

[0059] To reduce the ambient temperature resistor R S The voltage across both ends of the resistors R3 to R6 is used to suppress the self-heating effect. The resistance expressions of the third to sixth resistors R3 to R6 are:

[0060]

[0061] Where n is the resistor voltage divider ratio coefficient.

[0062] When n is 3, the ambient temperature resistance R S The self-heating power is reduced to that of the classic single-bridge constant temperature difference circuit. This reduces its self-heating temperature by 95%.

[0063] If the heating resistor R H and ambient temperature resistance R S The temperature coefficients of the first and second potentiometers R p1 、R p2 Adjust to 0.5 times of the maximum resistance value, at this time the overheat temperature is controlled by the resistor R T The specific expression is:

[0064]

[0065] Among them, R P2M The second potentiometer R p2 The maximum value, R S0 is the resistance value of the resistor at the ambient temperature of 0℃, α S is the temperature coefficient of the resistance at ambient temperature.

[0066] If there is a process error, the heating resistor R H and ambient temperature resistance R S If the temperature coefficients are inconsistent, the second potentiometer R p2 The overheat temperature is controlled by the resistance R T and the second potentiometer R p2 Joint decision, the specific expression is:

[0067]

[0068] If there is a process error, the heating resistor R H and ambient temperature resistance R S The resistance ratio If it deviates from the design value, the first potentiometer R needs to be adjusted p1 The resistance value of the bridge arm is set to make the resistance ratio of the upper and lower parts of each bridge arm equal. The specific expression is:

[0069]

[0070] If the ambient temperature changes, the positive and negative input voltages of the third operational amplifier A3 are:

[0071]

[0072] Among them, V + is the positive input voltage of the third operational amplifier A3, V - is the negative input voltage of the third operational amplifier A3, V CTD is the emitter voltage of transistor Q1.

[0073] Combining equations (3), (5), (6) and (7) we can get V + =V - , the circuit proposed by the present invention makes up for the heating resistor R H and ambient temperature resistance R S process error, suppressing the ambient temperature resistance R S The self-heating effect of the flow meter is accurately controlled to operate in constant temperature difference mode.

[0074] In order to verify the effect of the circuit proposed by the present invention, the circuit of the present invention is compared with the circuit of the present invention in the simulation test. Figure 4 According to the user manual, at 0°C, the resistance of the MEMS thermal flow meter's heating resistor is 30.8Ω, and the resistance of the ambient temperature resistor is 606Ω. The temperature coefficients of both are 3740ppm / K. The overheating temperature of the heating resistor can be set to 30℃. However, actual tests show that the resistance of the heating resistor of the MEMS thermal flow meter is 30.5Ω at 0℃, and the temperature coefficient α H The ambient temperature resistance is 3430ppm / K, the resistance is 626Ω, and the temperature coefficient is α S It is 3480ppm / K.

[0075] Figure 5 This comparison shows the temperature control accuracy of the proposed circuit and a classic single-bridge constant temperature difference circuit within an ambient temperature range of 0°C to 40°C. Simulation test results show that process errors cause the average overheat temperature of the heating resistor in the classic single-bridge constant temperature difference circuit to be 38.72°C, with an average temperature control error exceeding 29%. In contrast, the proposed circuit achieves an average overheat temperature of 29.85°C, with an average temperature control error of less than 0.5% and a maximum temperature control error of only 0.55°C, effectively compensating for the effects of process errors.

[0076] Figure 6This comparison shows the self-heating power of the ambient temperature resistor in the circuit proposed by the present invention and in a classic single-bridge constant temperature difference circuit within an ambient temperature range of 0°C to 40°C. Simulation test results show that the average self-heating power of the ambient temperature resistor in the classic single-bridge constant temperature difference circuit is as high as 4.2mW, while the average self-heating power of the ambient temperature resistor in the circuit proposed by the present invention is only 0.19mV, only 4.5% of that in the classic single-bridge constant temperature difference circuit, effectively suppressing the self-heating effect of the ambient temperature resistor.

[0077] The simulation test results show that the circuit proposed in this invention effectively suppresses the heating resistance R H and ambient temperature resistance R S The process error in resistance and temperature coefficient is S The self-heating power at both ends is reduced by more than 95%, which greatly suppresses the self-heating effect, thereby achieving the purpose of heating resistor R H Precise constant temperature difference control.

[0078] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A low self-heating constant temperature difference control circuit for compensating process errors of thermal flowmeters, characterized in that: include: Heating resistor R H , Ambient temperature resistance R S , control resistance R T , starting resistor R B , the first potentiometer R p1 , the second potentiometer R p2 , first to sixth resistors R1 to R6, transistor Q1, first operational amplifier A1, second operational amplifier A2, third operational amplifier A3 and power supply VCC; Heating resistor R H One end of the first resistor R1 and the first potentiometer R p1 One end is connected to the positive input terminal of the first operational amplifier A1, and the heating resistor R H The other end is grounded; The negative input terminal of the first operational amplifier A1 is connected to the output terminal of the first operational amplifier A1 and one end of a sixth resistor R6, respectively. The other end of the sixth resistor R6 is connected to one end of a fifth resistor R5 and the negative input terminal of the third operational amplifier A3, respectively. The other end of the fifth resistor R5 is grounded. One end of the third resistor R3 is connected to one end of the fourth resistor R4 and the positive input terminal of the second operational amplifier A2, respectively, and the other end of the third resistor R3 is grounded; The negative input terminal of the second operational amplifier A2 is connected to the output terminal of the second operational amplifier A2 and one end of the second resistor R2, and the other end of the second resistor R2 is connected to the control resistor R T One end of the second potentiometer R p2 One end is connected to the positive input terminal of the third operational amplifier A3, and the control resistor R T The other end is connected to the ambient temperature resistor R S One end of the second potentiometer R p2 The other end of the ambient temperature resistor R S The other end is connected to the heating resistor R H The other end is connected to the ground; The output terminal of the third operational amplifier A3 is connected to the base of the transistor Q1, and the collector of the transistor Q1 is connected to the starting resistor R B One end of the transistor Q1 is connected to the power supply VCC, and the emitter of the transistor Q1 is connected to the starting resistor R B The other end of the fourth resistor R4, the other end of the first resistor R1 and the first potentiometer R p1 The other end of the connection; Among them, the heating resistor R H The resistance value satisfies: ； in, The heating resistance is 0 The resistance value when is the temperature coefficient of the heating resistor, is the average Celsius temperature of the heating resistor; Ambient temperature resistance R S The resistance value satisfies: ； in, The ambient temperature resistance is 0 The resistance value when is the temperature coefficient of the ambient temperature resistance, is the average temperature of the resistor in degrees Celsius relative to the ambient temperature.

2. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flowmeter according to claim 1 is characterized in that: Heating resistor R H and ambient temperature resistance R S The temperature coefficient varies within ±10%.

3. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flowmeter according to claim 1, characterized in that: Heating resistor R H and ambient temperature resistance R S The resistance ratio varies within the range of ±10%.

4. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flowmeter according to claim 1, characterized in that: The first to sixth resistors R1 to R6 are fixed resistors without a temperature coefficient.

5. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flow meter according to claim 1, characterized in that: The first potentiometer R p1 and the second potentiometer R p2 It is a low temperature drift potentiometer.

6. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flow meter according to claim 1, characterized in that: The voltage of the power supply VCC is 5V.

7. The low self-heating constant temperature difference control circuit for compensating process errors of a thermal flow meter according to claim 1, characterized in that: The analog-to-digital converter ADC1 is also included; the two differential inputs of the analog-to-digital converter ADC1 are the heating resistor R H and the voltage across the first resistor R1.

8. The control method for the low self-heating constant temperature difference control circuit for compensating the process error of the thermal flow meter according to claim 1 is characterized in that: The first resistor R1, the second resistor R2, the heating resistor R H and ambient temperature resistance R S Form a Wheatstone bridge; The third resistor R3 and the fourth resistor R4 of the right arm of the Wheatstone bridge divide the voltage and pass it through the second operational amplifier A2 for buffering, thereby reducing the ambient temperature resistance R S The bias voltage at both ends, suppressing the ambient temperature resistor R S The self-heating effect of the left arm of the Wheatstone bridge is H After one end is buffered by the first operational amplifier A1, the voltage is divided by the fifth resistor R5 and the sixth resistor R6 to complete the matching of the two arms of the bridge and control the heating resistor R H The superheat temperature remains stable; The resistance expressions of the third to sixth resistors R3 to R6 are: ； Among them, n is the resistance voltage divider ratio coefficient; When the heating resistor R H and ambient temperature resistance R S When the temperature coefficient is consistent, the overheat temperature is controlled by the control resistor R T The specific expression is: ； in, The second potentiometer R p2 The maximum value of The ambient temperature resistance is 0 The resistance value when is the temperature coefficient of the ambient temperature resistance, is the average temperature of the heating resistor in Celsius.

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