Gas sensor

Abstract

The technical problem of the present disclosure is to reduce the difference in thermal history between a thermistor constituting a detection element and a thermistor constituting a reference element. [Solution] A gas sensor (1) is provided with: a detection circuit (10) including thermistors (Rd1, Rd2); heater resistors (MH1, MH2) for heating the thermistors (Rd1, Rd2), respectively; and a control circuit (20) that controls the connection relationship of the detection circuit (10) and the heating temperature of the heater resistors (MH1, MH2). The control circuit (20) heats the heater resistors (MH1, MH2) to 150 DEG C and 300 DEG C, respectively, during the period (T1), and connects the thermistors (Rd1, Rd2) in series. During the period (T2), the heater resistors (MH1, MH2) are respectively heated to 300 DEG C and 150 DEG C, and the connection relationship is switched so that the amounts of current flowing through the thermistors (Rd1, Rd2) are different. As a result, the difference between the self-heating amounts of the thermistors (Rd1, Rd2) during the period (T2) is reduced.

Description

Technical Field

[0001] The present disclosure relates to a gas sensor. Background Art

[0002] In Patent Document 1, a gas sensor is disclosed which calculates the concentration of a gas to be measured based on the level of a detection signal that appears at the connection point of two thermistors connected in series. In the gas sensor described in Patent Document 1, after obtaining a detection signal by heating the thermistor constituting the detection element to 150°C and heating the thermistor constituting the reference element to 300°C, the difference in the thermal history of the two thermistors is eliminated by heating the thermistor constituting the detection element to 300°C and heating the thermistor constituting the reference element to 150°C.

[0003] Prior Art Documents

[0004] Patent Documents

[0005] Patent Document 1: International Publication WO2020 / 031517 Summary of the Invention

[0006] Technical Problem to be Solved by the Invention

[0007] However, in the gas sensor described in Patent Document 1, it is also known that there are slight differences in the thermal history of the two thermistors.

[0008] In the present disclosure, a gas sensor in which the difference in the thermal history of the two thermistors is further reduced will be described.

[0009] Technical Means for Solving the Technical Problem

[0010] The gas sensor of the present disclosure includes: a detection circuit including a first thermistor and a second thermistor; a first heater and a second heater that respectively heat the first thermistor and the second thermistor; and a control circuit that controls the connection relationship of the detection circuit and the heating temperatures of the first heater and the second heater. In a first period, the control circuit heats the second heater to a higher temperature than the first heater and connects the first thermistor and the second thermistor in series, thereby generating an output signal representing the concentration of the gas to be measured based on the detection signal that appears at the connection point between the first thermistor and the second thermistor. In a second period, the control circuit heats the first heater to a higher temperature than the second heater and switches the connection relationship so that the amount of current flowing through the first thermistor is different from the amount of current flowing through the second thermistor.

[0011] Advantages of the Invention

[0012] According to the present disclosure, it is possible to provide a gas sensor that can further reduce the difference in the thermal history between two thermistors. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 FIG. is a circuit diagram showing the structure of a gas sensor 1 according to a first embodiment of the technology based on the present disclosure.

[0014] Figure 2 FIG. is a timing diagram for explaining the operation of the gas sensor 1.

[0015] Figure 3 FIG. is a graph showing the temperature characteristics of the thermistors Rd1 and Rd2.

[0016] Figure 4 FIG. is a circuit diagram showing the structure of a gas sensor 2 according to a second embodiment of the technology based on the present disclosure.

[0017] Figure 5 FIG. is a timing diagram for explaining the operation of the gas sensor 2.

[0018] SYMBOL DESCRIPTION

[0019] 1, 2: Gas sensors

[0020] 10: Detection circuit

[0021] 20: Control circuit

[0022] 21: AD converter

[0023] 22, 23: DA converters

[0024] 24: MPU

[0025] 25: Variable power supply

[0026] 26: Variable current source

[0027] 27: Fixed current source

[0028] MH1, MH2: Heater resistors

[0029] R1: Fixed resistor

[0030] Rd1, Rd2: Thermistors

[0031] SW1, SW2: Switches

[0032] a: Common node

[0033] b, c: Selection nodes DETAILED DESCRIPTION OF THE EMBODIMENTS

[0034] Hereinafter, embodiments of the technology of the present disclosure will be described in detail with reference to the drawings.

[0035] Figure 1 This is a circuit diagram showing the structure of the gas sensor 1 according to the first embodiment of the technology of the present disclosure.

[0036] As Figure 1 shown, the gas sensor 1 of the first embodiment includes: a detection circuit 10 including thermistors Rd1, Rd2, and a fixed resistor R1; heaters MH1, MH2 for heating the thermistors Rd1, Rd2 respectively; and a control circuit 20 for controlling the detection circuit 10 and the heaters MH1, MH2. The gas sensor 1 according to the present embodiment is a heat conduction type gas sensor for detecting the concentration of CO2 gas in the atmosphere, but is not particularly limited.

[0037] The detection circuit 10 includes thermistors Rd1, Rd2, a fixed resistor R1, and switches SW1, SW2. The thermistors Rd1, Rd2 are detection elements made of materials having a negative resistance temperature coefficient such as composite metal oxides, amorphous silicon, polycrystalline silicon, and germanium, for example. Both the thermistors Rd1, Rd2 detect the concentration of CO2 gas, but their operating temperatures are different from each other as will be described later. Here, the thermistor Rd1 constitutes a detection element, and the thermistor Rd2 constitutes a reference element.

[0038] Both the switches SW1, SW2 have one common node a and two selection nodes b, c, and one of the selection nodes b, c is connected to the common node a. As will be described later, both the switches SW1, SW2 are configured to select the selection node b during the measurement operation and select the selection node c during the virtual heating operation.

[0039] As Figure 1 shown, the common node a of the switch SW1 is connected to one end of the thermistor Rd1, the selection node b of the switch SW1 is connected to the selection node b of the switch SW2, and the selection node c of the switch SW1 is connected to one end of the fixed resistor R1. The other end of the thermistor Rd1 is connected to a variable power supply 25 supplying the power supply potential VDDS, and the other end of the fixed resistor R1 is connected to a wiring supplied with the ground potential GND. In addition, the common node a of the switch SW2 is connected to one end of the thermistor Rd2, the selection node b of the switch SW2 is connected to the selection node b of the switch SW1, and the selection node c of the switch SW2 is connected to the variable power supply 25. The other end of the thermistor Rd2 is connected to a wiring supplied with the ground potential GND.

[0040] Thus, when the measurement operation of selection node b is selected, the thermistors Rd1 and Rd2 are connected in series between the variable power supply 25 and the ground. On the other hand, when the virtual heating operation of selection node c is selected, the thermistor Rd1 and the fixed resistor R1 are connected in series between the variable power supply 25 and the ground, and the thermistor Rd2 is connected in parallel with the thermistor Rd1 and the fixed resistor R1. The resistance value of the fixed resistor R1 is, for example, 51 kΩ.

[0041] The control circuit 20 includes an AD converter (ADC) 21, DA converters (DAC) 22, 23, an MPU 24, and a variable power supply 25. The AD converter 21 performs AD conversion on the detection signal that appears at the selection node b of the switches SW1, SW2, that is, the detection signal that appears at the connection point between the thermistors Rd1 and Rd2 during the measurement operation, and supplies its value to the MPU 24. The MPU 24 generates an output signal OUT representing the concentration of CO2 gas based on the detection signal obtained by the AD conversion. In addition, the MPU 24 controls the connection relationship of the detection circuit 10 by controlling the switches SW1, SW2. The DA converters 22, 23 apply a specified voltage to the heater resistors MH1, MH2 by performing DA conversion on the digital value supplied from the MPU 24. That is, the heating temperature of the heater resistors MH1, MH2 is controlled by the MPU 24. The level of the power supply potential VDDS output from the variable power supply 25 is also controlled by the MPU 24.

[0042] Next, the operation of the gas sensor 1 of the present embodiment will be described.

[0043] Figure 2 is a timing chart for explaining the operation of the gas sensor 1 of the present embodiment.

[0044] As Figure 2 shown, based on the gas sensor 1 of the present embodiment, a measurement operation is performed during period T1, and a virtual heating operation is performed during period T2. The measurement operation and the virtual heating operation are performed alternately.

[0045] During the measurement operation performed during period T1, under the control of the MPU 24, the heater resistor MH1 is heated to 150 °C, and the heater resistor MH2 is heated to 300 °C. As Figure 3 shown, the temperature characteristics of the thermistors Rd1, Rd2 are different from each other, and are designed such that the resistance value of the thermistor Rd1 heated to 150 °C is close to the resistance value of the thermistor Rd2 heated to 300 °C. During Figure 3In the example shown, the resistance value of the thermistor Rd1 heated to 150 °C is 5.1 kΩ, and the resistance value of the thermistor Rd2 heated to 300 °C is 4.0 kΩ. The resistance value of the thermistor Rd1 heated to 150 °C and the resistance value of the thermistor Rd2 heated to 300 °C may also be substantially the same.

[0046] As described above, during the measurement operation, due to the selection nodes b of the selection switches SW1 and SW2, the thermistor Rd1 and the thermistor Rd2 are connected in series. In addition, the MPU 24 controls the variable power supply 25 to set the power supply potential VDDS during the measurement operation to the first level VDDS1. The first level VDDS1 is, for example, 2.7 V.

[0047] When there is CO2 gas in the measurement atmosphere in a state where the thermistor Rd1 as a detection element is heated to 150 °C, the heat dissipation characteristics of the thermistor Rd1 change according to its concentration. This change is manifested as a change in the resistance value of the thermistor Rd1. On the other hand, in a state where the thermistor Rd2 as a reference element is heated to 300 °C, even if there is CO2 gas in the measurement atmosphere, the heat dissipation characteristics of the thermistor Rd2 hardly change according to its concentration. Therefore, the change in the resistance value of the thermistor Rd2 heated to 300 °C caused by the concentration of CO2 gas is sufficiently small compared to the change in the resistance value of the thermistor Rd1 heated to 150 °C caused by the concentration of CO2 gas. The change in the resistance value of the thermistor Rd2 heated to 300 °C caused by the concentration of CO2 gas can be almost zero.

[0048] Thus, the level of the detection signal that appears at the connection point between the thermistor Rd1 and the thermistor Rd2 changes according to the concentration of CO2 gas in the measurement atmosphere. The detection signal is supplied to the MPU 24 via the AD converter 21, and the MPU 24 generates an output signal OUT representing the concentration of CO2 gas based on this.

[0049] During the virtual heating operation performed during the period T2, under the control of the MPU 24, the heater resistor MH1 is heated to 300 °C, and the heater resistor MH1 is heated to 150 °C. Thus, the difference in the thermal history between the thermistor Rd1 and the thermistor Rd2 during the measurement operation performed during the period T1 is canceled.

[0050] However, if the heating temperatures of the thermistors Rd1 and Rd2 during the virtual heating operation are simply swapped with those during the measurement operation, a small thermal history difference caused by the self-heating of the thermistors Rd1 and Rd2 will occur. That is, since the thermistor Rd1 is designed to have a specified resistance value when heated to 150°C and the thermistor Rd2 is designed to have a specified resistance value when heated to 300°C, if the heating temperatures of the two are swapped, the resistance value of the thermistor Rd2 becomes much higher than that of the thermistor Rd1. In Figure 3 the example shown, the resistance value of the thermistor Rd1 heated to 300°C is 0.4 kΩ, and the resistance value of the thermistor Rd2 heated to 150°C is 51.4 kΩ, resulting in a difference of more than a hundred times between the two resistance values. Therefore, during the virtual heating operation, just as during the measurement operation, when the thermistors Rd1 and Rd2 are connected in series, the self-heating amount of the thermistor Rd2 is larger than that of the thermistor Rd1.

[0051] Thus, in the present embodiment, switches SW1 and SW2 are used to switch the connection relationship of the detection circuit 10 during the virtual heating operation, thereby setting the currents flowing through the thermistor Rd1 and the thermistor Rd2 to different current amounts, and setting the power supply potential VDDS during the virtual heating operation to the second level VDDS2. The second level VDDS is, for example, 4.77 V.

[0052] In the case where the thermistors Rd1 and Rd2 are made of a material having a negative resistance temperature coefficient as in the present embodiment, the resistance value of the thermistor Rd2 during the virtual heating operation becomes very large. Therefore, during the virtual heating operation, it is necessary to make the current amount flowing through the thermistor Rd1 more than the current amount flowing through the thermistor Rd2. Thereby, the difference between the self-heating amount of the thermistor Rd1 during the virtual heating operation and the self-heating amount of the thermistor Rd2 during the virtual heating operation can be reduced.

[0053] Specifically, when the level of the power supply potential VDDS during the measurement operation is 2.7 V, the resistance value of the thermistor Rd1 heated to 150°C is 5.1 kΩ, and the resistance value of the thermistor Rd2 heated to 300°C is 4.0 kΩ, the power consumptions of the thermistors Rd1 and Rd2 during the measurement operation are 0.442 mW and 0.349 mW, respectively. Moreover, when the level of the power supply potential VDDS during the virtual heating operation is 4.77 V, the resistance value of the thermistor Rd1 heated to 300°C is 0.4 kΩ, and the resistance value of the thermistor Rd2 heated to 150°C is 51.4 kΩ, the power consumptions of the thermistors Rd1 and Rd2 during the virtual heating operation are 0.349 mW and 0.442 mW, respectively. In this case, if the heating times of the heater resistors MH1 and MH2 during the period T1 are made the same as the heating times of the heater resistors MH1 and MH2 during the period T2, not only can the difference in self-heating amounts between the thermistor Rd1 during the virtual heating operation and the thermistor Rd2 during the virtual heating operation be reduced, but also the self-heating amount of the thermistor Rd1 during the measurement operation and the self-heating amount of the thermistor Rd2 during the virtual heating operation are approximately the same, and the self-heating amount of the thermistor Rd1 during the measurement operation and the self-heating amount of the thermistor Rd2 during the virtual heating operation are approximately the same. Therefore, the thermal history difference caused by self-heating is almost completely canceled out.

[0054] However, in the present embodiment, it is not necessary to make the self-heating amount of the thermistor Rd1 during the measurement operation exactly the same as the self-heating amount of the thermistor Rd2 during the virtual heating operation, and to make the self-heating amount of the thermistor Rd1 during the measurement operation exactly the same as the self-heating amount of the thermistor Rd2 during the virtual heating operation. It is only necessary to reduce the self-heating amount difference by independently controlling the current amounts flowing through the thermistors Rd1 and Rd2 during the virtual heating operation. Therefore, it is not necessary to switch the level of the power supply potential VDDS during the measurement operation and the virtual heating operation either.

[0055] In addition, it is not necessary to make the current amount flowing through the thermistor Rd1 during the virtual heating operation larger than the current amount flowing through the thermistor Rd2. In cases where the conditions are different from those of the present embodiment, such as when the thermistors Rd1 and Rd2 are made of a material having a positive resistance temperature coefficient, during the virtual heating operation, the current amount flowing through the thermistor Rd1 may be made smaller than the current amount flowing through the thermistor Rd2.

[0056] Moreover, it is not necessary to strictly swap the heating temperatures of the thermistors Rd1 and Rd2 during the virtual heating operation with those during the measurement operation. As long as the difference in the thermal history between the thermistor Rd1 and the thermistor Rd2 is reduced, it is also possible to set the heating temperatures of the thermistors Rd1 and Rd2 during the virtual heating operation by considering the heating time, the ambient temperature, the self-heating amount, etc.

[0057] Figure 4 FIG. is a circuit diagram showing the structure of the gas sensor 2 according to the second embodiment of the technology of the present disclosure.

[0058] As Figure 4 shown, in the gas sensor 2 of the second embodiment, the fixed resistor R1 and the variable power supply 25 are omitted, and instead, a variable current source 26 and a fixed current source 27 are included in the control circuit 20, which is different from the gas sensor 1 of the first embodiment. The other basic structure is the same as that of the gas sensor 1 of the first embodiment, so the same reference numerals are assigned to the same elements, and the repeated description is omitted.

[0059] The variable current source 26 is connected to the other end of the thermistor Rd1, and the fixed current source 27 is connected to the selection node c of the switch SW2. Thus, during the measurement operation of selecting the selection node b, the thermistor Rd1 and the thermistor Rd2 are connected in series with the variable current source 26. On the other hand, during the virtual heating operation of selecting the selection node c, the thermistor Rd1 is connected to the variable current source 26, and the thermistor Rd2 is connected to the fixed current source 27.

[0060] Figure 5 FIG. is a timing chart for explaining the operation of the gas sensor 2 of the present embodiment.

[0061] As Figure 5 shown, also in the present embodiment, during the measurement operation performed during the period T1, the heater resistors MH1 and MH2 are heated to 150°C and 300°C, respectively, and during the virtual heating operation performed during the period T2, the heater resistors MH1 and MH2 are heated to 300°C and 150°C, respectively. In addition, during the measurement operation, the amount of the operation current IDDS1 supplied from the variable current source 26 is set to I1. Thus, during the measurement operation, the amount of current flowing through the thermistors Rd1 and Rd2 becomes I1. The amount of current I1 is, for example, 0.293 mA. Moreover, when the resistance value of the thermistor Rd1 heated to 150°C is 5.1 kΩ and the resistance value of the thermistor Rd2 heated to 300°C is 4.0 kΩ, the power consumption of the thermistors Rd1 and Rd2 during the measurement operation is 0.442 mW and 0.349 mW, respectively.

[0062] In contrast, during the virtual heating operation, the amount of the operation current IDDS1 supplied from the variable current source 26 is set to I2. The amount of the operation current IDDS2 supplied from the fixed current source 27 is I3 (<I2). Thus, during the virtual heating operation, the amount of current flowing through the thermistor Rd1 becomes I2, and the amount of current flowing through the thermistor Rd2 becomes I3. For example, the amount of current I2 is 0.927 mA, and the amount of current I3 is 0.093 mA. Further, when the resistance value of the thermistor Rd1 heated to 300°C is 0.4 kΩ and the resistance value of the thermistor Rd2 heated to 150°C is 51.4 kΩ, the power consumptions of the thermistors Rd1 and Rd2 during the virtual heating operation are 0.349 mW and 0.442 mW, respectively.

[0063] Therefore, if the heating time of the heater resistors MH1 and MH2 in the period T1 is made the same as the heating time of the heater resistors MH1 and MH2 in the period T2, the self-heat generation amount of the thermistor Rd1 during the measurement operation is approximately the same as the self-heat generation amount of the thermistor Rd2 during the virtual heating operation, and the self-heat generation amount of the thermistor Rd1 during the measurement operation is approximately the same as the self-heat generation amount of the thermistor Rd2 during the virtual heating operation.

[0064] As exemplified in the second embodiment, by using a plurality of current sources, different currents can flow through the thermistors Rd1 and Rd2 during the virtual heating operation.

[0065] The embodiments of the present disclosure have been described above, but the present disclosure is not limited to the above-described embodiments, and various changes can be made without departing from the gist of the present disclosure, and these are of course included in the scope of the present disclosure.

[0066] For example, in the above embodiment, the case where the measurement target gas is CO2 gas has been described as an example, but the present invention is not limited thereto. In addition, the sensor unit used in the present invention does not necessarily have to be a heat conduction type sensor, and other types of sensors such as a catalytic combustion type may be used. As an example, when the measurement target gas is CO gas, a catalytic combustion type sensor unit can be used.

[0067] The technology of the present disclosure includes but is not limited to the following structural examples.

[0068] The gas sensor of the present disclosure includes: a detection circuit including a first thermistor and a second thermistor; a first heater and a second heater that respectively heat the first thermistor and the second thermistor; and a control circuit that controls the connection relationship of the detection circuit and the heating temperatures of the first heater and the second heater. During a first period, the control circuit heats the second heater to a higher temperature than the first heater and connects the first thermistor and the second thermistor in series, thereby generating an output signal representing the concentration of the gas to be measured based on the detection signal that appears at the connection point between the first thermistor and the second thermistor. During a second period, the control circuit heats the first heater to a higher temperature than the second heater and switches the connection relationship so that the amount of current flowing through the first thermistor is different from the amount of current flowing through the second thermistor. Thereby, the difference in self-heating amount between the first thermistor and the second thermistor during the second period can be reduced.

[0069] In the above gas sensor, it may also be that the control circuit heats the first heater and the second heater to a first temperature and a second temperature respectively during the first period, and heats the second heater and the first heater to the first temperature and the second temperature respectively during the second period. Thereby, the difference in the thermal history received from the heaters can be reduced.

[0070] In the above gas sensor, it may also be that the heating times of the first heater and the second heater during the first period are the same as the heating times of the first heater and the second heater during the second period. Thereby, the difference in the thermal history received from the heaters can be further reduced.

[0071] In the above gas sensor, it may also be that the first thermistor and the second thermistor contain materials having a negative resistance temperature coefficient, and the control circuit switches the connection relationship during the second period so that the current flowing through the first thermistor is more than the current flowing through the second thermistor. Thereby, even if the resistance of the second thermistor is higher than the resistance of the first thermistor during the second period, the difference in self-heating amount can be reduced.

[0072] In the above gas sensor, it may also be that the detection circuit further includes a fixed resistor, and the control circuit connects the first thermistor in series with the fixed resistor and connects the second thermistor in parallel with the first thermistor and the fixed resistor during the second period. Thereby, the amount of current flowing through the first thermistor during the second period can be adjusted.

[0073] In the above-described gas sensor, alternatively, the control circuit applies a first voltage to a series circuit including the first thermistor and the second thermistor during a first period, and applies a second voltage different from the first voltage to a series circuit including the first thermistor and a fixed resistor during a second period. Thereby, the difference in self-heating amounts between the first thermistor and the second thermistor during the second period can be further reduced.

[0074] In the above-described gas sensor, alternatively, the control circuit includes a first current source and a second current source. During a first period, the first current source is used to supply current to the first thermistor and the second thermistor connected in series; during a second period, the first current source is used to supply current to the first thermistor. Thereby, different currents can be easily supplied to the first thermistor and the second thermistor during the second period.

[0075] In the above-described gas sensor, alternatively, the control circuit controls the current flowing through the first thermistor and the second thermistor such that: the self-heating amount of the first thermistor during the first period is the same as the self-heating amount of the second thermistor during the second period, and the self-heating amount of the second thermistor during the first period is the same as the self-heating amount of the first thermistor during the second period. Thereby, the difference in thermal history caused by the self-heating of the first thermistor and the second thermistor can be substantially completely canceled out.

Claims

1. A gas sensor, wherein, Comprising: A detection circuit including a first thermistor and a second thermistor; A first heater and a second heater for heating the first thermistor and the second thermistor respectively; And A control circuit for controlling the connection relationship of the detection circuit and the heating temperatures of the first heater and the second heater, In a first period, the control circuit heats the second heater to a higher temperature than the first heater, and connects the first thermistor and the second thermistor in series, thereby generating an output signal representing the concentration of the gas to be measured based on the detection signal appearing at the connection point of the first thermistor and the second thermistor; In a second period, the control circuit heats the first heater to a higher temperature than the second heater, and switches the connection relationship so that the amount of current flowing through the first thermistor is different from the amount of current flowing through the second thermistor.

2. The gas sensor according to claim 1, wherein, The control circuit heats the first heater and the second heater to a first temperature and a second temperature respectively in the first period, and heats the second heater and the first heater to the first temperature and the second temperature respectively in the second period.

3. The gas sensor according to claim 2, wherein, The heating times of the first heater and the second heater in the first period are the same as the heating times of the first heater and the second heater in the second period.

4. The gas sensor according to any one of claims 1 to 3, wherein, The first thermistor and the second thermistor comprise materials having a negative temperature coefficient of resistance, The control circuit switches the connection relationship in the second period so that the current flowing through the first thermistor is more than the current flowing through the second thermistor.

5. The gas sensor according to claim 4, wherein, The detection circuit further includes a fixed resistor, The control circuit connects the first thermistor in series with the fixed resistor in the second period, and connects the second thermistor in parallel with the first thermistor and the fixed resistor.

6. The gas sensor according to claim 5, wherein, The control circuit applies a first voltage to the series circuit including the first thermistor and the second thermistor in the first period, and applies a second voltage different from the first voltage to the series circuit including the first thermistor and the fixed resistor in the second period.

7. The gas sensor according to claim 4, wherein, The control circuit includes a first current source and a second current source. In the first period, the first current source is used to supply current to the first thermistor and the second thermistor connected in series; in the second period, the first current source is used to supply current to the first thermistor, and the second current source is used to supply current to the second thermistor.

8. The gas sensor according to any one of claims 1 to 3, wherein the control circuit controls the current flowing through the first thermistor and the second thermistor so that: the self-heating amount of the first thermistor in the first period is the same as the self-heating amount of the second thermistor in the second period, and the self-heating amount of the second thermistor in the first period is the same as the self-heating amount of the first thermistor in the second period.

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