阅读说明：本技术 一种基于ntc测温线性处理电路 (Temperature measurement linear processing circuit based on NTC ) 是由 许建波 周俊 陈方良 李锋 于 2021-07-06 设计创作，主要内容包括：本发明公开了一种基于NTC测温线性处理电路,包括恒流电路；一级跟随滤波电路,用于对恒流源作用在NTC电阻RT上产生的初级电压进行一级跟随处理,得到NTC电阻RT两端输入电压；对数运算电路,用于RT端电压进行对数运算处理,得到对数运算电路输出电压；差分抬升电路,用于对对数运算电路输出电压进行电压抬升处理,得到放大信号修正值；差分运算放大电路,用于对数运算电路输出电压信号进行运算放大处理,得到差分运算放大电压；除法器基准电路,用于对除法运算电路做被除数常数处理,得到常数；除法运算电路用于对差分放大后的电压进行除法运算处理,得到与NTC电阻温度T-(1)值成线性比的输出电压。提高了非线性测温器件测温精度。(The invention discloses a temperature measurement linear processing circuit based on an NTC (negative temperature coefficient), which comprises a constant current circuit; the first-stage following filter circuit is used for carrying out first-stage following processing on a primary voltage generated by the constant current source acting on the NTC resistor RT to obtain input voltages at two ends of the NTC resistor RT; the logarithm operation circuit is used for carrying out logarithm operation processing on the RT terminal voltage to obtain the output voltage of the logarithm operation circuit; the differential lifting circuit is used for carrying out voltage lifting processing on the output voltage of the logarithmic operation circuit to obtain an amplification signal correction value; the differential operational amplification circuit is used for carrying out operational amplification processing on the voltage signal output by the logarithmic operation circuit to obtain differential operational amplification voltage; the divider reference circuit is used for carrying out dividend constant processing on the division operation circuit to obtain a constant; the division operation circuit is used for carrying out division operation processing on the voltage after differential amplification to obtain the temperature T of the NTC resistor 1 The output voltage of which the value is linear ratio. The temperature measurement precision of the nonlinear temperature measurement device is improved.)

1. An NTC-based temperature measurement linear processing circuit, comprising:

the constant current circuit is used for providing a constant current source;

the first-stage following filter circuit is used for carrying out first-stage following processing on a primary voltage generated by the constant current source acting on the NTC resistor RT to obtain input voltages at two ends of the NTC resistor RT;

the logarithm operation circuit is used for carrying out logarithm operation processing on the RT terminal voltage of the NTC resistor to obtain the output voltage of the logarithm operation circuit linearly related to the NTC resistor;

the differential lifting circuit is used for carrying out voltage lifting processing on the output voltage of the logarithmic operation circuit to obtain an amplification signal correction value;

the differential operational amplification circuit is used for carrying out operational amplification processing on the voltage signal output by the logarithmic operation circuit to obtain differential operational amplification voltage;

the divider reference circuit is used for calculating the division operation circuit and performing dividend constant processing to obtain a constant;

the division operation circuit is used for carrying out division operation processing on the voltage after differential amplification to finally obtain the temperature T of the NTC resistor₁The output voltage of which the value is linear ratio.

2. The NTC temperature measurement-based linear processing circuit of claim 1, wherein the constant current circuit comprises a constant current source exciting circuit, a constant current follower circuit;

the constant current source exciting circuit includes: the circuit comprises a first resistor R1, a second resistor R2, a three-section adjustable shunt reference voltage source D1 and a third resistor R3; one end of the first resistor R1 is connected with a power supply, and the other end is connected with a 3-pin negative pin of a three-section adjustable shunt reference voltage source D1; one end of the second resistor R2 is connected with the 3 pin of the three-section adjustable shunt reference voltage source D1, and the other end is connected with the 1 pin of the three-section adjustable shunt reference voltage source D1; one end of the third resistor R3 is connected with the 1 pin of the three-section adjustable shunt reference voltage source D1, the other end is connected with the 2 pin of the three-section adjustable shunt reference voltage source D1, and the 2 pin of the three-section adjustable shunt reference voltage source D1 is grounded;

the constant current follower circuit comprises a first voltage stabilizing diode D2, a fourth resistor R4, a second voltage stabilizing diode D3, an NTC resistor RT and a first operational amplifier U1A; the positive end of the first voltage stabilizing diode D2 is connected with the pin 2 of the first operational amplifier U1A, and the negative end is connected with the pin 3 of the first operational amplifier U1A; 4 pins of the first operational amplifier U1A are connected with the positive electrode of a power supply, and 8 pins of the first operational amplifier U1A are connected with the negative electrode of the power supply; the end signal of the 3 pin of the adjustable shunt reference voltage source D1 is connected with the 3 pin of the first operational amplifier U1A; one end of a fourth resistor R4 is connected with the pin 2 of the first operational amplifier U1A, and the other end of the fourth resistor R4 is grounded; the positive end of the second voltage stabilizing diode D3 is connected with the pin 2 of the first operational amplifier U1A, and the negative end is connected with the pin 1 of the first operational amplifier U1A; one end of the NTC resistor RT is connected to the negative terminal of the second zener diode D3, and the other end is connected to the positive terminal of the second zener diode D3, and is connected in parallel to the second zener diode D3.

3. The NTC temperature measurement-based linear processing circuit of claim 2, wherein the first stage follower filter circuit is composed of a second operational amplifier U1B, a forward input resistor R5;

the positive end input resistor R5 is connected with the positive potential end of the NTC resistor RT and the positive end of the second operational amplifier U1B, and the output end of the second operational amplifier U1B is connected with the negative phase end to form a voltage follower.

4. The NTC temperature measurement-based linear processing circuit of claim 1, wherein the logarithmic operation circuit comprises a third operational amplifier U2A, a diode D4, an input resistor R6, a forward terminal to ground resistor R7;

one end of the input resistor R6 is connected with the first-stage following filter circuit, and the other end of the input resistor R6 is connected with a pin 7 of the second operational amplifier U1B; one end of a ground resistor R7 is connected with the pin 3 of the third operational amplifier U2A, and the other end is grounded; the positive terminal of the diode D4 is connected to pin 2 of the third operational amplifier U2A, and the negative terminal of the diode D4 is connected to pin 1 of the third operational amplifier U2A.

5. The NTC temperature measurement-based linear processing circuit of claim 1, wherein the differential operation boost circuit comprises a fifth resistor R8, a sixth resistor R9, a seventh resistor R10, an eighth resistor R11, a ninth resistor R12 and a first voltage regulator tube D5;

one end of the fifth resistor R8 is connected with the anode of the power supply, and the other end is connected with the pin 3 of the first voltage regulator tube D5; one end of the sixth resistor R9 is connected with the pin 3 of the first voltage regulator tube D5, and the other end is connected with the pin 1 of the first voltage regulator tube D5; one end of the seventh resistor R10 is grounded, the other end is connected with pin 1 of the first voltage regulator tube D5, and pin 2 of the first voltage regulator tube D5 is grounded; one end of the eighth resistor R11 is connected with pin 3 of the first voltage regulator tube D5, and the other end is connected with the ninth resistor R12; the other end of the ninth resistor R12 is grounded.

6. The NTC-based thermometric linear processing circuit of claim 1, wherein the differential operational amplifier circuit comprises a fourth operational amplifier U2B, a first proportional resistor R14, a second proportional resistor R16, a first proportional symmetric resistor R13, a second proportional symmetric resistor R15;

one end of the first proportional symmetrical resistor R13 is connected with the differential operational amplifier circuit, and the other end is connected with a pin 5 of the fourth operational amplifier U2B; one end of the first proportional resistor R14 is connected with GND, and the other end is connected with a pin 6 of the fourth operational amplifier U2B; one end of the second proportional resistor R16 is connected with the 6 pin of the fourth operational amplifier U2B, and the other end is connected with the 7 pin of the fourth operational amplifier U2B; one end of the second proportional symmetrical resistor R15 is connected with the 5 pin of the fourth operational amplifier U2B, and the other end is connected with the differential lifting circuit.

7. The NTC based thermometric linear processing circuit according to claim 1, wherein the divider reference circuit is composed of a second voltage regulator tube D6, a third proportional resistor R21, a fourth proportional resistor R22, and a power limiting resistor R20;

one end of the power limiting resistor R20 is connected with the anode of the power supply, and the other end is connected with the pin 3 of the second voltage regulator tube D6; one end of the third proportional resistor R21 is connected with the pin 3 of the second voltage regulator tube D6, and the other end is connected with the pin 1 of the second voltage regulator tube D6; one end of the fourth proportional resistor R22 is connected with pin 1 of the second voltage regulator tube D6, and the other end is grounded; pin 2 of the second voltage regulator tube D6 is grounded; the pin 3 of the second voltage regulator tube D6 is connected with one end of a tenth resistor R17, and the other end of the tenth resistor R17 is connected with the pin 2 of a fifth operational amplifier U3A.

8. The NTC temperature measurement based linear processing circuit of claim 1, wherein the division circuit comprises a sixth operational amplifier U3A, a multiplier, a tenth resistor R17, an eleventh resistor R18, a twelfth resistor R19; the tenth resistor R17 is connected with the divider reference circuit, the other end of the tenth resistor R17 is connected with the 2 pin of the sixth operational amplifier U3A, one end of the eleventh resistor R18 is connected with the 2 pin of the sixth operational amplifier U3A, and the other end of the eleventh resistor R18 is connected with the 7 pin of the multiplier; one end of the twelfth resistor R19 is connected with the pin 3 of the sixth operational amplifier U3A, and the other end is grounded; and a pin 6 of the multiplier is connected with a pin 1 of a sixth operational amplifier U3A.

9. The NTC-based thermometry linear processing circuit of claim 1, wherein the processed output voltage V_OUTAnd NTC resistance temperature T₁The relationship of the values is:

wherein V_OUTTo the final output voltage, T₁Is the NTC resistor temperature, B is the temperature constant of the NTC resistor, Vref3 provides the dividend constant, V, for the divider reference circuit_TIs the reverse cutoff voltage.

Technical Field

The invention belongs to the technical field of NTC temperature measurement application, and particularly relates to a linear processing circuit based on NTC temperature measurement.

Background

In recent years, NTC is widely applied to temperature measurement modules in various industries as a high-resolution temperature sampling sensing device, but the NTC has the defects of low linearity of resistance and temperature curve, and the like, so that it is difficult for design operators to sample temperature during use, and a mathematical linear fitting method often has deviation and also brings certain difficulty.

Disclosure of Invention

The invention aims to provide a linear processing circuit based on NTC temperature measurement, aiming at the nonlinear-linear processing of an NTC temperature detection circuit so as to improve the temperature measurement precision of the nonlinear temperature measurement device.

The technical solution for realizing the purpose of the invention is as follows:

an NTC-based thermometry linear processing circuit comprising:

the constant current circuit is used for providing a constant current source;

the first-stage following filter circuit is used for carrying out first-stage following processing on a primary voltage generated by the constant current source acting on the NTC resistor RT to obtain input voltages at two ends of the NTC resistor RT;

the logarithm operation circuit is used for carrying out logarithm operation processing on the RT terminal voltage of the NTC resistor to obtain the output voltage of the logarithm operation circuit linearly related to the NTC resistor;

the differential lifting circuit is used for carrying out voltage lifting processing on the output voltage of the logarithmic operation circuit to obtain an amplification signal correction value;

the differential operational amplification circuit is used for carrying out operational amplification processing on the voltage signal output by the logarithmic operation circuit to obtain differential operational amplification voltage;

the divider reference circuit is used for calculating the division operation circuit and performing dividend constant processing to obtain a constant;

the division operation circuit is used for carrying out division operation processing on the voltage after differential amplification to finally obtain the temperature T of the NTC resistor₁The output voltage of which the value is linear ratio.

Compared with the prior art, the invention has the following remarkable advantages:

the invention can realize the linear conversion of the output electric signal and the temperature resistor by the circuit configuration of the hardware parameters and the general hardware principle, does not need the participation of a software algorithm, can realize the linear real-time conversion of the temperature by configuring the hardware parameters, and is simple and rapid.

Drawings

Fig. 1 is a schematic block diagram of an NTC linear conversion circuit.

Fig. 2 is an enlarged view of the constant current source excitation circuit.

Fig. 3 is an enlarged view of the constant current circuit and the first-stage following filter circuit.

Fig. 4 is an enlarged view of the logarithmic operation circuit.

Fig. 5 is an enlarged view of the differential operational amplifier circuit.

Fig. 6 is an enlarged view of the division circuit.

FIG. 7 is an enlarged view of the differential lift circuit.

Fig. 8 is an enlarged view of the division reference circuit.

Detailed Description

The invention is further described with reference to the following figures and embodiments.

With reference to fig. 1, the NTC-based temperature measurement linear processing circuit of the present invention includes a constant current circuit, a first-stage following filter circuit, a logarithmic operation circuit, a differential operational amplifier circuit, a differential boost circuit, a trigger reference circuit, and a division operation circuit;

the constant current circuit is used for exciting a voltage V_ref1Processing a current source generated at a fourth resistor R4 to obtain a constant current source I; the constant current circuit comprises a constant current source exciting circuit and a constant current circuit.

The constant current circuit performs constant current filtering processing by utilizing the virtual short principle of operational amplifier, and the processing process comprises the following steps:

the constant voltage generated by the TL431 voltage stabilizer by the exciting voltage is connected with a fourth resistor R4 through the positive end and the negative end of the operational amplifier to generate a primary side constant current source I_in＝V_ref1the/R4 is based on the principle of operational amplifier U1A virtual short_in＝I。

(1) The constant current source exciting circuit includes: the circuit comprises a first resistor R1, a second resistor R2, a three-section adjustable shunt reference voltage source D1 and a third resistor R3;

the +/-15V power supply is connected with one end of a first resistor R1, and the other end of the first resistor R1 is connected with a 3-pin negative pin of the three-section adjustable shunt reference voltage source D1; one end of the second resistor R2 is connected with the 3 pin of the three-section adjustable shunt reference voltage source D1, and the other end is connected with the 1 pin of the three-section adjustable shunt reference voltage source D1; one end of the third resistor R3 is connected to the 1 pin of the three-segment adjustable shunt reference voltage source D1, the other end is connected to the 2 pin of the three-segment adjustable shunt reference voltage source D1, and the 2 pin of the three-segment adjustable shunt reference voltage source D1 is grounded.

Wherein R is₃、R₂As a TL431 constant voltage output proportional resistor, R1 is used as a power limiting resistor of a TL431 voltage stabilizing tube, and the voltage stabilizing tube is prevented from being burnt by overlarge excitation current.

Constant current source excitation voltage V provided by the constant current source excitation circuit_ref1Comprises the following steps:

wherein V is the voltage of the constant current source excitation circuit.

(2) The constant current follower circuit comprises a first voltage stabilizing diode D2, a fourth resistor R4, a second voltage stabilizing diode D3, an NTC resistor RT and a first operational amplifier U1A.

The positive end of the first voltage stabilizing diode D2 is connected with the pin 2 of the first operational amplifier U1A, and the negative end is connected with the pin 3 of the first operational amplifier U1A; the 4 pins of the first operational amplifier U1A are connected to the +/-15V power supply, and the 8 terminal of the first operational amplifier U1A is connected to the-15V power supply; 3-pin terminal V of adjustable shunt reference voltage source D1_ref1The signal is connected with a pin 3 of a first operational amplifier U1A; one end of the fourth resistor R4 is connected to pin 2 of the first operational amplifier U1A, and the other end of the fourth resistor R4 is grounded. The positive end of the second voltage stabilizing diode D3 is connected with the 2 pin of the first operational amplifier U1A, and the negative end is connected with the 1 pin of the first operational amplifier U1A. One end of the NTC resistor RT is connected to the negative terminal of the second zener diode D3, and the other end is connected to the positive terminal of the second zener diode D3, and is connected in parallel to the second zener diode D3.

The first operational amplifier U1A adopts double operational amplifiers, the first voltage stabilizing diode D2 is used as the front stage voltage stabilizing diode of the first operational amplifier U1A, the second voltage stabilizing diode D3 is used as the rear-end voltage stabilizing diode, and the fourth resistor R4 is a constant current resistor.

Voltage V across NTC resistor RT_iComprises the following steps:

the first-stage following filter circuit is used for carrying out first-stage following processing on a primary voltage generated by the constant current source acting on the NTC resistor RT to obtain a stable input voltage V at two ends of the NTC resistor RT_i。

The first-stage following filter circuit consists of a second operational amplifier U1B and a forward end input resistor R5;

the positive end input resistor R5 is connected with the positive potential end of the NTC resistor RT and the positive end of the second operational amplifier U1B, and the output end of the second operational amplifier U1B is connected with the negative phase end to form a voltage follower. The forward input resistor R5 acts as the resistance of the NTC resistor RT terminal potential to the input of the second operational amplifier U1B.

The second operational amplifier U1B adopts a TL082 type dual operational amplifier, and is characterized by low input bias voltage and offset current, short-circuit protection at the output, high input impedance at the input stage, built-in frequency compensation circuit and high slew rate.

The logarithm operation circuit is used for carrying out logarithm operation processing on the RT end voltage of the NTC resistor to obtain a parameter linearly related to the NTC resistor.

The logarithmic operation circuit comprises a third operational amplifier U2A, a diode D4, an input resistor R6 and a forward end to ground resistor R7;

one end of the input resistor R6 is connected with the 2 pin of the third operational amplifier U2A, and the other end of the input resistor R6 is connected with the 7 pin of the second operational amplifier U1B; one end of a ground resistor R7 is connected with the pin 3 of the third operational amplifier U2A, and the other end is grounded; the positive terminal of the diode D4 is connected to pin 2 of the third operational amplifier U2A, and the negative terminal of the diode D4 is connected to pin 1 of the third operational amplifier U2A.

The logarithm operation circuit performs logarithm extraction linear correlation term processing, namely logarithm extraction processing is performed on the voltage of the RT acquisition terminal. The treatment process comprises the following steps:

the logarithmic characteristic of the current and the voltage of the diode D4 and the characteristic of the virtual short and the virtual break of the operational amplifier are utilized to obtain the output voltage V of the logarithmic operation circuit_out1。

Wherein V_INOutputting voltage for the constant current circuit; i is_SIs the saturation current through diode D4; v_TThe reverse cutoff voltage of diode D4.

Wherein the input resistor R6 is connected with the output end of the first-stage following filter circuit.

The differential operational amplification circuit is used for carrying out logarithmic processing on the sampling voltage signal; then outputs voltage V to the logarithmic operation circuit_OUT1(V_OUT1Smaller is mV level) signal to obtain differential operational amplification voltage V_OUT2。

The differential operational amplifier circuit comprises a fourth operational amplifier U2B, proportional resistors R14 and R16 and proportional symmetrical resistors R13 and R15;

one end of the first proportional symmetrical resistor R13 is connected with pin 1 of the third operational amplifier U2A, and the other end of the first proportional symmetrical resistor R13 is connected with pin 5 of the fourth operational amplifier U2B; one end of the first proportional resistor R14 is connected with GND, and the other end is connected with a pin 6 of the fourth operational amplifier U2B; one end of the second proportional resistor R16 is connected to the 6 pin of the fourth operational amplifier U2B, and the other end is connected to the 7 pin of the fourth operational amplifier U2B. One end of the second proportional symmetrical resistor R15 is connected with the 5 pin of the fourth operational amplifier U2B, and the other end is connected with the middle of the eighth resistor R11 and the ninth resistor R12 of the differential lifting circuit.

And the differential operational amplification circuit and the differential lifting circuit carry out signal joint processing.

The differential lifting circuit is used for outputting a voltage V to the logarithmic operation circuit_OUT1And carrying out voltage lifting processing to obtain an amplification signal correction value.

The differential operation lifting circuit comprises a fifth resistor R8, a sixth resistor R9, a seventh resistor R10, an eighth resistor R11, a ninth resistor R12 and a first voltage regulator tube D5(TL 431);

one end of the fifth resistor R8 is connected with plus 15V, and the other end is connected with pin 3 of the first voltage regulator tube D5; one end of the sixth resistor R9 is connected with the pin 3 of the first voltage regulator tube D5, and the other end is connected with the pin 1 of the first voltage regulator tube D5; one end of the seventh resistor R10 is grounded, the other end is connected with pin 1 of the first voltage regulator tube D5, and pin 2 of the first voltage regulator tube D5 is grounded; one end of the eighth resistor R11 is connected with pin 3 of the first voltage regulator tube D5, and the other end is connected with the ninth resistor R12; the other end of the ninth resistor R12 is grounded.

The differential operation lifting circuit lifts the voltage of the differential operation amplifying circuit;

output voltage V of differential operational amplifier circuit_OUT2：

V_OUT2＝V_out1*(R16/R14)+2.5*(R9/R10)*R12/(R11+R12)

Wherein R13, R14, R15 and R16 are used as differential operational amplifier proportional resistors, and R8 is used as a first power limiting resistor of a voltage regulator tube D5(TL431), so that the first voltage regulator tube D5 is prevented from being burnt by overlarge current. The constant "2.5" in the formula is the amplification of the first zener diode D5 (diode).

Wherein: r13 ═ R14

R15＝R16

The divider reference circuit is used for calculating the division operation circuit; performing dividend constant processing to obtain a constant;

the divider reference circuit consists of a second voltage regulator tube D6(TL431), proportional resistors R21 and R22 and a power limiting resistor R20;

one end of the power limiting resistor R20 is connected to +/-15V, and the other end is connected to pin 3 of the second voltage regulator tube D6; one end of the third proportional resistor R21 is connected with the pin 3 of the second voltage regulator tube D6, and the other end is connected with the pin 1 of the second voltage regulator tube D6; one end of the fourth proportional resistor R22 is connected with pin 1 of the second voltage regulator tube D6, and the other end is grounded; pin 2 of the second voltage regulator tube D6 is grounded; the pin 3 of the second voltage regulator tube D6 is connected with one end of a tenth resistor R17, and the other end of the tenth resistor R17 is connected with the pin 2 of a fifth operational amplifier U3A.

The divider reference circuit provides a dividend constant V_ref3The treatment process comprises the following steps:

V_ref3＝2.5*(1+R21/R22)

wherein R21, R22 are as proportional resistance, and power limiting resistance R20 is as second steady voltage D6(TL431) power limiting resistance, prevent that the electric current is too big to burn out first stabilivolt D5. The constant "2.5" in the formula is the amplification of the second regulated voltage D6 (diode).

The division operation circuit is used for carrying out differential amplification on the signal V_out2Performing division operation to obtain final output voltage V_OUT；

The division operation circuit comprises a sixth operational amplifier U3A, a multiplier, resistors R17, R18 and R19;

the multiplier can be directly obtained by a multiplier chip, the tenth resistor R17 is connected with the negative phase terminal of the sixth operational amplifier U3A, the eleventh resistor R18 is the input resistor of the multiplier, and the twelfth resistor R19 is the positive phase terminal of the operational amplifier and the ground resistor.

A tenth resistor R17 is connected with the pin 3 of the second voltage regulator tube D6, the other end of the tenth resistor R17 is connected with the pin 2 of the sixth operational amplifier U3A, one end of an eleventh resistor R18 is connected with the pin 2 of the sixth operational amplifier U3A, and the other end of the eleventh resistor R18 is connected with the pin 7 of the multiplier multi; one end of the twelfth resistor R19 is connected with the pin 3 of the sixth operational amplifier U3A, and the other end is grounded; and a pin 6 of the multiplier is connected with a pin 1 of a sixth operational amplifier U3A.

The division operation circuit performs signal division processing; division operation circuit input voltage U₀₁Comprises the following steps:

U_O1＝K×V_ref3×V_OUT

R₁₇＝R₁₈

wherein K is the multiplication coefficient of the multiplier MULTIPILERB and can be freely selected and matched.

NTC resistance temperature T₁Comprises the following steps:

(NTC temperature and resistance value of resistance push-type)

B is the temperature constant of the NTC resistor, the temperature constant is selected according to the difference of NTC resistance materials, and a general NTC resistor data manual is embodied;

r is the resistance value of NTC at the normal temperature of 20 ℃; t is₂The temperature is normal temperature, and is generally 20 ℃; according to the configuration

Will T₁Into the above formula, V_OUTAnd temperature T₁Is in direct proportion; as shown in the following formula:

wherein T is₁Proportional to lnR_T

Wherein the content of the first and second substances,at infinitesimal small quantity, approximately 0, or at the time of hardware parameter configurationWherein the calculation is based on the configuration circuitIs a constant; then V_OUTAnd NTC resistance temperature T₁The value is linear ratio:

I_Sis the saturation current through diode D4; i is_RIs a constant current through resistor RT.

The NTC-based temperature measurement linear processing circuit utilizes hardware parameters (such as resistance, capacitance, diode, operational amplifier and the like) to process NTC resistance end potential acquisition voltage signals according to NTC temperature resistance characteristics, and finally outputs voltage signals V_OUTWith the measured temperature T₁Is in direct proportion.