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 1999 Microchip Technology Inc. DS00685B-page 1 AN685 INTRODUCTION There is a variety of temperature sensors on the market all of which meet specific application needs. The most common sensors that are used to solve these applica- tion problems include the thermocouple, Resistive Temperature Detector (RTD) thermistor, and sili- con-based sensors. For an overview and comparison of these sensors, refer to Microchip’s AN679, “Temper- ature Sensing Technologies”. This application note focuses on circuit solutions that use Negative Temperature Coefficient (NTC) ther- mistors in the design. The Thermistor has a non-linear resistance change-over temperature. The degree of this non-linearity will be discussed in the “Hardware Linearization Solutions” section of this application note. From this discussion, various linearization resistor net- works will be shown with error analysis included. Finally, the signal conditioning path for the thermistor system will be covered with complete application cir- cuits from sensor or microprocessor. THERMISTOR OVERVIEW The term “thermistor” originated from the descriptor THERMally Sensitive ResISTOR. The two basic types of thermistors are the Negative Temperature Coeffi- cient (NTC) and Positive Temperature Coefficient (PTC). The NTC thermistor is best suited for precision temperature measurement. The PTC is best suited for switching applications. This application note will only discuss NTC applications. The NTC thermistor is used in three different modes of operation which services a variety of applications. One of the modes exploits the resistance-versus-tempera- ture characteristics of the thermistor. The other two modes take advantage of the voltage-versus-current and current-over-time characteristics of the thermistor. Voltage-Versus-Current Mode Voltage-versus-current applications use one or more thermistors that are operated in a self-heated, steady-state condition. An application example for an NTC thermistor in this state of operation would be using a flow meter. In this type of circuit, the thermistor would be in an ambient self-heated condition. The ther- mistor’s resistance is changed by the amount of heat generated by the power dissipated by the element. Any change in the flow of the liquid or gas across the device changes the power dissipation factor of the thermistor element. In this manner, the resistance of the ther- mistor is changed, relative to the degree of cooling pro- vided by the flow of liquid or gas. A useful thermistor graph for this phenomena is shown in Figure 1. The small size of the thermistor allows for this type of appli- cation to be implemented with minimal interference to the system. Applications such as vacuum manometers, anemometers, liquid level control, fluid velocity and gas detection are used with the thermistors in voltage-ver- sus-current mode. FIGURE 1: When a thermistor is overheated by its own power, the device operates in the voltage-versus- current mode. In this mode, the thermistor is best suited to sense changes in the ambient conditions, such as changes in the velocity of air flow across the sensor. Current-Over-Time Mode The current-over-time characteristics of a thermistor also depends on the dissipation constant of the ther- mistor package as well as element’s heat capacity. As current is applied to a thermistor, the package will begin to self-heat. If the current is continuous, the resistance of the thermistor will start to lessen. The thermistor cur- rent-time characteristics can be used to slow down the affects of a high voltage spike, which could be for a short duration. In this manner, a time delay from the thermistor is used to prevent false triggering of relays. Author: Bonnie C. Baker Microchip Technology Inc. 50 20 10 5 2 1 0.5 0.2 0.1 0.01 0.1 1 10 100 A pp lie d Vo lta ge (V ) 100mW 10mW 50mW 5mW 1mW 30K Current (mA) Thermistors in Single Supply Temperature Sensing Circuits AN685 DS00685B-page 2  1999 Microchip Technology Inc. The effect of the thermistor current-over-time delay is shown in Figure 2. This type of time response is rela- tively fast as compared to diodes or silicon based tem- perature sensors. The diode and silicon based sensors require several minutes to reach their steady state tem- perature. In contrast, thermocouples and RTDs are equally as fast as the thermistor, but they don’t have the equivalent high level outputs. Applications based on current-over-time characteristics include time delay devices, sequential switching, surge suppression or in rush current limiting. FIGURE 2: The time constant of the thermal mass of the thermistor sensor can be used to time delay a reaction to changes in conditions in a circuit. If a thermistor is overdriven, the thermal mass time constant of the sensor eventually causes the thermistor to overheat, reducing its resistance. Resistance-Versus-Temperature Mode By far, applications using the first mode, resistance-ver- sus-temperature, NTC Thermistor configurations, are the most prevalent. These circuits perform precision temperature measurement, control and compensation. Unlike applications that are based on the voltage-ver- sus-current and current-over-time characteristics of the thermistor, the resistance-versus-temperature circuits depend on the thermistor being operated in a “zero-power” condition. This condition implies that there is no self-heating of the thermistor as a conse- quence of current or voltage excitation. The resis- tance-versus-temperature response of a 10kΩ, NTC thermistor is shown in Figure 3. The resistance across the thermistor is relatively high in comparison to the RTD element which is usually in the hundreds of ohms range. Typically, the 25°C rating for thermistors is from 1kΩ up to 10MΩ . The housing of the thermistor varies as the requirements for hermetic- ity and ruggedness vary, but in all cases, there are only two wires going to the element. This is possible because of the resistance of the wiring over tempera- ture is considerably lower than the thermistor element. Consequently, a four wire configuration is not neces- sary, as it is with the RTD element. (Refer to AN687, “RTD Temperature Sensing Circuits” for details.) FIGURE 3: In precision temperature measurement environments, the thermistor is used in a “zero power” condition. In this condition, the power consumption of the thermistor has a negligible affect on the elements resistance. This is a graph of an NTC 10kΩ thermistor resistance-versus-temperature. Since the thermistor is a resistive element, current exci- tation is required. The current can originate from a volt- age or current reference, as will be shown in the “Hardware Linearization Solutions” section of this application note. The performance of the thermistor in Figure 3 is fairly repeatable as long as the power across the device does not exceed the power dissipa- tion capability of the package. Once this condition is violated, the thermistor will self-heat and artificially decrease in resistance, giving a higher than actual tem- perature reading. 180 160 140 120 100 80 60 40 20 0 10 20 30 40 50 60 70 80 Time (Sec) Cu rr en t ( mA ) V=6V V=9V V=12V V=16V V=18V 10,000,000 1,000,000 100,000 10,000 1,000 100 -100 -50 0 50 100 150 Temperature (°C) N TC T he rm is to r R es is ta nc e (Ω ) o f 1 0k Ω @ 25 ° C Th er m is to r NTC Thermistor Linearity  1999 Microchip Technology Inc. DS00685B-page 3 AN685 Figure 3 illustrates the high degree of non-linearity of the thermistor element. Although the thermistor has consid- erably better linearity than the thermocouple linearity, the thermistor still requires linearization in most temperature sensing circuits. The non-linear response of the ther- mistor can be corrected in software with an empirical third-order polynomial or a look-up table. There are also easy hardware linearization techniques that can be applied prior to digitalization of the output of the ther- mistor. These techniques will be discussed later in this application note. The third-order polynomial is also called the Steinhart-Hart Thermistor equation. This equation is an approximation and can replace the expo- nential expression for a thermistor. Wide industry accep- tance makes it the most useful equation for precise thermistor computation. The Steinhart-Hart equation is: where: T is the temperature of the thermistor in Kelvin. A0, A1, A3, B0, B1, and B3, are contents provided by the thermistor manufacturer. RT is the thermocouple resistance at temperature, T. With a typical thermistor, this third-order linearization formula provides ±0.1°C accuracy over the full temper- ature range. This is usually better than the accuracy of individual elements from part to part. Although the temperature range of the thermistor is a little better than the diode or silicon-based temperature sensor (−55°C to +175°C), it is still limited to a practical range of −100°C to +175°C. This can also be compared to the temperature sensing range of the RTD (−200°C to 600°C) or the thermocouple which ranges up to 1820°C. The advantages versus disadvantages of the ther- mistor are summarized in Table 1. Thermistors are manufactured by a large variety of ven- dors. Each vendor carefully specifies their thermistor characteristics with temperature, depending on their manufacturing process. Of all of the temperature sen- sors, the thermistor is the least expensive sensing ele- ment on the market. Prices start at $0.10 with some vendors and range up to $25. The thermistor is used in a large variety of applications such as automotive monitor and control exhaust emis- sions, ice detection, skin sensors, blood and urine ana- lyzers, refrigerators, freezers, mobile phones, base stations laser drives, and battery pack charging. In the precision instrumentation applications, thermistors are used in hand-held meters and temperature gauges. T 1/(A0 A1(ln RT) A+ + 3 lnR( T 3 )= lnRT B0 B1/T B3/T3+ += ADVANTAGES DISADVANTAGES Fast Non-Linear Small Excitation Required Two-Wire Limited TemperatureRange Inexpensive Self-Heating Fragile TABLE 1: Summary of Thermistor Advantages and Disadvantages. AN685 DS00685B-page 4  1999 Microchip Technology Inc. THE TEMPERATURE- RESISTIVE MODE OF THE THERMISTOR An electrical configuration for the thermistor is shown in Figure 4. This illustrates a seemingly obvious way to excite the thermistor and measure the change in resis- tance where the sensing element is excited with a cur- rent source. FIGURE 4: Common sense would dictate that the thermistor be excited by a precision constant current source as shown in this figure. A picture of an NTC Thermistor is shown on the right. With this style of excitation, the magnitude of the cur- rent source is typically below 100µA, preferably 20µA. Lower currents prevent the thermistor from entering a self-heating condition as described previously. This style of excitation is effective for sensing a limited range of temperatures. Larger ranges of temperature have deltas in resistance that are too high to accurately con- vert the resistance to voltage without bumping into the noise limitations of the analog signal path. As an example, the temperature range of a typical thermistor from BetaTHERM is −80°C to 150°C. The change is resistance for a 10kΩ @ 25°C thermistor from BetaTHERM over its temperature range is shown in Table 2. It is useful to note that the differential resistance for a 10°C delta at high temperature is significantly smaller than a 10°C delta at low temperatures. For instance, the change in resistance of the device in Table 2 from 125°C to 135°C is 76.28Ω (340.82Ω − 264.54Ω). The change in resistance of the same thermistor from −25°C to −15°C is 58.148kΩ. This diversity in the ratio of resistance to temperature over the range of ther- mistor creates an awkward analog problem. If the ther- mistor in this example is excited with a 20µA current source, the analog circuit must discriminate between 0.015V deltas at high temperatures and 1.16V deltas at low temperatures for ∆10°C of resolution. This forces the LSB size in a linear digitizing system to be 1/2 of 0.015V. This would require a 9.57-bit system to achieve 10°C accuracy from the system over a temperature span of -25°C to 135°C (delta of 160°C). Precision Current Source <100µA VOUT NTC Thermistor Available typically 10kΩ @ 25°C Temp (°C) R Value (Ω) Temp (°C) R Value (Ω) Temp (°C) R Value (Ω) -80 7296874 0 32650.8 75 1480.12 -75 4713762 5 253985.5 80 1256.17 -70 3095611 10 19903.5 85 1070.58 -65 2064919 15 15714.0 90 916.11 -60 1397935 20 12493.7 95 786.99 -55 959789 25 10000 100 678.63 -50 667828 30 8056.0 105 587.31 -45 470609 35 6530.1 110 510.06 -40 335671 40 5324.9 115 44.48 -35 242195 45 4366.9 120 388.59 -30 176683 50 3601.0 125 340.82 -25 130243 55 2985.1 130 299.82 -20 96974 60 2487.1 135 264.54 -15 72895 65 2082.3 140 234.08 -10 55298 70 1751.6 145 207.70 -5 42314.6 150 184.79 TABLE 2: Resistive changes with temperature of a BetaTHERM, 10kΩ @ 25 °C (10K3A1) NTC Thermistor in its “zero power” mode.  1999 Microchip Technology Inc. DS00685B-page 5 AN685 LINEARIZATION SOLUTIONS It is obvious in this example that the conversion process is inefficient if a linear response is required. It is also obvious that the digital output word will require a look-up table to linearize the response. Additionally, tempera- ture accuracy is usually required for most systems. These problems can be solved to a small degree by using a high resolution Analog-To-Digital (A/D) Convert- ing device. In this scenario, bits will still be thrown away, but the LSB size is smaller. An alternative is to imple- ment linearization with the analog hardware. A simple approach to a first level linearization of the thermistor output is to use one of the three circuits shown in Figure 5. In Figure 5a. the thermistor is placed in series with a standard resistor (1%, metal film) and a voltage source. The temperature response and linearity of the system shown in Figure 5a. is shown in Figure 6. In this figure, the series thermistor system responds to temperature in a linear manner over a limited temperature range. The linearization resistor’s value (RSER) should be equal to magnitude of the thermistor at the mid-point of the temperature range of interest. This creates a response where the output slope of the resistive network is at its steepest at this mid-point temperature. If high precision is required, this range is typically +/-25°C around the nominal tempera- ture of the thermistor at the RSER value. In Figure 5b., the thermistor is placed in parallel with a standard resistor (RPAR), which creates a composite resistor element. This type of resistive configuration is typically used in system feedback loops and used for automatic gain control circuits. The resistance to temperature response along with the linearization error of this circuit configuration is shown in Figure 7. Once again, the optimum linearity response of this resistive network is obtained at the point where the thermistor resistance and RPAR are equal. A third linearization approach is shown in Figure 5c. This circuit combines the parallel configuration in Figure 5b. with an additional reference resistor and a capacitor. The switchable reference is used to charge and discharge the parallel NTC resistance and the ref- erence resistor against the integrating capacitor, CINT. With this circuit, the NTC resistance is biased to a volt- age reference and the integrating capacitor charges. FIGURE 5: The series configuration (a) requires a voltage excitation. The parallel configuration (b) can be used in the feedback loop of an amplifier and does not require a precision source. The parallel configuration can be combined with a capacitor (c) which provides a linear circuit response with time. FIGURE 6: The series configuration response of the circuit shown in Figure 5a. has good linear response in a ±25°C range surrounding the temperature where both resistors (NTC and RSER) are equal. The error in this range is typically within ±1%. VREF = 5V. FIGURE 7: The parallel configuration response of the circuit shown in Figure 5c. allows for a counter to be used to determine the relative resistance of the NTC element. VOUT NTC Thermistor VREF (Precision Voltage Reference) RUSER (±1% tolerance, metal film) NTC Thermistor RPAR (±1% tolerance, metal film) VOUT NTC Thermistor RPAR (±1% tolerance, metal film) RREF (+/–1% tolerance, metal film) CINT NPO ceramic, Polycarbonate, Polystyrene, or Silver Mica) a. b. c. VREF Voltage Out with 10kΩ NTC in Series with 10kΩ Resistor and 5V Excitation (Keystone Thermometrics MS97A 10kΩ @25°C) 5.0 4.0 3.0 2.0 1.0 0.0 -50 -25 0 25 50 75 100 Temperature (°C) V O UT (V ) Er ro r (° C ) 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 Error Resistance Parallel Resistance with 10kΩ NTC in Parallel with 10kΩ Resistor (Keystone Thermometrics MS97A 10kΩ @25°C) 10.0 8.0 6.0 4.0 2.0 0.0 -50 -25 0 25 50 75 100 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 Temperature (°C) R es is ta nc e (kΩ ) Er ro r (° C ) Error Resistance AN685 DS00685B-page 6  1999 Microchip Technology Inc. Once the voltage at the top of the integrating capacitor reaches a threshold value VTH (Figure 8), the integra- tion time is recorded and the switching voltage refer- ence is set to zero which discharges the integrating capacitor. FIGURE 8: The RC time response of the circuit shown in Figure 5c. allows for the microcontroller counter to be used to determine the relative resistance of the NTC element. Once the integrating capacitor is discharged, the refer- ence voltage is applied to the reference resistor RREF. This circuit is allowed to integrate until VOUT reaches VTH and the time of that integration period is recorded. The integration time of this circuit can be calculated using: If the ratio of VTH:VREF is kept constant, the unknown resistance of the RNTC || RPAR can be determined with: In this configuration, the resistance calculation of the parallel combination of RNTC || RPAR is independent of CINT. The implementation of this linearization circuit will be discussed with further detail in the “Thermistor Signal Conditioning Circuits” of this application note. The circuits in Figure 5, along with the other configura- tions shown in Figure 9 linearize the thermistor to vari- ous ways. Figure 9a. uses the combination of the parallel and serial configurations shown in Figure 5 to extend the linear temperature response beyond 50°C. Figure 9b. demonstrates a way that the initial DC volt- age of a thermistor linearization circuit can be removed by employing a bridge configuration. The circuit in Figure 9c. uses a switching network to adjust the lin- earization range of the of the NTC Thermistor. Addi- tionally, there is a resistor divider added that implements a bridge configuration in order to reduce DC errors. The response of all of these networks can easily be modeled in an excel spreadsheet or mathcad which can be used to generate the appropriate look-up tables. The next section of this application note will use the networks in Figure 5 to implement complete application circuits. FIGURE 9: Other Thermistor Linearization Circuits. V O UT (V ) 0 t1 t2 Time(s) VTH RNTC||RPAR RREF VO UT VREF 1 e t/RC– –( ) or= t RC ln 1 VTH/VREF–( )= RNTC||RPAR t2/t1( ) RREF×= a. Parallel Series Composition b. Bridge Network c. Switchable Temperature Ranges NTC NTC1 NTC2 RPAR RSER NTC2RSER1 NTC1 RSER2 RSER RREF RREF RSERRSERRSER  1999 Microchip Technology Inc. DS00685B-page 7 AN685 THERMISTOR SIGNAL CONDITIONING CIRCUITS There is a large variety of application circuits where the thermistor can be utilized. The three circuits in this application note use the thermi