July 3, 1997

Spice subcircuit models thermistors

Lutz Wangenheim, Hochschule, Bremen, Germany

The subcircuit in Figure 1 is a simple and efficient behavioral model for a thermistor, implemented in PSpice (Microsim, Irvine, CA). The model simulates realistic thermistor parameters for all standard analyses (transient, ac, and dc). You can set all relevant thermistor parameters--nominal resistance, nominal and ambient temperatures, and material and thermal constants--during the call of the subcircuit. Listing 1 gives the parameter definitions for the subcircuit. The model reflects Equation 1, traditionally used to describe the resistance-temperature characteristic of thermistors:

(1)

where R_T is the resistance at thermistor-body temperature T_B, R_NOM is the nominal resistance at nominal (standard reference) temperature T_NOM, and B is the material constant (in Kelvin) that describes the temperature sensitivity.

Note that Equation 1 is valid only within a limited temperature range, because it does not reflect the actual temperature dependence of the material constant, B. However, with respect to manufacturing tolerances of B, the equation provides a useful approximation. The sub9circuit establishes thermal feedback by using a conventional ohmic resistor, representing R_NOM, in series with a voltage source E_TEMP that represents the temperature-dependent term. The independent zero-voltage source, V_SENSE, senses the current, I_T, through the circuit.

The voltage, V_T=I_TR_T, generated between thermistor nodes 1 and 2 is the sum of the voltage across R_NOM and the output, V_TEMP, of the voltage source, E_TEMP:

Replacing R_T by Equation 1 and solving for V_TEMP yields the control function for E_TEMP. You can derive the function by applying the analog-behavioral model of PSpice in Listing 1:

Because all control parameters of the dependent source must be constants, currents, or voltages, you need some extra circuitry to compute the body temperature, T_B, and convert it to a corresponding voltage. Therefore, you use a dependent current source, G_PWR, controlled by the voltage-current product, V_TI_T, to generate a voltage across resistor R_TH at Node 5. This voltage represents the power-dependent portion of the body temperature, T_B, if you set the value of the thermal resistance, R_TH, to the reciprocal of the thermistor's dissipation factor, D. Capacitor C_TH in parallel with R_TH models the thermal time constant, lower case tau, of the thermistor body.

For ambient temperature-to-voltage conversion, a constant current, I_AMB=1A, must produce a voltage at Node 6 that is numerically equal to the ambient temperature, T_AMB, in Kelvin. This temperature constitutes the second portion of T_B. To satisfy this equivalency, you use a resistor model for R_AMB with a nominal value of 300.15 ohms and a linear temperature coefficient of TC=1/300.15=3.33×10₃. During simulation runs, you can set the ambient temperature (for PSpice, nominally 27°C, or 300.15K) with a global.TEMP statement.

Note that ac simulation, which is a linear (small-signal) analysis, must not cause any change in the thermistor's electrical resistance. Therefore, the voltage at Node 5, a measure of internal heating, must not contain any ac portion that may result from the nonlinear control operation (current-voltage multiplication) of the behavioral-modeling block, G_PWR. Unfortunately, if any dc flows through the thermistor during bias-point calculation (before the ac analysis), the output of G_PWR will always contain such an unwanted ac portion. Therefore, to make the ac voltage at Node 5 negligible, you should increase the value of C_TH accordingly.

During ac simulations, you should set the time constant, lower case tau=R_THC_TH, to a much larger value than 1/f_MIN, the start frequency of the ac analysis. Thus, the current-voltage characteristic of the thermistor becomes a function of only its nominal value, R_NOM; the ambient temperature, T_AMB; and the dc bias flowing through the device. Click here to download the PSpice file from DI-SIG, #2043. (DI #2043)

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