Designers often use thermistors rather than other temperature sensors because thermistors offer high sensitivity, compactness, low cost, and small time constants. But most thermistors’ resistance-versus-temperature characteristics are highly nonlinear and need correction for applications that require a linear response. Using a thermistor as a sensor, the simple circuit in **Figure 1** provides a time period varying linearly with temperature with a nonlinearity error of less than 0.1K over a range as high as **30K.** You can use a frequency counter to convert the period into a digital output. An approximation derived from **Bosson’s** Law for thermistor resistance, R_{T}, as a function of temperature, θ, comprises **R _{T}=AB^{–θ}** (see sidebar “Exploring

**Bosson’s**Law and its equation”). This relationship closely represents an actual thermistor’s behavior over a narrow temperature range.

**Figure 1**This simple circuit linearizes a thermistor’s response and produces an output period that’s proportional to temperature.

You can connect a parallel resistance, R_{P}, of appropriate value across the thermistor and obtain an effective resistance that tracks fairly close to AB^{–θ }30K. In **Figure 1**, the network connected between terminals A and B provides an effective resistance of R_{AB }AB^{–θ}. JFET Q_{1} and resistance R_{S} form a current regulator that supplies a constant current sink, I_{S}, between terminals D and E.

Through buffer-amplifier **IC _{1}**, the voltage across

**R**excites the

_{4}**RC**circuit comprising

**R**and

_{1}**C**in series, producing an exponentially decaying voltage across

_{1}**R**when

_{1}**R**is greater than R

_{2}_{AB}. At the instant when the decaying voltage across R

_{1}falls below the voltage across thermistor R

_{T}, the output of comparator IC

_{2}changes its state. The circuit oscillates, producing the voltage waveforms in

**Figure 2**at IC

_{2}‘s output. The period of oscillation, T, is

**T=2R**This equation indicates that T varies linearly with thermistor temperature θ.

_{1}C_{1}ln(R_{2}/R_{AB})2R_{1}C_{1}[in(R_{2}/A)+θlnB].**Figure 2**Waveforms show input to comparator IC

_{2}(lower trace) and its output (upper trace). In the lower trace, IR

_{2}represents the voltage across

**R**.

_{2}You can easily vary the conversion sensitivity, **ΔT/Δθ,** by varying resistor **R _{1} **‘s value. The current source comprising Q

_{1}and R

_{1}renders the output period,

**T,**largely insensitive to variations in supply voltage and output load. You can vary the period, T, without affecting conversion sensitivity by varying R

_{2}. For a given temperature range, θ

_{L}to θ

_{H}, and conversion sensitivity, S

_{C}, you can design the circuit as follows: Let θ

_{C}represent the center temperature of the range. Measure the thermistor’s resistance at temperatures θ

_{L}, θ

_{C}, and θ

_{H}. Using the three resistance values R

_{L}, R

_{C}, and R

_{H}, determine R

_{P}, for which R

_{AB}at θ

_{C}represents the geometric mean of R

_{AB}at θ

_{L}and θ

_{H}. For this value of R

_{P}, you get R

_{AB}exactly equal to AB

^{–θ}at the three temperatures, θ

_{L}, θ

_{C}, and θ

_{H}. For a given temperature range, θ

_{L}to θ

_{H}, and conversion sensitivity, S

_{C}, you can design the circuit as follows: Let θ

_{C}represent the center temperature of the range. Measure the thermistor’s resistance at temperatures θ

_{L}, θ

_{C}, and θ

_{H}. Using the three resistance values R

_{L}, R

_{C}, and R

_{H}, determine R

_{P}, for which R

_{AB}at θ

_{C}represents the geometric mean of R

_{AB}at θ

_{L}and θ

_{H}. For this value of R

_{P}, you get R

_{AB}exactly equal to AB

^{–θ}at the three temperatures, θ

_{L}, θ

_{C}, and θ

_{H}.

**Read More: Temperature-to-period circuit provides linearization of thermistor response**