The excellent linearity of integrated-circuit temperature sensors makes them ideal for direct analog compensation of the thermally induced errors inherent in many circuits. For example, a negative-sloped temperature sensor could compensate for an increase in amplifier bias current resulting from a rise in temperature.
Some circuits, however, exhibit a positive temperature coefficient in one temperature range and negative coefficient in another. One example is the frequency drift of XT-cut crystals, which have a parabolic curve with the center frequency typically specified at 25°C. The dual-slope temperature sensor circuit in Figure 1 combines one negative-sloped and one positive-sloped temperature sensor to create a V-shaped output, which can be used to compensate for a dual-temperature-coefficient thermal response.
The transfer function of the LM19 (IC1) can be closely approximated at room temperature as a straight line with the equation:
where T is temperature in °C. The transfer function of the LM61 (IC2) is a straight line with the equation:
The two lines are plotted in Figure 2, which shows that the temperature of intersection (TINT) is 58.55°C. Since the LM19 and LM61 essentially do not sink current (less than 10 µA), VOUT will be equal to whichever device has the higher output voltage. This results in a V-shaped output curve with a minimum at TINT.
To use this circuit to compensate for a dual-temperature-coefficient circuit, it is desirable to have the minimum of the V-shaped curve occur at the same temperature as the maximum of the thermal response being compensated. To reduce TINT to the desired temperature (e.g., 25°C), an additional offset voltage VOS is added to the LM61 via the R1-R2 voltage divider, giving a new equation for the LM61 output:
VOS is calculated by setting equations 1 and 3 equal to each other and substituting the desired TINT for T. For a TINT of 25°C, the value of VOS is 0.728 V. The values of R1 and R2 must therefore be selected such that
I1 is determined by R1 and R2, and it should be set to significantly more than the quiescent current through the LM61 (125 µA max) in order to reduce errors caused by this quiescent current passing through R2. Choosing I1 to be 10 times greater than the quiescent current gives the condition:
Solving the two equations 4 and 5 for the two variables R1 and R2 results in the values R1 = 398 O and R2 = 582 O. The circuit in Figure 1 uses the standard resistor values of 360 O and 560 O to satisfy Equation 5 and gives a ratio of 0.636, very close to that of Equation 4.
Finally, R3 was selected so that I2 is within the operating range of the LM4041 voltage reference.
Figure 3 shows the output of the dual-slope temperature sensor circuit, measured over a temperature range of -25°C to 85°C. The average error over the full temperature range was 25.4 mV (approximately 2.5°C), and the maximum error was 46.4 mV (4.6°C).