**The Crocus CTSR2xxC series is a family of magnetic sensors designed for sensing weak magnetic fields – in fact, they are as much as 15 times more sensitive than other magnetic sensors in use today.**

This Design Note explores three common techniques which may be used to minimise the effects of temperature on the Crocus CTSR2xxC magnetic sensors.

The Crocus magnetic sensor is a four-terminal device: two input terminals and two output terminals that are fully electrically isolated. The two input terminals are used to bias the sensor while the two output terminals, V_{B} and V_{BGND}, are connected to the sensor output resistor, R_{OUT}, which changes resistance when exposed to a magnetic field. The output resistance also changes with temperature, and needs to be temperature-compensated.

The CTSR218V-IQ2 datasheet shows that the temperature coefficient is negative. That is to say when temperature increases it reduces the sensor’s output resistance R_{OUT}, as shown in Figure 1.

The units on the y axis, R_{OUT}/R25C, may be explained by reference to an example. From the CTSR218C-IQ2 datasheet: R_{OUT} = 18kΩ @ 25°C

A change in temperature from 25°C to 70°C can be estimated using the the graph in Figure 1: It can be estimated that R_{OUT}/R25C is approximately 0.95 at 70°C. So the calculation to find the resistance of the sensor at 70°C is:

**R(70C) = R25C * R _{OUT}@70C/R25 = 18000 * 0.95 = 17.1kΩ**

Another, more accurate way to calculate the resistance at a particular temperature is to use the temperature coefficient of resistance in the datasheet. But the important question is how can the temperature effects be mitigated? Three specific techniques are described in the following sections.

**Half-bridge temperature compensation**

One way to easily compensate for the temperature effects on the Crocus sensor is to arrange the sensing circuit in a half-bridge circuit, shown in Figure 2.

The theory of operation for the circuit is based on the voltage-divider equation:

**V _{OUT} = V1 * (R_{OUT}2/(R_{OUT}2+R_{OUT}1))**

As the resistance of Sensor 1, R_{OUT}1, increases due to temperature, the resistance of Sensor 2 will also increase since both sensors have the same temperature coefficient as they are made of the same material. The output voltage will not change with changes in temperature since – according to the voltage-divider equation – the output voltage is constant if the ratio of R_{OUT}2 to R_{OUT}1 remains constant.

**Compensation using resistance with a positive temperature coefficient**

The concept behind using another Temperature Sensitive Resistor (TSR) is to neutralise the change in the sensor’s resistance with temperature. This calls for a TSR that has the same temperature coefficient as the sensor, with the opposite sign, naturally.

In fact, it is possible to tune the effects of the temperature coefficient of the TSR to exactly fit the application by adding a few passive components to the compensation circuit.

This second technique applies a single-sensor circuit, as opposed to the dual-sensor circuit described above, as shown in Figure 3.

The TSR in the diagram has a positive temperature coefficient equal to 0.14%/°C. As mentioned earlier, the TSR must be tuned to match the temperature coefficient of the sensor, which is -0.1%/°C. This is done by adding a series resistor, RS, and a parallel resistor, RP, as shown in Figure 3.

The values of these components will depend on the resistive value of the TSR and its temperature coefficient. To simplify the calculation of RS and RP, it is helpful to calculate an equation of the temperature coefficient of the Crocus sensor. An Excel spreadsheet makes it is easy to find the linear equation of a set of any data.

The first step is to generate a table of values of the sensor’s output resistance at various temperatures. This can be plotted in a chart such as that shown in Figure 4.

Also shown in Figure 4 is the plot of the resistive network comprised of the TSR in parallel with the resistor RP. The value of the parallel resistor was determined by an iterative process to match the slope of the sensor’s temperature equation but with the opposite sign. As Figure 4 shows, the slopes of the two linear plots are equal but with opposite signs.

**Temperature compensation using software**

The technique of temperature compensation involves software and the use of a microcontroller. To compensate for the temperature coefficient of the Crocus magnetic sensor in firmware, the temperature must be measured. Then, for each temperature reading, the microcontroller simply subtracts the known effects of the temperature from the output resistance of the sensor. The compensation is then directly applied to the output signal which is displayed in digital form.

All three techniques described in this Design Note work well with a Crocus magnetic sensor, because the temperature effects on the sensor are well defined and repeatable.

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