# Pressure sensors get dynamic temperature compensation

One of the fundamental tasks when dealing with any type of sensors would be the compensation of offset and span drift in regards to temperature. Having a look on a typical pressure sensor characteristic, we may come across with the following thermal behavior in Figure 1.

**Figure 1: Output vs. pressure differential (Motorola MPX (V) 10).**

The curve easily demonstrates the relationship between temperature, offset and span: temperature has a negative effect on span and offsets. The traditional way to deal with this drift would be to build up a simple signal conditioning circuit that would be calibrated at a reference temperature (usually at 20°C), followed by a characterization of the complete (analog) system (sensor + signal conditioner) across the whole dynamic temperature range. The measured curve would then be uploaded in a nonvolatile lookup table that provides a compensational value. This value would then be used in order to correct the drift in the digital domain. More complex systems could also use this value in order to retune span and offset in the analog domain as a function of temperature in a dynamic way.

Another alternative way to deal with this issue would be by using a dynamic current source, with a thermal behavior that compensates the sensor's drift. With this analog approach, the sensor's overall performance would dramatically increase.

**The pressure sensor**

**Figure 2: Pressure sensor block diagram.**

Under ideal conditions both resistor parameters R and _R would be exactly the same for each sector of the bridge; the total resistor value RB for one sensor would then be:

**Equation 1**

The above relationship clearly demonstrates that an ideal pressure sensor will not change its resistor value with changing pressure ( ≥ _R ), but should be totally balanced. In such a case, the differential voltage VD = V1 - V2 could be determined with the following matrix:

**Equation 2**

This term leads to the following relationship between V1 and V2:

**Equation 3**

**The impact of temperature**

**Equation 4**

Instead of dealing with a constant value we now add a temperature depending, proportional factor. Equation (3) essentially implies a linear dependency of VD with respect to _R, that is, the effect of pressure. However, assuming a first order characteristic of the offset in regards to temperature, equation (3) needs to be modified in the following way:

**Equation 5**

While R0/Δ T would represent the Temperature Coefficient (= TC) of the bridge resistor value, k • (VB/Δ T) reflects the TC of the sensor's offset. Using both terms, equation (4) and (5) we will yield a useful expression which demonstrates a link between VD and IB in the following way:

**Equation 6**

The differential voltage VD is now not only a function of pressure (→ Δ R), but also a function of temperature (→ T/Δ T). This drift has to be compensated by a dynamic IB.

**The solution**

An alternative, more elegant approach would be using a lookup-table driven current source, such as the X9530 of Xicor. (See the block diagram in Figure 3.)

**Figure 3: X9530 block diagram.**

The signal flow for the device in Figure 3 is very simple: an incoming analog signal VSense (like the voltage provided by a temp sensor) or the value provided by the internal thermal resistor will be converted into a digital value through the ADC. This will represent a specific address of the look-up-table that will contain a compensational value. Once the correction had been finished the corresponding output DAC 1 or 2 will be recalibrated.

Keeping in mind what had been said before, the only action that is required would be the storage of appropriate compensational factors in the memory sectors 1 and 2 based upon the relationship pointed out through the equation (6). This can be performed through the I ²C interface. However, once the proper values had been uploaded, there won't be any further need for an interacting _C. If desired, the measured temperature value can be requested and read out through the same interface. Finally, two independent outputs can simultaneously be driven based upon two independent table sectors in order to correct two unlinked analog parameters. This product is available with a variety of options, as pointed out in Table 1

**Table 1: Sensor conditioners product range.**

**Conditioners product range**
The internal temperature sensor's ADC resolution will address an accuracy level of 6 Bit (64 steps), which represents 2.18 • (k/step) for a thermal range of -40°C ≤ T ≤ +100°C. Under normal conditions, this should be more then enough for these type of applications. A limitation of the operating temperature range would obviously increase the available ADC's precision.

The maximum DAC output current would be of 1.6 mA with an accuracy of 8 Bit (256 steps). This reflects a precision of 6.25 • (μ A/step). The DAC's polarity can independently be selected in order to provide a current sink or current source.