Design How-To

# automotive pressure sensor calibration

Abstract

Pressure sensors are widely used in automotive systems. In this article we present a brief description of the architecture of pressure sensors. We also describe a calibration process for pressure sensors that use mixed-signal integrated circuits as signal conditioners.

Background

From an electrical/electronics engineering perspective, a passenger car is an aggregation of various control systems that interact with each other in complex ways. Each control system is made up of a plant, sensors, actuators and an electronic control unit (ECU).

**Figure 1**shows a block diagram representation of an automotive control system.

Figure 1: Block diagram representation of an automotive control system.

The ECU is typically a printed circuit board (PCB) with many circuits. These circuits include passive components such as resistors, capacitors, inductors, varistors, and integrated circuits (ICs) such as microcontrollers, regulators, communication transceivers, transistors and so on. The microcontroller in an ECU has non-volatile memory that is used to store control algorithms. The microcontroller also has computation engines to execute the control algorithms and thereby achieve the intended plant behavior.

Some examples of automotive ECUs include:

1. Engine – controls engine performance and emissions

2. Transmission – controls automatic transmission

3. Electronic stability control – controls braking system

4. Chassis – supports ride control system

5. Instrument cluster – provides information to the driver

6. Heating, ventilation, and air conditioning (HVAC) – controls climate inside the cabin

One of the important aspects of automotive control systems is the sensor. The sensor is used to convert the physical entity of interest into an electrical quantity so that the ECU can use it to perform control actions.

An automotive system uses a variety of sensors such as:

1. Temperature – measures temperature of various fluids such as intake air, exhaust gases, cabin interior, and brake fluid

2. Gas – measures oxygen and NOX content in the exhaust gases

3. Humidity – measures cabin humidity for use in HVAC ECU

4. Vibration – measures engine knock for use in engine ECU

5. Pressure – measures various fluid pressure including manifold absolute pressure (MAP), boost pressure, vapor pressure in fuel tanks, compressor pressure in HVAC systems, brake fluid pressure, etc.

Pressure Sensors

A typical sensor in automotive applications has two building blocks (

**Figure 2**):

1. sense element

2. signal conditioner

Figure 2: Block diagram representation of a typical sensor.

Sense element

The primary purpose of the sense element (SE) is to convert the physical quantity into electrical signal, typically voltage.

The majority of automotive pressure sense elements are based on resistors or capacitors. In resistor-based pressure sensors, resistors are implanted on a flexible diaphragm that flexes with pressure. In the case of capacitive-based pressure sensors, the flexible diaphragm that flexes with pressure has a metal plate that is one electrode of a capacitor.

The sense element undergoes a change in its value (either change in resistance or change in capacitance) as the pressure changes. The pressure can be inferred by measuring this electrical value.

With regard to pressure sensors based on resistive-bridge, the resistors that change in value typically are arranged in bridge configuration.

**Figure 3**shows full Wheatstone bridge arrangement of the resistors. As the pressure changes, the value of resistance in each bridge leg changes. This in turn causes the output of the Wheatstone bridge to change.

Figure 3: Resistors arranged in Wheatstone bridge configuration to form the pressure sensor.

Note that the resistance itself changes either because the length of each resistor changes as the diaphragm flexes, which is a strain gauge effect, or because of change in resistivity of the resistor as the diaphragm flexes, known as a piezoelectric effect. Furthermore, in both strain gauge and piezoelectric effects, the resistances change linearly with pressure. This is because the resistance is given by

**Equation 1**:

Ideal sense element

In an ideal SE, the output of the bridge is given by

**Equation 2**:

From

**Equation 2**, one can infer that the output of the Wheatstone bridge changes linearly with resistance. Furthermore, since each resistor value changes linearly with pressure, one can infer that the Wheatstone bridge output changes linearly with pressure.

Non-ideal sense element

The bridge output, however, suffers from non-idealities.

**Figure 4**shows the non-idealities exhibited by the Wheatstone bridge output as the pressure changes. The non-idealities are a result of mismatches in the resistor value in each leg, as well as mismatches in resistor value change with pressure. These individual mismatches result in the output to exhibit a non-ideal macro behavior.

Figure 4. Pressure sense element output.

**Figure 4**, which shows the variation of the bridge output with pressure, shows the following specific non-idealities:

• Offset – non-zero output at minimum pressure

• Span – very small output, typically in tens to hundreds of mV

• Nonlinearity (NL) – output changes nonlinearly with pressure

• Temperature coefficient (TC) – output change with temperature for a given pressure

Because manufacturing tolerances of the resistors vary, each sense element has a unique non-ideality. In other words, each sense element has a unique relationship between the pressure and its output, making it difficult to infer fluid pressure from the bridge output.

Signal conditioner

The primary purpose of the signal conditioner (SC) is to process the output of the sense element for its non-idealities and provide the processed output to the ECU.

One way to eliminate the non-idealities is to precision trim the resistors so that all the resistors are well-matched. However, this is usually an expensive process. An alternative to precision-trimming is to employ a signal conditioner to eliminate the non-idealities of the SE.

The block diagram in

**Figure 5**represents a sense element signal conditioner for Wheatstone bridge. The signal conditioner receives power from the outside world. The regulators are used to generate the bridge supply as well as supplies for various circuits in the signal conditioner. The analog front-end (AFE) is the “first” interface to the sense element output. The compensation block eliminates the non-idealities exhibited by the sense element. The compensated output is then sent to the outside world using the output block. The output forms could be analog or digital output, such as LIN and SENT protocol. Automotive pressure sense element signal conditioners also include other functions such as diagnostics. The diagnostics block detects faults in either the sense element or the signal conditioner.

Figure 5: Block diagram representation of a sense element signal conditioner.

The signal conditioner can be built using discrete electronic components or comes in the form of highly integrated circuits such as Texas Instruments’ PGA400, which has a mixed-signal architecture non-idealities are corrected primarily in the digital domain.

Removing the Non-Idealities

In mixed-signal conditioners, compensation is accomplished primarily in the digital domain. To perform compensation in the digital domain, mixed-signal devices employ analog-to-digital converters (ADC) to digitize the analog output of the Wheatstone bridge. In these devices, the principal purpose of the AFE is to scale the Wheatstone bridge’s output to fit into the ADC’s dynamic input range.

Analog front-end

Consider, for example, that the Wheatstone bridge varies from VMIN to VMAX while the ADC dynamic range is AMIN to AMAX. The bridge output can be scaled to fit into the ADC dynamic range using the scaling

**Equation 3**:

In other words, the output of the AFE (which is the input to the ADC) can be expressed using

**Equation 4**:

From

**Equation 4**, one can infer that the scaling is accomplished by the AFE using a gain and an offset. The gain and offset values in the AFE are implemented as programmable values to account for variable offsets and bridge output spans. The variable offsets and gains are implemented in discrete steps. Even though Equation 2 gives the ideal scaling, AFE output is given by

**Equation 5**:

The result of these discrete steps in gain and offset is that the bridge output cannot be exactly scaled to fit into the entire dynamic range of the ADC input. The minimum bridge output is scaled to A’MIN, which is greater than AMIN, while the maximum bridge output is scaled to A’MAX, which is less than AMAX.

**Figure 6**summarizes the scaling process.

Figure 6: The AFE scales the sense element output to fit into the ADC dynamic range.

Compensation

The compensation for the sense element output is the process of eliminating the non-idealities exhibited by the sense element. The compensation in the digital domain is achieved using nonlinear equations. One example of a nonlinear equation is given in

**Equation 6**:

Compensation equations can take any form similar to Equation 6. For instance, TI’s PGA400 offers customers the flexibility to implement a compensation equation that is appropriate for their sense element.

Calibration

Having chosen a compensation equation, the various coefficients in the compensation equation have to be determined. However, before one can do this, the AFE gain and offset also need to be determined. That is, the calibration process needs to determine two sets of unknown variables:

1. AFE gain and offset values

2. compensation equation coefficient values

**Figure 7**shows a high-level flow chart for pressure sensor calibration using mixed-signal conditioners. This flow-chart illustrates that the calibration is a two-step process. The first step is determines the AFE scaling factors and the second step determines the digital equation coefficients.

Figure 7: The calibration using mixed-signal devices is a two-step process.

Determining the unknown variables requires appropriate calibration equipment in the production line, which also involves time on the production line. In other words, the calibration of every sense element involves cost. This cost is proportional to the time spent in the calibration process. Hence, the calibration process involves a tradeoff between the number of unknown coefficients, which directly translates the end-accuracy of the pressure sensor, and the time spent in the calibration process, which translates to cost. Or, the higher the accuracy desired, the more costly the calibration process may become.

Note that the calibration is performed after the sense element is connected to the signal conditioner.

Analog front-end calibration

The AFE calibration is usually an online process. That is, the gain and the offset in the AFE are adjusted while the sense element is exposed to certain pressure and temperature conditions (

**Figure 8**). The sense element is first exposed to a temperature T1 and pressure P1, or the minimum pressure that the sense element has to measure. The AFE offset is then adjusted so that the AFE output is as close as possible to the minimum ADC input value. The pressure is then changed to P2, which is the maximum pressure that the sense element has to measure. At the maximum pressure value, the gain is adjusted so that the AFE output is as close as possible to the maximum ADC input value. For this method to be valid, it is assumed that the offset scales with the AFE gain, which is the case with the PGA400.

Figure 8: AFE calibration.

Digital coefficient calibration

Once the AFE is calibrated, one can determine the digital coefficients. Determining the actual digital coefficients is an “offline” process. For instance, the sense element is exposed to different temperature and pressure conditions and the ADC outputs are recorded. The recorded ADC values are then used to compute the digital coefficients offline.

**Figure 9**summarizes the digital coefficient calibration process. The number of temperature and pressure set points at which the digital representation of temperature and the bridge output are recorded typically depends on the number of coefficients.

Figure 9: Digital coefficient calibration.

Calculating digital coefficients

Consider the compensation equation given by

**Equation 6**. This compensation equation consists of five coefficients. Hence the temperature and the pressure ADC values are recorded at five unique temperature and pressure point.

If the desired value at the ith set point is yi, i=1, 2, 3, 4, 5, then the matrix given by Equation 7 can be constructed as:

The unknown coefficients can be computed using the matrix inversion formula given by Equation 8:

Eq. 8

Standard tools such as Microsoft™ Excel or Mathworks® Matlab® can be used to calculate the unknown coefficient values.

References

•

**Download a datasheet for the PGA400-Q1**.

• For more information about automotive solutions from TI, visit:

**www.ti.com/automotive-ca**.

Arun Tej Vemuri is a systems engineer with TI’s Kilby Labs. Prior to joining Kilby Labs, Arun was part of TI’s mixed-signal Automotive group where he was responsible for product definition of automotive sensor signal conditioners. Arun received his Ph.D. in Electrical Engineering from the University of Cincinnati, Ohio, his MS in Systems Science from IISc Bangalore, India, and BSEE in Electrical Engineering from IIT Roorkee, India. Arun can be reached at ti_arunvemuri@list.ti.com.