# Pressure Sensing

#### Description

Force, pressure, and stress are generally all grouped into the same measurement category. There are subtle differences: force is a push or pull upon an object from another object, stress is a result of force applied to an object per unit area that causes a deformation, and pressure is a type of stress normally associated with a force applied by a gas or liquid. We won't get into deep physics here; the design considerations, circuits, and block diagram pages focus on how to process a signal from a transducer that responds to different types of forces applied to solids, liquids, or gasses and how to select a signal chain for the application.

#### Design Considerations

The need to measure force generally arises in order to keep a system either under control or alternatively, in one piece. For example, a steam boiler made with a certain thickness of steel plate can resist a certain amount of pressure. If the pressure exceeds the material's threshold the boiler will rupture or explode. By measuring and monitoring the pressure within the boiler, certain controls can be added to the boiler, like a relief valve or signal that reduces the heat applied to the boiler in order to avoid a catastrophic event. Pressure transducers are used to measure this type of force. Another example: a bridge doesn't move, usually, but it is subject to forces due to weather (wind and temperature differentials) and load (weight of the structure and vehicles traversing the bridge). These conditions cause stress within the materials, and if the materials receive stress beyond what they are capable of handling the material can tear apart. Strain gauges are used to measure these forces and can determine if a structure is abnormally deforming so action can be taken before a failure occurs.

#### Signal Chain Functions and Operation

The accurate measurement of force, pressure, and stress requires a transducer or sensor capable of providing a signal that reflects the force, pressure, or stress that a measured object is experiencing. The ideal transducer provides a linear output – an output that increases linearly with increasing pressure or stress, and subsequently decreases linearly as the pressure or stress decreases. Most transducers however operate with some degree of non-linearity. For accurate measurements the signal usually must be linearized within the input circuitry.

Most force sensing transducers provide an output signal level that is very low, in the sub millivolt to tens of millivolts range. This range is similar in magnitude to the electrical noise within an environment. So circuitry must be designed to amplify the signal while filtering or rejecting noise. Fortunately the measurement of force does not require exceptionally high sampling rates, making filtering easier. Most signal chains are designed to meet an accuracy objective which includes low drift in time and with temperature changes. The circuitry must provide exceptional reliability.

Most pressure or force transducers take the electrical form of a Wheatstone bridge:

Figure 1. Wheatstone bridge diagram

A Wheatstone bridge circuit, once balanced, outputs a voltage proportional to the change in resistance of one or more of the resistors within the bridge. A strain gauge or MEMS transducer is essentially a variable resistor and when used for measuring force is placed into a Wheatstone bridge circuit either with other strain gauges or other precision resistors so that the bridge is nulled. When one or more of the strain gauges experiences stress or deformation, a voltage appears on the bridge output.

The purpose of the signal chain is to accurately bring a very small analog signal to digital. To do this, the sensor signal chain performs the following functions:

1. Transducer excitation

Accurate and stable voltage or current sources with low-temperature drift are required for sensor excitation. To easily eliminate effects of reference voltage tolerance, it is common practice to use the same reference for both the sensor excitation and the analog-to-digital converter (ADC). This makes the signals ratiometric, eliminating first-order tolerances allowing the use of less accurate references, or alternately providing higher performance from a given reference.

2. Signal amplification

In many designs the transducer's output full scale range will be very low (e.g., 20mV), while the input full scale range of ADC is much wider (e.g., 2V). In such cases, the transducer's output signal must be amplified to match the input range of the ADC before it is converted by the ADC to digital.

3. Filtering

The bandwidth of the sensor transducer signal is generally narrow and the sensitivity to noise is high. It is, therefore, useful to limit the signal bandwidth by filtering to reduce the total noise. Filtering is usually accomplished using a passive filter.

4. Analog to digital conversion

This process involves accurately converting the analog signal into digital without introducing any artifacts or abnormalities during the conversion. Two primary converter architectures that are used in sensor signal chains are: SAR and Delta Sigma. Delta Sigma converters provide a good combination of low power, high resolution (up to 24-bit) and digital signal processing at low sampling rate. This meets the requirement for many sensors with low bandwidth signal. A fast SAR ADC provides a good combination of low power, medium/high resolution (up to 20-bit), fast settling time and no latency. This might be more appropriate when fast acquisition or many channels are being multiplexed into one ADC.

5. Linearization

Some sensors have a non-linear output. If the sensor output characteristic is well known and repeatable, the output can be linearized thereby increasing the accuracy of the design. These days generally digital linearization is more cost effective and more flexible. Digital linearization uses a lookup table after the signal is digitized to provide a correct linearized value for each output code from the ADC. Some more complex solutions may also require the use of digital signal processing (DSP) techniques for signal manipulation, error compensation, gain, and filtering depending on the transducer and the degree of accuracy required.

#### Physical Elements of the Signal Chain

The design engineer who needs to measure a force usually starts with a signal chain that encompasses:

1. Input multiplexor to handle multiple signals in one chain.
2. One or more op amps for amplification and filtering.
3. An analog-to-digital converter.
4. One or more voltage references
5. A microcontroller for digital signal processing and communications.

While custom signal chains can be designed to meet exact performance and cost needs, it is also possible that a modern, highly integrated single chip AFE product might fit the design parameters, especially if the design is for a mainstream application. At a minimum, AFE ICs integrate an ADC and a programmable-gain amplifier. See the section below "Highly integrated Signal Chains" for more information

#### Specifying a Custom Signal Chain

The engineer's main task is to specify a signal chain that will reliably provide the signal measurements within the specified uncertainty range while also meeting cost constraints. There are many available performance tradeoffs especially when cost is a factor.

For the sensor signal chain, the quality of measurement is taken in account by:

• Accuracy or systematic error
• Precision or random error

Systematic error sources can be classified into three main categories:

• Gain error
• Offset error
• Linearity error

Precision or random error sources include:

• Quantization Noise
• Thermal noise
• Shot Noise
• Flicker noise

The total error in the system is the combination of both error types.  Generally speaking each error type contributes about half of the total error, so to improve the quality of the measurements provided by the signal chain; the individual components should be chosen and configured to minimize both error types.

Let's review primary selection criteria for each element in a custom signal chain.

The most basic parameters involved in selecting an ADC are:

1. Channels required
2. Sampling rate
3. Nominal resolution

Channels Required

Most ADCs provide one input channel but some products also integrate a multiplexor function to provide multi-input functionality.

Sampling rate:

Sampling rate for sensor applications is generally considered to be fairly low from a technology standpoint. Usually 50 samples a second will work, so multiply this by the number of channels being serviced by the same ADC to get your required sampling rate. Today's ADC technology provides much greater sampling rates in most cases, even when cost is a primary factor.

Resolution:

The resolution of an ADC is the number of steps, or divisions, that the ADC can divide the maximum input voltage into. For example a 12-bit ADC can provide 212 or 4096 divisions and a 16-bit ADC can provide 216 or 65536 divisions.

The resolution provided by the 2n formula is the ideal resolution and most ADCs usually don't meet this ideal resolution due to physical factors, most importantly thermal noise generated by the device and the signal chain. Some ADCs will provide a "noise-free resolution" spec. Use this specification as the converter's resolution to remove effects of noise.

As an example, if building a postage weigh scale, and the spec is to accurately measure to the nearest tenth of an ounce over a 10 pound range, you'll need an ADC capable of providing a minimum of 1,600 divisions, but to get repeatable accuracy to take into account thermal noise, other converter noise, and other signal chain errors, you'll usually multiply this value by 10, so for this application, 16,000 divisions. In this application a 16-bit ADC could most likely provide the needed resolution, if the input provided by the transducer is close to the converter's input range.

A typical 16-bit ADC that has an input (full scale) range of 3 Volts can resolve input divisions of 3/216 or 46 µVolts. If the maximum input signal can only reach 1V, due to an amplification limitation, the maximum number of divisions that the ADC will be able to detect is 1/3 of the max, or about 22,000 divisions. This would still be good enough to meet the postage scale example specs.

Thermal Noise effect on Resolution

Because of the noise errors accumulated within an ADC actual output codes generated by an ADC are never a single value. They are a range of values represented by histogram having an approximate Gaussian distribution. To ensure that the ADC will provide the needed resolution for the input voltage range it is a good idea to calculate the number noise free input divisions that the converter can provide (if it hasn't been provided in the product specification).

Statistics tells us that with Gaussian curves, 99% of the values output will fall within 6.6 sigma of the mean value, with the mean value centered on the most probable or expected division.

Figure 2. Noise free range illustrated

To help calculate this value most ADCs contain a parameter called VRMS Noise. Find this value on the datasheet. Multiply it by 6.6 to get the minimum noise free step in terms of Voltage that the converter can provide. Then take the input range and divide it by the minimum noise free step to get the noise free resolution. If this number is more than the number of divisions required in the application then the selected ADC should fit. If not, and it is not possible to further amplify the input from the sensor element, look for an ADC with a lower VRMS Noise specification. Here's an example:

The MAX11205 16-bit ADC provides a thermal noise specification of: 720nVRMS Noise

With an amplified sensor voltage input of 1 Volt, the number of noise free input divisions that the ADC can provide is:

1 / (.00000720 x 6.6) = 213,000

The MAX11205 has an exceptionally low VRMS Noise specification, and so it can easily provide the noise free resolution that the above application requires.

Alternate phrasing for specifications involving the calculation of noise free resolution include: noise-free counts or codes inside the range.

Most high-precision ADC data sheets specify thermal noise as input referred noise and provide the specification in RMS noise or peak-to-peak noise. Sigma Delta converter data sheets typically report input referred noise or peak-to-peak noise vs. data rate output. The input referred noise is typically measured with input shorted and the noise is calculated from noise histogram plots.

Single or double ended inputs

ADC ICs are available with single-ended or differential inputs. For designs that require high precision and sensing of very low input voltage changes, an ADC with differential inputs is recommended. The differential input provides the best noise rejection, and wider dynamic range compared to a single-ended input. See application note 1108, "Understanding Single-Ended, Pseudo-Differential and Fully-Differential ADC Inputs", to obtain a more in-depth understanding.

INL – Integral Non-Linearity

In designs that require lower resolution ADCs, such as 10-bit through 16-bit converters, the INL parameter is a key parameter in determining the accuracy of the device. INL error is described as the deviation, in LSB or percent of full-scale range (FSR), of an actual transfer function from a straight line. All else being equal choose the ADC with a lower INL parameter in order to select the ADC that will provide the best accuracy. See application note 283, "INL/DNL Measurements for High-Speed Analog-to-Digital Converters (ADCs)", for a more in-depth understanding.

#### Selecting an Op Amp

The function of the op amp in a signal chain is to amplify the output of the transducer in a linear fashion so that the maximum transducer output approximately matches the input range of the ADC. This acts to maximize the resolution of the signal chain.

Most load cells will provide a "span" or "sensitivity" specification that provides the maximum change of the cell's output for every Volt of excitation. Common ranges for load cells are 2mV/V to 20mV/V. Typically excitation voltages range from 3V to 5V. With this, the maximum output provided by transducers of this type can range from 10mV to 100mV, a fairly wide range but very dependent on the selected transducer.

The amplifier should convert this range to the maximum input range that the ADC can accommodate. Typically the ADC has a useable input range of from 2.5V to 3.3V. So the input amplifier might have to provide gains of 50 to 200 depending on the application.

The input op amp needs to amplify signals that are in the microvolt and millivolt range, the same range as naturally occurring noise. It is important that this circuit is selected properly and also laid out properly to prevent the amplification step from introducing errors. Look for low-noise amplifiers (LNAs) with extremely low offset voltage (VOS), low temperature, and offset drifts for this application.

In most small signal designs a low noise "auto-zero" op amp is the preferred op amp type. This will minimize the offset error potential in your signal chain. The MAX44246 is an example of this type of op amp. The diagram below shows a typical op amp deployment. Note the use of dual single ended op amps in lieu of an instrumentation amplifier. This approach provides better results when used with differential input ADCs.

Figure 3. Typical Op Amp deployment within a pressure sensing signal chain

Tip: Most pressure transducers take the form of a Wheatstone bridge. Please see application note 3426, "Resistive Bridge Basics: Part One", for in-depth information about working with Wheatstone bridge circuits.

#### Selecting a Multiplexor

When selecting a multiplexor the design engineer primarily needs to know the basics: the number of input channels. In addition, the multiplexor must be able to accommodate the full input voltage range. In addition make sure the switching speed is fast enough for the application. Generally the product with the lowest "on" resistance that meets your cost goals is the best.

#### Selecting a Reference

The voltage reference provides a known voltage level at a high precision. Any deviation of the stated reference level can induce error into the system. For the sensor measurement application, the output of the reference is used as an input to the ADC or AFE and also as excitation to the transducer. This way if the reference voltage varies due to noise or other anomaly, both the sensor input and ADC experiences the same variance, reducing the total error.

The voltage reference contributes to systematic and random error. The reference noise source degrades the noise performance of the ADC. So a reference with better performance than the ADC should be chosen. The reference's initial error and drift over temperature and time for a high precision system is one of the most important contributors of gain error. For systems that are calibrated, the drift over temperature and time is the most critical parameter.

Key parameters in selecting a reference include: load drive, initial accuracy, noise, temperature drift, and stability. The load drive in a pressure sensor application can be higher than in many other applications due to the need to drive the transducer. Transducer load can be in the range of 10 to 20 milliamps for a typical pressure transducer in addition to that required by the ADC.

The MAX6325/MAX6341/MAX6350 are low-noise, precision voltage references with extremely low, 0.5ppm/°C, typical temperature coefficients and excellent, ±0.02% initial accuracy. These references are recommended for signal chains with ADCs of 16-bit resolution and up.

For more in-depth information on selecting voltage references, please see this application note:

Application Note 2879: "Selecting the Optimum Voltage Reference"

#### Correcting Errors

Achieving accuracy in an application means having to be able to correct for linearization errors, component offset errors, and system noise.

As you work through the math required to calculate the operating voltages of the circuit, rounding, and measuring tolerances can quickly cause errors to build up.

For example, linearity of the devices from the load cell through the op amp and ADC will add error into the design. Fortunately today it is very easy to correct errors through digital linearization. Essentially this process uses a lookup table that provides the ideally expected digital output for every actual digital output received. The key to digital linearization is that it can remove errors that are repeatable.

Errors due to minor differences between component values used on individual circuits have to be calibrated out; usually this is a one-time adjustment. Errors due to noise have to be averaged out by taking multiple readings and presenting an average reading as the final output – ADCs that employ the delta-sigma algorithm have this type of averaging built-in.

#### Highly integrated Signal Chains

Many signal chain applications can be implemented with a highly integrated AFE chip. The benefit of using a single chip or integrated signal chain IC is that it makes the design much easier, reducing component selection time, layout, and troubleshooting, while also generally providing improved specifications for an application. The integration of the input op amp with the ADC on a single chip can provide much better total system performance. The tradeoff in using this approach might be less optimization from a cost standpoint.

At a minimum, an integrated signal chain IC will include a programmable gain op amp and an ADC. Some AFE ICs also provide an input multiplexor for implementing 1 to 4 channels. The output of an AFE is traditionally serial digital with I2C and SPI being favored interface standards.

Selecting an integrated AFE is much the same as selecting a discrete signal chain, though fewer design options will be available. For example amplifier gain may be limited, and you'll most likely have to over-specify some parameters to get the overall desired performance.

Just like selecting a discrete signal chain, when choosing an AFE (for example PGA + ADC), after selecting the number of channels required, sampling rate and the nominal resolution, it is again important to carefully evaluate the specifications that have the most impact on systematic and random error (those that have the most effect on accuracy and precision). For the most part, this is thermal noise and noise free resolution.

Noise performance specifications and terms like noise-free range or effective resolution that indicate how well an AFE can distinguish a fixed input level are reported typically in the datasheets. Alternate phrasing for these applications might be noise-free counts or codes inside the range.

For thermal noise, most high-precision AFE data sheets specify input referred noise, in terms of RMS noise or peak-to-peak noise. The input referred noise is typically measured with input shorted and the noise is calculated from noise histogram plots. AFE data sheets that use Sigma Delta converters with a PGA typically report input referred noise or peak-to-peak noise in a table vs. data rate output and PGA gain.

Examples of integrated signal chain products from Maxim that are optimal for use in pressure sensor applications include: the MAX1415, a two channel 16 bit ADC with integrated PGA; and the MAX11270, a high end 24-bit ADC with PGA.

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