Linearity in measuring devices

10/15/2010


Dear Control Engineering: Sometimes I see the term “linearity” used in reference to measuring devices. What does this mean?

Linearity reflects the ability of a sensor to respond to changes in a measured variable in the same way across the full range. If you’ve seen old pressure gages, they often have uneven scales where the divisions are larger at one end of the scale than the other. This compensates for non-linearities in the flexing of the bourdon tube. The same concepts apply to electronic devices, whether they are process instrments such a flowmeters, or discrete devices such as proximity sensors.

Let’s use a temperature sensor as an example. It has to convert a temperature to a voltage (thermocouple) or resistance (RTD, thermistor). As the temperature changes, the voltage or resistance has to change with it. If a device has high linearity, the amount of voltage or resistance change will be the same per change in temperature across the full range of the device.

In the case of a type K thermocouple, for example, when in roughly the middle of its measuring range (500 °C) a change of 10 °C will cause a change of 0.427 mV. If the device is truly linear, that change in voltage per degree will be the same over the entire measuring range. As a matter of fact, it isn’t. At the low extreme (-250 °C) a 10 °C change is 0.017 mV. At the opposite extreme of 1,370 °C, a 10 °C change is 0.340 mV.

Thermistor resistance curve.Thermistors are generally regarded as non-linear. In an article The Challenges of Temperature Sensing, we included this graph of a typical thermistor response curve. What the graph shows is that at the low end of the range, a small change in temperature causes a large change in resistance. However the opposite is the case at the high end. The range of highest linearity for this device is roughly between -20 and 20 °C.

If you buy a temperature measuring device, or any other type of electronic sensor for that matter, the electronics in the transmitter will be designed to compensate for the non-linearities of the sensing element. You probably won’t even know that they’re there. The manufacturer will limit the effective range of the device such that it will cut off the worst areas at the extremes. If the behavior of the sensor is not predictable and repeatable beyond certain points, those areas should be excluded.

Peter Welander, pwelander@cfemedia.com



Engineers' Choice Awards
The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by Control Engineering subscribers.
System Integrator Giants
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
System Integrator of the Year
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
How to Maximize Factory Automation Efficiency with Low Cost Machine Vision
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Wireless Reliability in Harsh Environments
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
Human Factors and the Impact on Plant Safety
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
August 2018
Augmented reality and virtual reality education, autotuning PID control, cybersecurity advice, educating engineers
July 2018
Ladder logic best practices and object-oriented programming, safety instrumented systems, enclosure design issues and challenges, process control advice
June 2018
Discrete and process sensor fundamentals, autotuning controls, system integrator roundtable
Edge Computing
This article collection contains several articles on how today's technologies heap benefits onto an edge-computing architecture such as faster computing, better networking, more memory, smarter analytics, cloud-based intelligence, and lower costs.
Data Center Design
Data centers, data closets, edge and cloud computing, co-location facilities, and similar topics are among the fastest-changing in the industry.
PLCs
Programmable logic controllers (PLCs) represent the logic (decision) part of the control loop of sense, decide, and actuate. Featured articles in this digital report compare PLCs and programmable automation controllers (PACs), industrial PCs, and robotic controllers.
SIDB

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

August 2018
SCADA standardization, capital expenditures, data-driven drilling and execution
June 2018
Machine learning, produced water benefits, progressive cavity pumps
April 2018
ROVs, rigs, and the real time; wellsite valve manifolds; AI on a chip; analytics use for pipelines
John O. Ayuk, PE, CFSE, PMP, CAP
Automation Engineer; Wood Group
Doug Baker
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
Data Centers: Impacts of Climate and Cooling Technology
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
Safety First: Arc Flash 101
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
Critical Power: Hospital Electrical Systems
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
Engineers' Choice Awards
The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by Control Engineering subscribers.
System Integrator Giants
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
System Integrator of the Year
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
How to Maximize Factory Automation Efficiency with Low Cost Machine Vision
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Wireless Reliability in Harsh Environments
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
Human Factors and the Impact on Plant Safety
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
August 2018
Augmented reality and virtual reality education, autotuning PID control, cybersecurity advice, educating engineers
July 2018
Ladder logic best practices and object-oriented programming, safety instrumented systems, enclosure design issues and challenges, process control advice
June 2018
Discrete and process sensor fundamentals, autotuning controls, system integrator roundtable
Edge Computing
This article collection contains several articles on how today's technologies heap benefits onto an edge-computing architecture such as faster computing, better networking, more memory, smarter analytics, cloud-based intelligence, and lower costs.
Data Center Design
Data centers, data closets, edge and cloud computing, co-location facilities, and similar topics are among the fastest-changing in the industry.
PLCs
Programmable logic controllers (PLCs) represent the logic (decision) part of the control loop of sense, decide, and actuate. Featured articles in this digital report compare PLCs and programmable automation controllers (PACs), industrial PCs, and robotic controllers.
SIDB

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

August 2018
SCADA standardization, capital expenditures, data-driven drilling and execution
June 2018
Machine learning, produced water benefits, progressive cavity pumps
April 2018
ROVs, rigs, and the real time; wellsite valve manifolds; AI on a chip; analytics use for pipelines
John O. Ayuk, PE, CFSE, PMP, CAP
Automation Engineer; Wood Group
Doug Baker
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
Data Centers: Impacts of Climate and Cooling Technology
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
Safety First: Arc Flash 101
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
Critical Power: Hospital Electrical Systems
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
Engineers' Choice Awards
The Engineers' Choice Awards highlight some of the best new control, instrumentation and automation products as chosen by Control Engineering subscribers.
System Integrator Giants
The System Integrator Giants program lists the top 100 system integrators among companies listed in CFE Media's Global System Integrator Database.
System Integrator of the Year
Each year, a panel of Control Engineering and Plant Engineering editors and industry expert judges select the System Integrator of the Year Award winners in three categories.
How to Maximize Factory Automation Efficiency with Low Cost Machine Vision
This eGuide illustrates solutions, applications and benefits of machine vision systems.
Wireless Reliability in Harsh Environments
Learn how to increase device reliability in harsh environments and decrease unplanned system downtime.
Human Factors and the Impact on Plant Safety
This eGuide contains a series of articles and videos that considers theoretical and practical; immediate needs and a look into the future.
August 2018
Augmented reality and virtual reality education, autotuning PID control, cybersecurity advice, educating engineers
July 2018
Ladder logic best practices and object-oriented programming, safety instrumented systems, enclosure design issues and challenges, process control advice
June 2018
Discrete and process sensor fundamentals, autotuning controls, system integrator roundtable
Edge Computing
This article collection contains several articles on how today's technologies heap benefits onto an edge-computing architecture such as faster computing, better networking, more memory, smarter analytics, cloud-based intelligence, and lower costs.
Data Center Design
Data centers, data closets, edge and cloud computing, co-location facilities, and similar topics are among the fastest-changing in the industry.
PLCs
Programmable logic controllers (PLCs) represent the logic (decision) part of the control loop of sense, decide, and actuate. Featured articles in this digital report compare PLCs and programmable automation controllers (PACs), industrial PCs, and robotic controllers.
SIDB

Find and connect with the most suitable service provider for your unique application. Start searching the Global System Integrator Database Now!

August 2018
SCADA standardization, capital expenditures, data-driven drilling and execution
June 2018
Machine learning, produced water benefits, progressive cavity pumps
April 2018
ROVs, rigs, and the real time; wellsite valve manifolds; AI on a chip; analytics use for pipelines
John O. Ayuk, PE, CFSE, PMP, CAP
Automation Engineer; Wood Group
Doug Baker
System Integrator; Cross Integrated Systems Group
Jose S. Vasquez, Jr.
Jose S. Vasquez, Jr.
Fire & Life Safety Engineer; Technip USA Inc.
Data Centers: Impacts of Climate and Cooling Technology
This course focuses on climate analysis, appropriateness of cooling system selection, and combining cooling systems.
Safety First: Arc Flash 101
This course will help identify and reveal electrical hazards and identify the solutions to implementing and maintaining a safe work environment.
Critical Power: Hospital Electrical Systems
This course explains how maintaining power and communication systems through emergency power-generation systems is critical.
click me