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The s Variable: Euler’s Relation and Phasor Expressions of Waveforms

The s Variable: Euler’s Relation and Phasor Expressions of Waveforms

A powerful mathematical concept useful for analyzing practically any physical system – electrical…


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Transfer Function Analysis

Transfer Function Analysis

An extremely important topic in engineering is that of transfer functions. Simply defined, a transfer function…


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Transmitter Damping Adjustments

Transmitter Damping Adjustments

The vast majority of modern process transmitters (both analog and digital) come equipped with a feature known…


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Problem-solving by Simplification

Problem-solving by Simplification

A whole class of problem-solving techniques focuses on altering the given problem into a simpler form that is…


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Legal Code

Legal Code

Creative Commons Attribution 4.0 International Public License By exercising the Licensed Rights (defined…


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Phasors, Phase Shift and Phasor Algebra

Phasors, Phase Shift and Phasor Algebra

Phasors are to AC circuit quantities as polarity is to DC circuit quantities: a way to express the…


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Practical Measures of Reliability

Practical Measures of Reliability

In reliability engineering, it is important to be able to quantity the reliability (or conversely, the…


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Analog Electronic PID Controllers

Analog Electronic PID Controllers

Constructing PID control systems using discrete components is a fairly simple method involving operational…


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Thermocouple Types, Junctions, Connector and Tip Styles

Thermocouple Types, Junctions, Connector and Tip Styles

RTDs are completely passive sensing elements, requiring the application of an externally-sourced electric…


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Introduction to Inductors and Inductance

Introduction to Inductors and Inductance

Any conductor possesses a characteristic called inductance: the ability to store energy in the form of a…


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FOUNDATION Fieldbus H1 Protocol Segment Troubleshooting

FOUNDATION Fieldbus H1 Protocol Segment Troubleshooting

Feedback obtained from industrial users of FF reveal a common pattern: Fieldbus is a powerful and reliable…


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Conservation Laws

Conservation Laws

The Law of Mass Conservation states that matter can neither be created nor destroyed. The Law of Energy…


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Controller Output Current Loops

Controller Output Current Loops

The simplest form of 4-20 mA current loop is the type used to represent the output of a process controller,…


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Phasors, Phase Shift and Phasor Algebra

Phasors, Phase Shift and Phasor Algebra

Phasors are to AC circuit quantities as polarity is to DC circuit quantities: a way to express the…


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Polyphase AC Power

Polyphase AC Power

“Polyphase” means “many phases,” describing a form of AC electrical system where…


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Kirchhoff’s Current and Voltage Laws

Kirchhoff’s Current and Voltage Laws

Two extremely important principles in electric circuits were codified by Gustav Robert Kirchhoff in the year…


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Symbolic Versus Numerical Calculus

Symbolic Versus Numerical Calculus

Calculus has a reputation for being difficult to learn, and with good reason. The traditional approach to…


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LRV and URV Settings, Digital Trim (Digital Transmitters)

LRV and URV Settings, Digital Trim (Digital Transmitters)

The advent of “smart” field instruments containing microprocessors has been a great advance for…


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Stoichiometry and the Law of Mass Conservation

Stoichiometry and the Law of Mass Conservation

Stoichiometry is the accounting of atoms before and after a chemical reaction. It is an expression of the Law…


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Basics of pH Measurement in Industrial Control

Basics of pH Measurement in Industrial Control

Hydrogen ion activity in aqueous (water-solvent) solutions is a very important parameter for a wide variety of…


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Chromatography: Methods, Detectors and Species

Chromatography: Methods, Detectors and Species

Imagine a major marathon race, where hundreds of runners gather in one place to compete. When the starting gun…


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Control Valve Characterization

Control Valve Characterization

Control valves are supposed to deliver reliable, repeatable control of process fluid flow rate over a wide…


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Ladder Diagram (LD) Structure Commands

Ladder Diagram (LD) Structure Commands

The simple PLC ladder diagram (LD) commands consist of contacts and coils, arranged in sequences that mimic…


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The International System of Units

The International System of Units

The very purpose of physics is to quantitatively describe and explain the physical world in as few terms as…


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Analytical Measurements of Chemical Compositions

Analytical Measurements of Chemical Compositions

A great many chemical composition measurements may be made indirectly by means of electricity, if those…


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Elementary Thermodynamics

Elementary Thermodynamics

Thermodynamics is the study of heat, temperature, and their related effects in physical systems. As a subject,…


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Calibration Errors and Testing

Calibration Errors and Testing

The efficient identification and correction of instrument calibration errors is an important function for…


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Introduction to Protective Relaying

Introduction to Protective Relaying

Circuit breakers used in residential, commercial, and light industrial service are self-tripping devices: they…


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Pilot Valves and Pneumatic Amplifying Relays

Pilot Valves and Pneumatic Amplifying Relays

Self-balancing mechanisms consisting solely of a baffle/nozzle detector coupled to a feedback bellows, while…


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