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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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Legal Code

Legal Code

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


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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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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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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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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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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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Analog Electronic PID Controllers

Analog Electronic PID Controllers

Although analog electronic process controllers are considered a newer technology than pneumatic process…


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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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Tuning PID Controllers

Tuning PID Controllers

Learning how to tune PID controllers is a skill born of much practice. Regardless of how thoroughly you may…


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Rotating Phasor in Three-dimensional Form

Rotating Phasor in Three-dimensional Form

The following animation shows a rotating phasor in three-dimensional form. The phasor rotates in a complex…


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Weighfeeders

Weighfeeders

A special type flowmeter suited for powdered or granular solids is the weighfeeder. One of the most common…


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Colorimetric and Potentiometric pH Measurement

Colorimetric and Potentiometric pH Measurement

pH is the measurement of the hydrogen ion activity in a liquid solution. It is one of the most common forms of…


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Single-line Electrical Diagrams

Single-line Electrical Diagrams

Electrical power grids primarily consist of three-phase AC circuits. This means most power lines (transmission…


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the Negative Consequences of Poor PID Controller Tuning

the Negative Consequences of Poor PID Controller Tuning

Much has been written about the benefits of robust PID control. Increased productivity, decreased equipment…


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Practical PID Controller Features

Practical PID Controller Features

In order for any PID controller to be practical, it must be able to do more than just implement the PID…


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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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Advantages and Disadvantages of Pneumatic Instruments

Advantages and Disadvantages of Pneumatic Instruments

The disadvantages of pneumatic instruments are painfully evident to anyone familiar with both pneumatic and…


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Valve Positioners

Valve Positioners

The reason why a pneumatic control valve’s stem position corresponds linearly to the amount of air…


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Root Mean Square (RMS) Quantities

Root Mean Square (RMS) Quantities

It is often useful to express the amplitude of an alternating quantity such as voltage or current in terms…


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Basic Components Common to all Radio Systems

Basic Components Common to all Radio Systems

“Radio” systems use electromagnetic fields to communicate information over long distances through…


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The HART Digital/Analog Hybrid Standard

The HART Digital/Analog Hybrid Standard

A technological advance introduced in the late 1980’s was HART, an acronym standing for Highway…


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Physics and Chemistry Terminology and Definitions

Physics and Chemistry Terminology and Definitions

Atom: the smallest unit of matter that may be isolated by chemical means. Particle: a part of an atom,…


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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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Boiler Water Level Control System Example

Boiler Water Level Control System Example

Steam boilers are very common in industry, principally because steam power is so useful. Common uses for steam…


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Applications of Spectroscopy for Analytical Measurement

Applications of Spectroscopy for Analytical Measurement

Much of our knowledge about atomic structure comes from experimental data relating the interaction between…


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Radiation Level Measurement

Radiation Level Measurement

Certain types of nuclear radiation easily penetrates the walls of industrial vessels, but is attenuated by…


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FOUNDATION Fieldbus H1 Protocol Physical Layer

FOUNDATION Fieldbus H1 Protocol Physical Layer

Layer 1 of the OSI Reference Model is where we define the “physical” elements of a digital data…


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Flow Measurement from Differential Pressure

Flow Measurement from Differential Pressure

In our first signal characterization example, we tackle the problem of measuring fluid flow through a pipe. To…


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