Name: power and energy in electrical signals
Uploaded: 2024-09-26T13:16:53.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

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South Carolina College and Career Ready Science Standards

High School

Chemistry

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C-PS4-5

Energy and Power Signals

Consider an electric system with a resistor. Here, the voltage and current signals enable power and energy measurement across the resistor.
For a continuous-time signal, the total energy over the time interval is defined as the integral of the square of the signal&#39;s magnitude over the same interval.
The time-averaged power is calculated by dividing the total energy by the duration of the time interval.
For a discrete-time signal, the total energy over the time interval is computed by summing the squares of the signal&#39;s magnitude for all points within the interval, while the average power is found by dividing the total energy by 2N+1.
The expressions for total energy and power are redefined for continuous and discrete signals over the intervals &#8212;t1 to t2 and &#8211;n1 to n2.
Based on these definitions, there are three major types of signals.
Energy signals have finite total energy, resulting in zero average power.
Power signals have finite average power, which results in infinite energy.
Non-physical signals are signals where neither power nor energy are finite.

energy and power signals

In an electrical system with a resistor, voltage and current signals facilitate the measurement of power and energy across the resistor. For a continuous-time signal, the total energy over a time interval is defined as the integral of the square of the signal's magnitude over that interval. Mathematically, this is expressed as:
<img alt="Signal energy equation, \(E=\lim_{T\to\infty} \int_{-T/2}^{T/2} |x(t)|^2 dt\), mathematical formula." src="/files/ftp_upload/16038/16038_PT%20EQUATION_1v2.svg" style="text-align: center; height: 40px;" data-altupdatedat="1762173717000" data-alt="Equation1" />
The time-averaged power is calculated by dividing the total energy by the duration of the time interval, given by:
<img alt="Average power calculation formula; equation for signal processing analysis." src="/files/ftp_upload/16038/16038_PT%20EQUATION_2v2.svg" style="text-align: center; height: 40px;" data-altupdatedat="1762173717000" data-alt="Equation2" />
For a discrete-time signal, the total energy is computed by summing the squares of the signal's magnitude for all points within the interval:
<img alt="Power signal energy formula, \(E = \lim_{N \to \infty} \sum_{n=-N}^{+N} |x[n]|^2\); mathematical equation." src="/files/ftp_upload/16038/16038_PT%20EQUATION_3v2.svg" style="text-align: center; height: 40px;" data-altupdatedat="1762173717000" data-alt="Equation3" />
The average power is found by dividing the total energy by the number of points in the interval:
<img alt="Average power equation for discrete signals, &#931;x[n]^2, calculus formula, educational use." src="/files/ftp_upload/16038/16038_PT%20EQUATION_4v2.svg" style="text-align: center; height: 38px;" data-altupdatedat="1762173717000" data-alt="Equation4" />
These expressions for total energy and power are redefined for infinite time intervals to accommodate practical applications.
Based on these definitions, signals are categorized into three types: energy signals, power signals, and non-physical signals. Energy signals have finite total energy, resulting in zero average power. Conversely, power signals have finite average power, leading to infinite total energy over an infinite interval. Non-physical signals are those where neither power nor energy is finite, making them impractical for real-world applications. Understanding these classifications is vital for accurate signal analysis and efficient energy management in electrical systems.

Consider an electric system with a resistor. Here, the voltage and current signals enable power and energy measurement across the resistor.
For a ...

Education

JoVE Core

Electrical Engineering

Unit 1

Introduction to Signals and Systems

KEY TERMS AND CONCEPTS

power and energy in electrical signals

Power and energy in electrical signals are measured from voltage and current across a resistor. These signals help describe how much energy a signal carries and how much power it delivers over time.

For a continuous-time signal, total energy is found by integrating the square of the signal's magnitude over a chosen time interval. Time-averaged power is then the total energy divided by the length of that interval. For a discrete-time signal, total energy is found by summing the squares of the signal's magnitude at each point in the interval. Average power is the total energy divided by the number of points in that interval.

These definitions are also extended to infinite time intervals for practical use. Signals are then grouped into three categories: energy signals, power signals, and non-physical signals. Energy signals have finite total energy and zero average power. Power signals have finite average power but infinite total energy over an infinite interval. Non-physical signals have neither finite power nor finite energy, so they are not practical for real-world applications. Knowing these categories helps with signal analysis and energy management in electrical systems.

Power and Energy in Electrical Signals

signal and system

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Signals in signal processing are grouped by time behavior, amplitude, and whether they start before or after time zero. These signal classes help students describe and compare signals before they are analyzed or processed. A continuous-time signal has a value at every instant in time. A discrete-time signal has values only at specific moments, often written as x(n), where n is an integer. Discrete-time signals often come from systems with naturally discrete values, such as digital audio...

Power and energy in electrical signals are measured from voltage and current across a resistor. These signals help describe how much energy a signal carries and how much power it delivers over time. For a continuous-time signal, total energy is found by integrating the square of the signal's magnitude over a chosen time interval. Time-averaged power is then the total energy divided by the length of that interval. For a discrete-time signal, total energy is found by summing the squares of the...

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Complex Exponentials in Signal Behavior

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basic discrete time signals

Discrete-Time Signal Basics and Shapes

Discrete-time signals include several basic sequences used in signal processing. The unit step sequence is 1 for zero and positive values of the integer n. A graph of eight sample points shows it as a step that begins at n = 0 and stays constant after that. The unit impulse, also called the sample sequence, is 0 for every n except at n = 0, where it equals 1. This sequence is written as δ(n). It is the first difference of the unit step sequence, and the unit step sequence u(n) is the...

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Signal Transformations in Time and Amplitude

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized. Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly. Time scaling...

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System Properties: Linearity, Causality, Memory

System properties such as linearity, causality, and memory help describe how a system responds to input. These ideas are useful for studying and designing systems in engineering. A system can be checked by looking at how its output changes with different inputs. Linearity means the input-output relationship follows homogeneity and additivity. Homogeneity says that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Additivity means the response...

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Continuous and Discrete System Models

Continuous-time and discrete-time systems are two common ways to model signals and their outputs. In continuous-time systems, both input and output signals change smoothly as time moves continuously. These systems are often written with differential or algebraic equations. An RC circuit is one example of a continuous-time system. Its input and output voltage can be related by a differential equation based on Ohm’s law and the capacitor relation. Discrete-time systems work differently. Their...

key terms and concepts

Learn how voltage and current across a resistor are used to measure signal energy and average power, and how signals are classified as energy, power, or non-physical.

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Power and Energy in Electrical Signals

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