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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Waves and Their Applications in Technologies for Information Transfer

C-PS4-5

Energy and Power Signals

Stellen Sie sich ein elektrisches System mit einem Widerstand vor. Dabei ermöglichen die Spannungs- und Stromsignale die Leistungs- und Energiemessung über den Widerstand.
Bei einem zeitkontinuierlichen Signal ist die Gesamtenergie über das Zeitintervall definiert als das Integral des Quadrats der Größe des Signals über dasselbe Intervall.
Die zeitlich gemittelte Leistung wird berechnet, indem die Gesamtenergie durch die Dauer des Zeitintervalls dividiert wird.
Bei einem zeitdiskreten Signal wird die Gesamtenergie über das Zeitintervall berechnet, indem die Quadrate der Signalgröße für alle Punkte innerhalb des Intervalls summiert werden, während die durchschnittliche Leistung ermittelt wird, indem die Gesamtenergie durch 2N+1 dividiert wird.
Die Ausdrücke für Gesamtenergie und -leistung werden für kontinuierliche und diskrete Signale über die Intervalle — t1 bis t2 und –n1 bis n2 neu definiert.
Basierend auf diesen Definitionen gibt es drei Haupttypen von Signalen.
Energiesignale haben eine endliche Gesamtenergie, was zu einer durchschnittlichen Leistung von null führt.
Leistungssignale haben eine endliche durchschnittliche Leistung, was zu unendlicher Energie führt.
Nicht-physikalische Signale sind Signale, bei denen weder Leistung noch Energie endlich sind.

energie- und leistungssignale

In einem elektrischen System mit einem Widerstand erleichtern Spannungs- und Stromsignale die Messung von Leistung und Energie über den Widerstand. Bei einem kontinuierlichen Signal wird die Gesamtenergie über ein Zeitintervall als Integral des Quadrats der Signalgröße über dieses Intervall definiert. Mathematisch ausgedrückt wird dies wie folgt ausgedrückt:

<img alt="Equation1" src="/files/ftp_upload/16038/16038_PT%20EQUATION_1v2.svg" style="text-align: center; height: 40px;">

Die gemittelte Leistung wird berechnet, indem die Gesamtenergie durch die Dauer des Zeitintervalls geteilt wird, was gegeben ist durch:

<img alt="Equation2" src="/files/ftp_upload/16038/16038_PT%20EQUATION_2v2.svg" style="text-align: center; height: 40px;">

Bei einem zeitdiskreten Signal wird die Gesamtenergie berechnet, indem die Quadrate der Signalgröße für alle Punkte innerhalb des Intervalls summiert werden:

<img alt="Equation3" src="/files/ftp_upload/16038/16038_PT%20EQUATION_3v2.svg" style="text-align: center; height: 40px;">

Die durchschnittliche Leistung wird ermittelt, indem die Gesamtenergie durch die Anzahl der Punkte im Intervall geteilt wird:

<img alt="Equation4" src="/files/ftp_upload/16038/16038_PT%20EQUATION_4v2.svg" style="text-align: center; height: 38px;">

Diese Ausdrücke für Gesamtenergie und Leistung werden für unendliche Zeitintervalle neu definiert, um praktischen Anwendungen gerecht zu werden.

Basierend auf diesen Definitionen werden Signale in drei Typen kategorisiert: Energiesignale, Leistungssignale und nicht-physikalische Signale. Energiesignale haben eine endliche Gesamtenergie, was zu einer durchschnittlichen Leistung von Null führt. Umgekehrt haben Leistungssignale eine endliche Durchschnittsleistung, was zu einer unendlichen Gesamtenergie über ein unendliches Intervall führt. Nicht-physikalische Signale sind solche, bei denen weder Leistung noch Energie endlich sind, was sie für reale Anwendungen unpraktisch macht. Das Verständnis dieser Klassifizierungen ist für eine genaue Signalanalyse und ein effizientes Energiemanagement in elektrischen Systemen von entscheidender Bedeutung.

Energie- und Leistungssignale

Stellen Sie sich ein elektrisches System mit einem Widerstand vor. Dabei ermöglichen die Spannungs- und Stromsignale die Leistungs- und Energiemessung über den Widerstand.
Für eine ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

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Einführung in Signale und Systeme

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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

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Signals and Systems in Everyday Data

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Signal Types by Time and Amplitude

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...

energy and power 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...

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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...

classification of systems-i

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...

classification of systems-ii

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...

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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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