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

Considera un sistema elettrico con un resistore. In questo caso, i segnali di tensione e corrente consentono la misurazione della potenza e dell'energia attraverso il resistore.
Per un segnale a tempo continuo, l'energia totale nell'intervallo di tempo è definita come l'integrale del quadrato della grandezza del segnale nello stesso intervallo.
La potenza media nel tempo viene calcolata dividendo l'energia totale per la durata dell'intervallo di tempo.
Per un segnale a tempo discreto, l'energia totale nell'intervallo di tempo viene calcolata sommando i quadrati della grandezza del segnale per tutti i punti all'interno dell'intervallo, mentre la potenza media si trova dividendo l'energia totale per 2N+1.
Le espressioni per l'energia totale e la potenza sono ridefinite per i segnali continui e discreti negli intervalli: da t1 a t2 e da -n1 a n2.
Sulla base di queste definizioni, ci sono tre tipi principali di segnali.
I segnali di energia hanno un'energia totale finita, con conseguente potenza media pari a zero.
I segnali di alimentazione hanno una potenza media finita, che si traduce in energia infinita.
I segnali non fisici sono segnali in cui né la potenza né l'energia sono finite.

segnali di energia e potenza

In un sistema elettrico con un resistore, i segnali di tensione e corrente facilitano la misurazione della potenza e dell’energia attraverso il resistore. Per un segnale a tempo continuo, l'energia totale su un intervallo di tempo è definita come l'integrale del quadrato della grandezza del segnale su quell'intervallo. Matematicamente, questo è espresso come:

<img alt="Equation1" src="/files/ftp_upload/16038/16038_PT%20EQUATION_1v2.svg" style="height: 40px;">

La potenza media nel tempo è calcolata dividendo l'energia totale per la durata dell'intervallo di tempo, dato da:

<img alt="Equation2" src="/files/ftp_upload/16038/16038_PT%20EQUATION_2v2.svg" style="height: 40px;">

Per un segnale a tempo discreto, l'energia totale è calcolata sommando i quadrati della magnitudine del segnale per tutti i punti all'interno dell'intervallo:

<img alt="Equation3" src="/files/ftp_upload/16038/16038_PT%20EQUATION_3v2.svg" style="height: 40px;">

La potenza media è trovata dividendo l'energia totale per il numero di punti nell'intervallo:

<img alt="Equation4" src="/files/ftp_upload/16038/16038_PT%20EQUATION_4v2.svg" style="height: 38px;">

Queste espressioni per l’energia e per la potenza totali sono ridefinite per gli intervalli di tempo infiniti così da adattarsi alle applicazioni pratiche.

Sulla base di queste definizioni, i segnali sono classificati in tre tipi: segnali energetici, segnali di potenza e segnali non fisici. I segnali energetici hanno energia totale finita, con una conseguente potenza media pari a zero. Al contrario, i segnali di potenza hanno una potenza media finita, che porta ad un'energia totale infinita su un intervallo infinito. I segnali non fisici sono quelli in cui né la potenza né l'energia sono finite, questo li rende poco pratici per le applicazioni nel mondo reale. La comprensione di queste classificazioni è fondamentale per un'analisi accurata del segnale e per una gestione efficiente dell'energia nei sistemi elettrici.

Considera un sistema elettrico con un resistore. In questo caso, i segnali di tensione e corrente consentono la misurazione della potenza e dell'energia attraverso il resistore.
Per un ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Introduction to Signals and Systems

Introduzione ai segnali e ai sistemi

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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...

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...

even and odd signals

Signal Symmetry and Decomposition

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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...

basic operations on signals

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...

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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