Name: measuring sinusoid phase on an oscilloscope
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 20 s
Channel: JoVE

A análise de duas tensões senoidais em um osciloscópio com amplitude e período iguais, mas fases diferentes, envolve três etapas.
Primeiro, o valor pico a pico é medido, que é o dobro da amplitude. Em segundo lugar, o período e a frequência angular são determinados.
Terceiro, os valores de tensão para ambos os sinusóides são medidos em um tempo fixo para determinar o ângulo de fase, que depende se o sinusóide tem uma inclinação positiva ou negativa.
Uma representação gráfica pode ser usada para comparar dois senóides, onde o eixo horizontal representa a magnitude do cosseno e o eixo vertical representa a magnitude do seno.
Semelhante às coordenadas polares, os ângulos medidos no sentido anti-horário e horário a partir do eixo horizontal são positivos e negativos, respectivamente.
Subtraindo 90 graus do argumento do cosseno produz a função seno.
Dois sinusóides da mesma frequência - um na forma senoidal e outro na forma de cosseno, podem ser adicionados usando a representação gráfica.
A hipotenusa do triângulo retângulo representa a senóide resultante, e seu argumento medido a partir do eixo horizontal é igual ao inverso do cosseno da razão entre base e hipotenusa.

representação gráfica e analítica de sinusoides

A análise de duas tensões senoidais com amplitude e período iguais, mas fases diferentes em um osciloscópio, um instrumento usado para exibir e analisar formas de onda, envolve um processo de três etapas.

O primeiro passo é medir o valor pico a pico, que é o dobro da amplitude da senoide. Isso fornece informações sobre a oscilação máxima de tensão da forma de onda.

Em segundo lugar, o período e a frequência angular são determinados. O período é o tempo necessário para um ciclo completo da forma de onda, enquanto a frequência angular (frequentemente denotada pela letra grega ômega, ω) é a taxa na qual a forma de onda oscila.

A terceira etapa envolve medir os valores de tensão para ambas as senoides em um ponto fixo no tempo. Isto é usado para determinar o ângulo de fase, que depende se a senoide tem uma inclinação positiva ou negativa naquele ponto.

Uma representação gráfica pode ser empregada para comparar as duas senoides. Nesta representação, o eixo horizontal representa a magnitude do cosseno e o eixo vertical representa a magnitude do seno. Este arranjo lembra as coordenadas polares, onde os ângulos medidos no sentido anti-horário a partir do eixo horizontal são considerados positivos, enquanto aqueles medidos no sentido horário são considerados negativos.

Curiosamente, subtrair 90 graus do argumento de uma função cosseno resulta na função seno. Esta propriedade pode ser aproveitada ao lidar com sinusoides.

Para adicionar duas senoides da mesma frequência - uma na forma senoidal e outra na forma cosseno - a representação gráfica entra em ação novamente. A hipotenusa do triângulo retângulo formado por essas sinusoides representa a sinusoide resultante. O argumento desta senoide resultante, medida a partir do eixo horizontal, é igual ao cosseno inverso da razão entre a base e a hipotenusa.

Concluindo, o uso de um osciloscópio aliado a um sólido conhecimento dos princípios trigonométricos fornece um poderoso conjunto de ferramentas para analisar tensões senoidais. Esse conhecimento não apenas ajuda na compreensão do comportamento dos circuitos AC, mas também encontra aplicações em diversos campos, como telecomunicações, processamento de sinais e sistemas de energia.

Representação Gráfica e Analítica de Sinusoides

A análise de duas tensões senoidais em um osciloscópio com amplitude e período iguais, mas fases diferentes, envolve três etapas.
Primeiro, o pico a pico ...

graphical-and-analytic-representation-of-sinusoids

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

AC Circuit Analysis

Análise de Circuitos CA

KEY TERMS AND CONCEPTS

TERMOS E CONCEITOS-CHAVE

Graphical and Analytic Representation of Sinusoids

measuring sinusoid phase on an oscilloscope

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform.

Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate at which the waveform oscillates. After that, the voltage values of both sinusoids are checked at one fixed time. That comparison is used to find the phase angle. The phase angle depends on whether the sinusoid has a positive or negative slope at that point.

A graphical method can also be used to compare the two sinusoids. In this setup, the horizontal axis shows the magnitude of cosine, and the vertical axis shows the magnitude of sine. The arrangement is similar to polar coordinates. Angles measured counterclockwise from the horizontal axis are positive, while angles measured clockwise are negative. Another useful fact is that subtracting 90 degrees from the argument of a cosine function gives the sine function.

This graph can also help when adding two sinusoids with the same frequency, one in sine form and one in cosine form. The right triangle formed by the two components has a hypotenuse that represents the resultant sinusoid. The angle of that result, measured from the horizontal axis, equals the cosine inverse of the ratio of the base to the hypotenuse. Together, the oscilloscope and trigonometry give a strong way to analyze sinusoidal voltages. These ideas are useful for AC circuits and for fields such as telecommunications, signal processing, and power systems.

Measuring Sinusoid Phase on an Oscilloscope

measuring-sinusoid-phase-on-an-oscilloscope

sinusoidal sources

AC Waveform Basics and Phase

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graphical and analytic representation of sinusoids

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform. Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate...

phasors

Phasors for AC Circuit Analysis

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Phasor Rules for AC Circuit Analysis

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phasor relationships for circuit elements

phasor-relationships-for-circuit-elements

AC Circuit Phasors: Resistor, Inductor, Capacitor

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kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

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impedances and admittance

AC Circuit Response: Impedance and Admittance

AC circuit response changes with frequency, and impedance describes how resistors, inductors, and capacitors affect sinusoidal current flow. In phasor form, voltage and current are used to show this behavior in a clear way. Impedance is a key idea in AC circuit analysis because it measures opposition to current in an alternating circuit. These components behave differently in AC than in DC. In DC circuits, inductors act like short circuits and capacitors act like open circuits. In AC circuits,...

impedance combination

Series and Parallel Impedance Rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

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Impedance Matching with Mesh Currents

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AC Source Conversion in Circuit Analysis

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norton equivalent circuits

Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

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key terms and concepts

Learn how to measure peak-to-peak value, period, angular frequency, and phase angle of sinusoidal voltages using an oscilloscope and a graphical method.

Measuring Sinusoid Phase on an Oscilloscope | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Measuring Sinusoid Phase on an Oscilloscope

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