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

Анализ двух синусоидальных напряжений на осциллографе с одинаковыми амплитудой и периодом, но разными фазами включает в себя три этапа.
Сначала измеряется значение размаха до пика, которое в два раза больше амплитуды. Во-вторых, определяется период и угловая частота.
В-третьих, значения напряжения для обеих синусоид измеряются в фиксированное время для определения фазового угла, который зависит от того, имеет ли синусоида положительный или отрицательный наклон.
Графическое представление может быть использовано для сравнения двух синусоид, где горизонтальная ось представляет величину косинуса, а вертикальная ось представляет величину синуса.
Подобно полярным координатам, углы, измеренные против часовой стрелки и по часовой стрелке от горизонтальной оси, являются положительными и отрицательными соответственно.
Вычитание 90 градусов из аргумента косинуса дает функцию синуса.
Две синусоиды одинаковой частоты - одна в синусоиде, а другая в косинусной форме, могут быть добавлены с помощью графического представления.
Гипотенуза прямоугольного треугольника представляет собой результирующую синусоиду, а ее аргумент, измеренный от горизонтальной оси, равен косинусу, обратному отношению основания и гипотенузы.

Графическое и аналитическое представление синусоид

Graphical and Analytic Representation of Sinusoids

Анализ двух синусоидальных напряжений с одинаковой амплитудой и периодом, но разными фазами на осциллографе, инструменте, используемом для отображения и анализа сигналов, включает в себя трехэтапный процесс.

Первым шагом является измерение размаха значения, которое равно удвоенной амплитуде синусоиды. Это предоставляет информацию о максимальном размахе напряжения сигнала.

Затем определяются период и угловая частота. Период — это время, необходимое для одного полного цикла сигнала, а угловая частота (часто обозначаемая греческой буквой омега, ω) — это скорость, с которой колеблется сигнал.

Третий шаг включает измерение значений напряжения для обеих синусоид в фиксированный момент времени. Это делается для определения фазового угла, который зависит от того, имеет ли синусоида положительный или отрицательный наклон в этой точке.

Для сравнения двух синусоид можно использовать графическое представление. В этом представлении по горизонтальной оси откладывается значение косинуса, а по вертикальной оси - значение синуса. Такое расположение напоминает полярные координаты, где углы, измеренные против часовой стрелки от горизонтальной оси, считаются положительными, а углы, измеренные по часовой стрелке, считаются отрицательными.

Напомним, что вычитание 90 градусов из аргумента функции косинуса дает функцию синуса. Это свойство можно использовать при работе с синусоидами.

Чтобы сложить две синусоиды одинаковой частоты — одну в форме синуса, а другую в форме косинуса — снова можно использовать графическое. Гипотенуза прямоугольного треугольника, образованного этими синусоидами, представляет собой результирующую синусоиду. Аргумент этой результирующей синусоиды, отсчитываемый от горизонтальной оси, равен косинусу, обратному отношению основания к гипотенузе.

В заключение отметим, что использование осциллографа в сочетании с уверенным применением тригонометрических принципов даёт мощный набор инструментов для анализа синусоидальных напряжений. Эти знания не только помогают понять поведение цепей переменного тока, но также находят применение во многих областях, таких как телекоммуникации, обработка сигналов и энергосистемы.

Анализ двух синусоидальных напряжений на осциллографе с одинаковыми амплитудой и периодом, но разными фазами включает в себя три этапа.
Во-первых, от пика до пика...

graphical-and-analytic-representation-of-sinusoids

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

AC Circuit Analysis

Анализ цепей переменного тока

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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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...

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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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