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

L’analyse de deux tensions sinusoïdales sur un oscilloscope d’amplitude et de période égales mais de phases différentes implique trois étapes.
Tout d’abord, la valeur crête à crête est mesurée, ce qui correspond à deux fois l’amplitude. Deuxièmement, la période et la fréquence angulaire sont déterminées.
Troisièmement, les valeurs de tension pour les deux sinusoïdes sont mesurées à un moment fixe pour déterminer l’angle de phase, qui dépend du fait que la sinusoïde a une pente positive ou négative.
Une représentation graphique peut être utilisée pour comparer deux sinusoïdes, où l’axe horizontal représente l’intensité du cosinus et l’axe vertical représente l’intensité du sinus.
À l’instar des coordonnées polaires, les angles mesurés dans le sens inverse des aiguilles d’une montre et dans le sens des aiguilles d’une montre par rapport à l’axe horizontal sont respectivement positifs et négatifs.
En soustrayant 90 degrés de l’argument du cosinus, on obtient la fonction sinus.
Deux sinusoïdes de même fréquence, l’une sous forme sinusoïdale et l’autre sous forme cosinus, peuvent être ajoutées à l’aide de la représentation graphique.
L’hypoténuse du triangle rectangle représente la sinusoïde résultante, et son argument mesuré à partir de l’axe horizontal est égal au cosinus inverse du rapport de la base et de l’hypoténuse.

représentation graphique et analytique des sinusoïdes

Graphical and Analytic Representation of Sinusoids

L'analyse de deux tensions sinusoïdales d'amplitude et de période égales mais de phases différentes sur un oscilloscope, un instrument utilisé pour afficher et analyser les formes d'onde, implique un processus en trois étapes. La première étape consiste à mesurer la valeur crête à crête, qui correspond à deux fois l'amplitude de la sinusoïde. Cela fournit des informations sur l’oscillation de tension maximale de la forme d’onde. Deuxièmement, la période et la fréquence angulaire sont déterminées. La période est le temps nécessaire pour un cycle complet de la forme d'onde, tandis que la fréquence angulaire (souvent désignée par la lettre grecque oméga, ω) est la vitesse à laquelle la forme d'onde oscille. La troisième étape consiste à mesurer les valeurs de tension des deux sinusoïdes à un moment donné. Ceci est utilisé pour déterminer l'angle de phase, qui dépend si la sinusoïde a une pente positive ou négative en ce point. Une représentation graphique peut être utilisée pour comparer les deux sinusoïdes. Dans cette représentation, l'axe horizontal représente l'amplitude du cosinus et l'axe vertical représente l'amplitude du sinus. Cette disposition rappelle les coordonnées polaires, où les angles mesurés dans le sens inverse des aiguilles d'une montre à partir de l'axe horizontal sont considérés comme positifs, tandis que ceux mesurés dans le sens des aiguilles d'une montre sont considérés comme négatifs. Fait intéressant, soustraire 90 degrés à l’argument d’une fonction cosinus donne la fonction sinus. Cette propriété peut être exploitée lorsqu’il s’agit de sinusoïdes. Pour additionner deux sinusoïdes de même fréquence - l'une sous forme sinusoïdale et l'autre sous forme cosinus - la représentation graphique entre à nouveau en jeu. L'hypoténuse du triangle rectangle formé par ces sinusoïdes représente la sinusoïde résultante. L'argument de cette sinusoïde résultante, mesuré à partir de l'axe horizontal, est égal au cosinus inverse du rapport de la base à l'hypoténuse. En conclusion, l’utilisation d’un oscilloscope associée à une solide compréhension des principes trigonométriques fournit un ensemble d’outils puissants pour analyser les tensions sinusoïdales. Ces connaissances aident non seulement à comprendre le comportement des circuits alternatifs, mais trouvent également des applications dans de nombreux domaines tels que les télécommunications, le traitement du signal et les systèmes électriques.

Représentation graphique et analytique des sinusoïdes

L’analyse de deux tensions sinusoïdales sur un oscilloscope d’amplitude et de période égales mais de phases différentes implique trois étapes.
Tout d’abord, le pic à pic ...

graphical-and-analytic-representation-of-sinusoids

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

AC Circuit Analysis

Analyse des circuits CA

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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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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