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

L'analisi di due tensioni sinusoidali su un oscilloscopio con uguale ampiezza e periodo ma fasi diverse prevede tre passaggi.
Innanzitutto, viene misurato il valore picco-picco, che è il doppio dell'ampiezza. In secondo luogo, vengono determinati il periodo e la frequenza angolare.
In terzo luogo, i valori di tensione per entrambe le sinusoidi vengono misurati a un tempo fisso per determinare l'angolo di fase, che dipende dal fatto che la sinusoide abbia una pendenza positiva o negativa.
Una rappresentazione grafica può essere utilizzata per confrontare due sinusoidi, dove l'asse orizzontale rappresenta la grandezza del coseno e l'asse verticale rappresenta la grandezza del seno.
Analogamente alle coordinate polari, gli angoli misurati in senso antiorario e orario dall'asse orizzontale sono rispettivamente positivi e negativi.
Sottraendo 90 gradi dall'argomento del coseno si ottiene la funzione seno.
Due sinusoidi della stessa frequenza, una in seno e l'altra in forma di coseno, possono essere aggiunte utilizzando la rappresentazione grafica.
L'ipotenusa del triangolo rettangolo rappresenta la sinusoide risultante, e il suo argomento misurato dall'asse orizzontale è uguale all'inverso del coseno del rapporto tra base e ipotenusa.

rappresentazione grafica e analitica dei sinusoidi

L'analisi di due tensioni sinusoidali con uguale ampiezza e periodo, ma fasi diverse su un oscilloscopio, uno strumento utilizzato per visualizzare e analizzare le forme d'onda, prevede un processo in tre fasi.

Il primo passo è misurare il valore picco-picco, che è il doppio dell'ampiezza della sinusoide. Ciò fornisce informazioni sull'oscillazione massima della tensione della forma d'onda.

In secondo luogo, vengono determinati il periodo e la frequenza angolare. Il periodo è il tempo impiegato per un ciclo completo della forma d'onda, mentre la frequenza angolare (spesso indicata con la lettera greca omega, ω) è la velocità con cui la forma d'onda oscilla.

La terza fase, prevede la misurazione dei valori di tensione per entrambe le sinusoidi in un momento fisso. Questo viene utilizzato per determinare l'angolo di fase, che dipende dal fatto che la sinusoide abbia una pendenza positiva o negativa in quel punto.

Per confrontare le due sinusoidi è possibile utilizzare una rappresentazione grafica. In questa rappresentazione, l'asse orizzontale rappresenta l'ampiezza del coseno e l'asse verticale rappresenta l'ampiezza del seno. Questa disposizione ricorda le coordinate polari, dove gli angoli misurati in senso antiorario rispetto all'asse orizzontale sono considerati positivi, mentre quelli misurati in senso orario sono considerati negativi.

È interessante notare che sottraendo 90 gradi dall'argomento di una funzione coseno, si ottiene la funzione seno. Questa proprietà può essere sfruttata quando si ha a che fare con le sinusoidi.

Per sommare due sinusoidi della stessa frequenza - una in forma seno e l'altra in forma coseno - entra di nuovo in gioco la rappresentazione grafica. L'ipotenusa del triangolo rettangolo formato da queste sinusoidi rappresenta la sinusoide risultante. L'argomento di questa sinusoide risultante, misurata dall'asse orizzontale, è uguale all'inverso del coseno del rapporto tra base e ipotenusa.

In conclusione, l'uso di un oscilloscopio abbinato ad una solida conoscenza dei principi trigonometrici, fornisce un potente set di strumenti per analizzare le tensioni sinusoidali. Questa conoscenza non solo aiuta a comprendere il comportamento dei circuiti CA, ma trova anche applicazioni in numerosi campi come le telecomunicazioni, l'elaborazione dei segnali e i sistemi di alimentazione.

Rappresentazione Grafica e Analitica dei Sinusoidi

L'analisi di due tensioni sinusoidali su un oscilloscopio con uguale ampiezza e periodo ma fasi diverse prevede tre passaggi.
Innanzitutto, il picco-picco ...

graphical-and-analytic-representation-of-sinusoids

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

AC Circuit Analysis

Analisi dei circuiti in CA

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

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AC Circuit Phasors: Resistor, Inductor, Capacitor

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AC Circuit Rules with Phasor Diagrams

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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,...

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Series and Parallel Impedance Rules

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Norton Current in AC Circuit Analysis

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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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