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

Analyzing two sinusoidal voltages on an oscilloscope with equal amplitude and period but different phases involves three steps.
First, the peak-to-peak value is measured, which is twice the amplitude. Secondly, the period and angular frequency are determined.
Third, voltage values for both sinusoids are measured at a fixed time to determine the phase angle, which depends on whether the sinusoid has a positive or negative slope.
A graphical representation can be used to compare two sinusoids, where the horizontal axis represents the magnitude of cosine and the vertical axis represents the magnitude of sine.
Similar to polar coordinates, the angles measured counterclockwise and clockwise from the horizontal axis are positive and negative, respectively.
Subtracting 90 degrees from the argument of cosine yields the sine function.
Two same-frequency sinusoids- one in sine and the other in cosine form, can be added using the graphical representation.
The hypotenuse of the right-angled triangle represents the resultant sinusoid, and its argument measured from the horizontal axis equals the cosine inverse of the ratio of base and hypotenuse.

grafische en analytische weergave van sinusoïden

Graphical and Analytic Representation of Sinusoids

Het analyseren van twee sinusoïdale voltageen met gelijke amplitude en periode maar verschillende fasen op een oscilloscoop, een instrument dat wordt gebruikt om golfvormen weer te geven en te analyseren, omvat een proces in drie stappen. De eerste stap is het meten van de piek-tot-piekwaarde, die tweemaal de amplitude van de sinusoïde is. Dit geeft informatie over de maximale voltageszwaai van de golfvorm. Ten tweede worden de periode en de hoekfrequentie bepaald. De periode is de tijd die nodig is voor één volledige cyclus van de golfvorm, terwijl de hoekfrequentie (vaak aangegeven met de Griekse letter omega, ω) de snelheid is waarmee de golfvorm oscilleert. De derde stap omvat het meten van de voltageswaarden voor beide sinusoïden op een vast tijdstip. Dit wordt gebruikt om de fasehoek te bepalen, die afhangt van het feit of de sinusoïde op dat punt een positieve of negatieve helling heeft. Er kan een grafische weergave worden gebruikt om de twee sinusoïden te vergelijken. In deze weergave vertegenwoordigt de horizontale as de grootte van de cosinus, en de verticale as de grootte van de sinus. Deze opstelling doet denken aan poolcoördinaten, waarbij hoeken gemeten tegen de klok in vanaf de horizontale as als positief worden beschouwd, terwijl hoeken gemeten met de klok mee als negatief worden beschouwd. Interessant is dat het aftrekken van 90 graden van het argument van een cosinusfunctie de sinusfunctie oplevert. Deze eigenschap kan worden benut bij het omgaan met sinusoïden. Door twee sinusoïden met dezelfde frequentie toe te voegen - één in sinusvorm en de andere in cosinusvorm - komt de grafische weergave weer in beeld. De hypotenusa van de rechthoekige driehoek gevormd door deze sinusoïden vertegenwoordigt de resulterende sinusoïde. Het argument van deze resulterende sinusoïde, gemeten vanaf de horizontale as, is gelijk aan de cosinus-inverse van de verhouding van de basis tot de hypotenusa. Concluderend biedt het gebruik van een oscilloscoop, gekoppeld aan een goed begrip van trigonometrische principes, een krachtige toolset voor het analyseren van sinusoïdale voltageen. Deze kennis helpt niet alleen bij het begrijpen van het gedrag van AC-circuits, maar vindt ook toepassingen op tal van gebieden zoals telecommunicatie, signaalverwerking en energiesystemen.

Grafische en analytische weergave van sinusoïden

Analyzing two sinusoidal voltages on an oscilloscope with equal amplitude and period but different phases involves three steps.
First, the peak-to-peak ...

graphical-and-analytic-representation-of-sinusoids

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Electrical Engineering

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Unit 1

AC Circuit Analysis

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KEY TERMS AND CONCEPTS

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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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