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

Analiza dwóch napięć sinusoidalnych na oscyloskopie o równej amplitudzie i okresie, ale różnych fazach, obejmuje trzy kroki.
Najpierw mierzona jest wartość międzyszczytowa, która jest dwukrotnie większa od amplitudy. Po drugie, określa się okres i częstotliwość kątową.
Po trzecie, wartości napięcia dla obu sinusoid są mierzone w ustalonym czasie w celu określenia kąta fazowego, który zależy od tego, czy sinusoida ma nachylenie dodatnie czy ujemne.
Reprezentacja graficzna może być użyta do porównania dwóch sinusoid, gdzie oś pozioma reprezentuje wielkość cosinusa, a oś pionowa reprezentuje wielkość sinusoidy.
Podobnie jak w przypadku współrzędnych biegunowych, kąty mierzone w kierunku przeciwnym do ruchu wskazówek zegara i zgodnie z ruchem wskazówek zegara od osi poziomej są odpowiednio dodatnie i ujemne.
Odejmując 90 stopni od argumentu cosinusa, otrzymujemy funkcję sinus.
Dwie sinusoidy o tej samej częstotliwości - jedna w formie sinusoidalnej, a druga w postaci cosinusowej, można dodać za pomocą reprezentacji graficznej.
Przeciwprostokątna trójkąta prostokątnego reprezentuje wynikową sinusoidę, a jej argument mierzony od osi poziomej jest równy cosinusowej odwrotności stosunku podstawy i przeciwprostokątnej.

graficzne i analityczne przedstawienie sinusoid

Analiza dwóch napięć sinusoidalnych o równej amplitudzie i okresie, ale różnych fazach na oscyloskopie – instrumencie używanym do wyświetlania i analizowania przebiegów – obejmuje trzyetapowy proces.

Pierwszym krokiem jest zmierzenie wartości szczytowej, która jest dwukrotnością amplitudy sinusoidy. Daje to informacje o maksymalnym wychyleniu napięcia fali.

Po drugie, określa się okres i częstotliwość kątową. Okres to czas potrzebny na jeden pełny cykl przebiegu fali, natomiast częstotliwość kątowa (często oznaczana grecką literą omega, ω) to szybkość, z jaką fala oscyluje.

Trzeci krok polega na zmierzeniu wartości napięcia dla obu sinusoid w określonym punkcie czasu. Służy to do określenia kąta fazowego, który zależy od tego, czy sinusoidalna fala ma dodatni, czy ujemny nachylenie w tym punkcie.

Do porównania dwóch sinusoid można zastosować reprezentację graficzną. W tej reprezentacji oś pozioma przedstawia wielkość cosinusa, a oś pionowa przedstawia wielkość sinusa. Układ ten przypomina współrzędne biegunowe, gdzie kąty mierzone przeciwnie do ruchu wskazówek zegara od osi poziomej są uważane za dodatnie, podczas gdy te mierzone zgodnie z ruchem wskazówek zegara są uważane za ujemne.

Co ciekawe, odejmowanie 90 stopni od argumentu funkcji cosinus daje funkcję sinus. Tę właściwość można wykorzystać w przypadku sinusoid.

Aby dodać dwie sinusoidy o tej samej częstotliwości - jedną w postaci sinusoidalnej, a drugą w postaci cosinusoidalnej - ponownie pojawia się reprezentacja graficzna. Przeciwprostokątna trójkąta prostokątnego utworzonego przez te sinusoidy reprezentuje sinusoidę wynikową. Argument tej wynikowej sinusoidy, mierzony od osi poziomej, jest równy odwrotności cosinusa stosunku podstawy do przeciwprostokątnej.

Podsumowując, użycie oscyloskopu w połączeniu z dogłębnym zrozumieniem zasad trygonometrycznych zapewnia zestaw narzędzi do analizy napięć sinusoidalnych. Wiedza ta nie tylko pomaga w zrozumieniu zachowania obwodów prądu przemiennego, ale także znajduje zastosowanie w wielu dziedzinach, takich jak telekomunikacja, przetwarzanie sygnałów i systemy zasilania.

Graficzne i analityczne przedstawienie sinusoid

Analiza dwóch napięć sinusoidalnych na oscyloskopie o równej amplitudzie i okresie, ale różnych fazach, obejmuje trzy kroki.
Po pierwsze, od szczytu do szczytu ...

graphical-and-analytic-representation-of-sinusoids

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

AC Circuit Analysis

Analiza obwodów prądu przemiennego

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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

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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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