Name: phasors for ac circuit analysis
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 12 s
Channel: JoVE

Fazory są zespolonymi reprezentacjami sinusoid, w których wielkość wskazówki jest równa amplitudzie, a kąt jest równy fazie mierzonej od dodatniej osi x.
Upraszczają one analizę obwodów prądu przemiennego, eliminując zależność prądu i napięcia od czasu, przekształcając obwód w równoważną formę prądu stałego.
Fasory mogą być reprezentowane w formie prostokątnej, biegunowej lub wykładniczej przy użyciu tożsamości Eulera.
Aby uzyskać fazor sinusoidy w postaci sinusoidalnej, najpierw przekształć go w formę cosinusową, a następnie wyraź go jako rzeczywistą część liczby zespolonej.
Fazor tej sinusoidy jest równy niezależnej od czasu części liczby zespolonej.
I odwrotnie, sinusoidę danego wskaznika uzyskuje się przez pomnożenie wskazówki przez czynnik czasu i uwzględnienie jego rzeczywistej części.
Phasory mogą być reprezentowane jako obracające się wektory lub sinory w kierunku przeciwnym do ruchu wskazówek zegara na złożonej płaszczyźnie o stałej częstotliwości kątowej, a przedstawiające je diagramy są znane jako diagramy wskazówkowe.
Rzut obracających się sinorów na oś rzeczywistą reprezentuje sinusoidy.

fazory

Fazory są potężnym narzędziem matematycznym wykorzystywanym do analizy obwodów prądu przemiennego (AC). Zapewniają one złożoną reprezentację liczbową sinusoidy, przy czym wielkość fazora jest równa amplitudzie sinusoidy, a kąt fazora reprezentuje fazę mierzoną od dodatniej osi x.

Jedną z istotnych zalet stosowania fazorów jest to, że upraszczają one analizę obwodów prądu przemiennego, eliminując zależność prądu i napięcia od czasu. Ta transformacja umożliwia analizę obwodu prądu przemiennego tak, jakby był on równoważną formą prądu stałego (DC), dzięki czemu obliczenia są prostsze.

Fazory można przedstawić w różnych formach – prostokątnej, biegunowej lub wykładniczej – przy użyciu tożsamości czterech kwadratów Eulera, podstawowego wzoru w analizie złożonej, który ustanawia głęboki związek między funkcjami trygonometrycznymi i wykładniczymi.

Aby otrzymać fazor sinusoidy w postaci sinusoidalnej, należy najpierw przekształcić ją do postaci cosinusoidalnej, a następnie przedstawić ją jako część rzeczywistą liczby zespolonej.  Fazor tej sinusoidy jest równy niezależnej od czasu części tej liczby zespolonej. Itej sinusoidy równa się niezależnej od czasu części tej liczby zespolonej. Z drugiej strony, sinusoidę odpowiadającą danemu wektorowi fazowemu można uzyskać, mnożąc fazor przez czynnik czasowy i biorąc jego część rzeczywistą.

W kontekście graficznym, fazory mogą być wizualizowane jako obracające się wektory, wirujące w kierunku przeciwnym do ruchu wskazówek zegara na płaszczyźnie zespolonej ze stałą częstotliwością kątową. Wykresy przedstawiające te obracające się wektory znane są jako diagramy wskazowe.

Kluczową koncepcją w zrozumieniu diagramu wskazowego jest to, że rzut obracających się wirujących wektorów na rzeczywistą oś reprezentuje sinusoidy. Oznacza to, że poziome położenie wektora w dowolnym momencie odpowiada chwilowej wartości reprezentowanej przez niego funkcji sinusoidalnej.

Fazory

Wskazy są zespolonymi reprezentacjami sinusoid, w których wielkość wskazówki jest równa amplitudzie, a kąt jest równy fazie mierzonej od ...

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

Phasors

phasors for ac circuit analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis.

Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in rectangular, polar, or exponential form.

Euler’s identity links trigonometric functions and exponential functions, and it helps convert between these phasor forms. To find the phasor of a sinusoid in sine form, the signal is first written in cosine form. It is then expressed as the real part of a complex number, and the phasor is the time-independent part of that number.

A sinusoid can also be recovered from a phasor. The phasor is multiplied by a time factor, and then the real part is taken. In a graph, phasors appear as rotating vectors, or sinors, on the complex plane.

These rotating sinors move counterclockwise with constant angular frequency. The diagrams that show them are called phasor diagrams. The projection of a sinor onto the real axis gives the sinusoid, so the horizontal position at any moment shows the instantaneous value of the wave.

Phasors for AC Circuit Analysis

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phasors

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

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key terms and concepts

Learn how phasors represent AC sinusoids, simplify circuit analysis, and appear as rotating vectors on the complex plane in phasor diagrams.

Phasors for AC Circuit Analysis | 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

Phasors for AC Circuit Analysis

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