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

페이저(phaser)는 사인파의 크기가 진폭과 같고 각도가 양의 x축에서 측정된 위상과 같은 사인파의 복잡한 표현입니다.
전류 및 전압의 시간 의존성을 제거하고 회로를 등가 DC 형태로 변환하여 AC 회로 분석을 단순화합니다.
페이저는 오일러의 아이덴티티(Euler's identity)를 사용하여 직사각형, 극좌표 또는 지수 형태로 표현할 수 있습니다.
사인 형태로 정현파의 위상을 얻으려면 먼저 코사인 형태로 변환한 다음 복소수의 실수 부분으로 표현하십시오.
이 정현파의 페이저는 복소수의 시간 독립 부분과 같습니다.
반대로, 주어진 페이저의 정현파는 페이저에 시간 계수를 곱하고 실수 부분을 취하여 얻습니다.
페이저는 일정한 각도 주파수를 가진 복잡한 평면에서 시계 반대 방향으로 회전하는 벡터 또는 시너로 나타낼 수 있으며, 이를 묘사하는 다이어그램을 페이저 다이어그램이라고 합니다.
실수 축에서 회전하는 sinors의 돌출은 정현파를 나타냅니다.

페이저

페이저는 교류(AC) 회로를 분석하는 데 사용되는 강력한 수학적 도구입니다. 이는 정현파의 진폭과 동일한 페이저의 크기와 양의 x축에서 측정된 위상을 나타내는 페이저의 각도를 사용하여 정현파의 복소수 표현을 제공합니다.

페이저 사용의 중요한 이점 중 하나는 전류와 전압의 시간 의존성을 제거하여 AC 회로 분석을 단순화한다는 것입니다. 이러한 변환을 통해 AC 회로를 등가 직류(DC) 형태인 것처럼 분석할 수 있으므로 계산이 더욱 간단해집니다.

위상기는 삼각함수와 지수함수 사이의 깊은 관계를 설정하는 복잡한 분석의 기본 공식인 오일러 항등식을 사용하여 직사각형, 극형 또는 지수형 등 다양한 형태로 표현될 수 있습니다.

사인 형태의 정현파 페이저를 얻으려면 먼저 이를 코사인 형태로 변환한 다음 복소수의 실수부로 표현해야 합니다. 이 정현파의 페이저는 이 복소수의 시간 독립적인 부분과 같습니다. 반대로, 주어진 페이저의 정현파는 페이저에 시간 요소를 곱하고 실제 부분을 취하여 얻을 수 있습니다.

그래픽 맥락에서 페이저는 일정한 각주파수를 갖는 복소 평면에서 시계 반대 방향으로 회전하는 회전 벡터 또는 '사인'으로 시각화할 수 있습니다. 이러한 회전 사인을 묘사하는 다이어그램은 페이저 다이어그램으로 알려져 있습니다.

페이저 다이어그램을 이해하는 데 있어 핵심 개념은 회전 사인을 실제 축에 투영한 것이 사인곡선을 나타낸다는 것입니다. 이는 특정 시점에서 사인의 수평 위치가 그것이 나타내는 정현파 함수의 순간값에 해당함을 의미합니다.

페이저(phasor)는 사인파(phasor)의 크기가 진폭과 같고 각도(angle)가 에서 측정된 위상과 같은 사인파의 복잡한 표현입니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Circuit Analysis

교류 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

sinusoidal sources

AC Waveform Basics and Phase

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity. A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is...

graphical and analytic representation of sinusoids

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...

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...

phasor arithmetics

Phasor Rules for AC Circuit Analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

phasor relationships for circuit elements

phasor-relationships-for-circuit-elements

AC Circuit Phasors: Resistor, Inductor, Capacitor

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state. Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor...

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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

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

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AC Circuit Node Method in an Angioplasty Model

AC circuit node analysis is used to study an angioplasty system with a catheter turbine. The system helps remove plaque deposits from coronary arteries. Its electrical model is similar to a dual-node RLC circuit driven by a current-controlled voltage source. The analysis begins by collecting the input source voltage, inductance, and capacitance values. These measurements are used to find the driving voltage for the catheter shaft. The circuit is then viewed in the frequency domain, where...

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AC Source Conversion in Circuit Analysis

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norton equivalent circuits

Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

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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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