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

오실로스코프에서 진폭과 주기는 같지만 위상이 다른 두 개의 정현파 전압을 분석하려면 세 가지 단계를 거쳐야 합니다.
먼저, 진폭의 두 배인 peak-to-peak 값을 측정합니다. 둘째, 주기와 각도 주파수가 결정됩니다.
셋째, 두 정현파에 대한 전압 값은 위상각을 결정하기 위해 고정된 시간에 측정되며, 이는 정현파가 양의 기울기 또는 음의 기울기를 갖는지 여부에 따라 달라집니다.
그래픽 표현을 사용하여 두 개의 정현파를 비교할 수 있으며, 여기서 가로축은 코사인의 크기를 나타내고 세로축은 사인의 크기를 나타냅니다.
극좌표와 유사하게, 수평축에서 시계 반대 방향과 시계 방향으로 측정된 각도는 각각 양수와 음수입니다.
코사인 인수에서 90도를 빼면 사인 함수가 생성됩니다.
두 개의 동일한 주파수 정현파(하나는 사인 형태이고 다른 하나는 코사인 형태)는 그래픽 표현을 사용하여 추가할 수 있습니다.
직각 삼각형의 빗변은 결과 정현파를 나타내며 가로축에서 측정된 인수는 밑변과 빗변의 비율의 코사인 역과 같습니다.

정현파의 그래픽 및 분석적 표현

파형을 표시하고 분석하는 데 사용되는 장비인 오실로스코프에서 진폭과 주기는 동일하지만 위상이 다른 두 개의 정현파 전압을 분석하려면 3단계 과정이 필요합니다.

첫 번째 단계는 정현파 진폭의 두 배인 피크 대 피크 값을 측정하는 것입니다. 이는 파형의 최대 전압 스윙에 대한 정보를 제공합니다.

둘째, 주기와 각주파수가 결정됩니다. 주기는 파형의 완전한 한 주기에 걸리는 시간인 반면, 각주파수(흔히 그리스 문자 오메가, Ω로 표시됨)는 파형이 진동하는 속도입니다.

세 번째 단계에서는 고정된 시점에서 두 정현파의 전압 값을 측정하는 작업이 포함됩니다. 이는 정현파가 해당 지점에서 양의 기울기를 갖는지 또는 음의 기울기를 갖는지에 따라 달라지는 위상 각도를 결정하는 데 사용됩니다.

두 정현파를 비교하기 위해 그래픽 표현을 사용할 수 있습니다. 이 표현에서 가로축은 코사인의 크기를 나타내고, 세로축은 사인의 크기를 나타냅니다. 이 배열은 수평 축에서 시계 반대 방향으로 측정된 각도가 양수로 간주되고 시계 방향으로 측정된 각도가 음수로 간주되는 극좌표를 연상시킵니다.

흥미롭게도 코사인 함수의 인수에서 90도를 빼면 사인 함수가 생성됩니다. 이 속성은 정현파를 처리할 때 활용될 수 있습니다.

동일한 주파수의 두 정현파(하나는 사인 형식, 다른 하나는 코사인 형식)를 추가하려면 그래픽 표현이 다시 작동합니다. 이러한 정현파에 의해 형성된 직각 삼각형의 빗변은 결과 정현파를 나타냅니다. 수평 축에서 측정된 이 결과 정현파의 인수는 밑변과 빗변 비율의 코사인 역과 같습니다.

결론적으로, 삼각법 원리에 대한 확고한 이해와 함께 오실로스코프를 사용하면 정현파 전압을 분석하기 위한 강력한 도구 세트가 제공됩니다. 이 지식은 AC 회로의 동작을 이해하는 데 도움이 될 뿐만 아니라 통신, 신호 처리, 전력 시스템과 같은 다양한 분야에서도 응용할 수 있습니다.

오실로스코프에서 진폭과 주기는 같지만 위상이 다른 두 개의 정현파 전압을 분석하려면 세 가지 단계를 거쳐야 합니다.
첫째, 피크 투 피크 ...

graphical-and-analytic-representation-of-sinusoids

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

AC Circuit Analysis

교류 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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

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

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...

impedances and admittance

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,...

impedance combination

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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Impedance Matching with Mesh Currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

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AC Source Conversion in Circuit Analysis

AC source conversion is a circuit analysis method used in the frequency domain. It changes a voltage source in series with an impedance into a current source in parallel with the same impedance, or it converts a current source back into a voltage source. The source values must keep the correct relationship during each change. This method helps solve for an unknown voltage in a circuit that includes a current source and components such as resistors, capacitors, and inductors. Each of these...

th&#233venin equivalent circuits

Finding Voltage and Impedance in Circuit A

The household power distribution system can be simplified with Thevenin's theorem. In this system, distribution lines and transformers form the main network. Electrical appliances can be treated as load impedance, which makes the circuit easier to analyze. An AC circuit can be split into two parts, circuit A and circuit B, with a single pair of terminals between them. Circuit A can then be replaced by its Thevenin equivalent circuit. That equivalent has a voltage source in series with an...

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...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

Analyzing mixed-frequency linear circuits starts with the principle of superposition. In a linear circuit, the total output from several inputs is the sum of the outputs from each input acting alone. Here, the inputs are the voltages from independent voltage sources and the currents from independent current sources. When one source is kept active, every other independent source is set to zero. A 0-V voltage source becomes a short circuit, and a 0-A current source becomes an open circuit. This...

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Analyzing an Op Amp Audio Filter

An op amp audio filter shapes an amplified sound signal by strongly reducing the lower-frequency parts. In this circuit, the focus is on a basic filter setup used after an amplifier in an audio system. The filter uses an operational amplifier in an inverting arrangement with resistors R1 and R2 and a capacitor C1. The analysis starts with a known input signal and asks for the output signal. To solve it, the capacitor impedance is found first. That requires the angular frequency from the...

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Capacitance Multiplier Circuit for Larger Capacitance

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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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