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

振幅と周期が等しいが位相が異なるオシロスコープで2つの正弦波電圧を分析するには、3つのステップが必要です。
まず、振幅の2倍であるピークツーピーク値が測定されます。次に、周期と角周波数が決定されます。
第三に、両方の正弦波の電圧値を一定の時間に測定して、正弦波の傾きが正か負かに応じて位相角を決定します。
グラフィカル表現を使用して 2 つの正弦波を比較できます (横軸は余弦の大きさを表し、縦軸は正弦の大きさを表します)。
極座標と同様に、水平軸から反時計回りと時計回りに測定される角度は、それぞれ正と負です。
cosine の引数から 90 度を引くと、sine 関数が得られます。
2つの同じ周波数の正弦波(1つは正弦波、もう1つは余弦波形式)は、グラフィカル表現を使用して追加できます。
直角三角形の斜辺は結果として得られる正弦波を表し、水平軸から測定されたその引数は、底辺と斜辺の比率の余弦逆数に等しくなります。

正弦波のグラフィック表現と解析表現

Graphical and Analytic Representation of Sinusoids

波形の表示と分析に使用される機器であるオシロスコープで、振幅と周期が等しいが位相が異なる 2 つの正弦波電圧を分析するには、3 段階のプロセスが必要です。

最初のステップは、正弦波の振幅の 2 倍であるピークツーピーク値を測定することです。 これにより、波形の最大電圧振幅に関する情報が得られます。

次に、周期と角周波数が決定されます。 周期は波形の 1 つの完全なサイクルにかかる時間であり、角周波数 (ギリシャ文字のオメガ、ω で表されることが多い) は波形が振動する速度です。

3 番目のステップでは、固定時点での両方の正弦波の電圧値を測定します。 これは、正弦波のその点での傾きが正か負かによって決まる位相角を決定するために使用されます。

グラフ表示を使用して 2 つの正弦波を比較できます。 この表現では、横軸はコサインの大きさを表し、縦軸はサインの大きさを表します。 この配置は極座標を彷彿とさせます。水平軸から反時計回りに測定した角度は正とみなされ、時計回りに測定した角度は負とみなされます。

興味深いことに、コサイン関数の引数から 90 度を引くと、サイン関数が得られます。 この特性は、正弦波を扱うときにも利用できます。

同じ周波数の 2 つの正弦波 (1 つはサイン形式、もう 1 つはコサイン形式) を追加するには、グラフィック表現が再び機能します。 これらの正弦波によって形成される直角三角形の斜辺は、結果として得られる正弦波を表します。 この結果として得られる正弦波の引数は、水平軸から測定すると、底辺と斜辺の比のコサイン逆数に等しくなります。

結論として、三角関数の原理をしっかりと理解しながらオシロスコープを使用すると、正弦波電圧を解析するための強力なツールセットが得られます。 この知識は、AC 回路の動作を理解するのに役立つだけでなく、電気通信、信号処理、電力システムなどの多くの分野にも応用できます。

振幅と周期が等しいが位相が異なるオシロスコープで2つの正弦波電圧を分析するには、3つのステップが必要です。
まず、ピークツーピーク...

graphical-and-analytic-representation-of-sinusoids

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

AC Circuit Analysis

交流回路解析

KEY TERMS AND CONCEPTS

主要用語と概念

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...

node analysis for ac circuits

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...

mesh analysis for ac circuits

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...

source transformation for ac circuits

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...

op amp ac circuits

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...

design example: capacitance multiplier circuit

design-example-capacitance-multiplier-circuit

Capacitance Multiplier Circuit for Larger Capacitance

A capacitance multiplier circuit creates a larger effective capacitance from a small physical capacitor. In integrated circuit technology, this approach is useful when a small capacitor is not enough. The circuit can multiply capacitance by as much as 1000, so a 10-pF capacitor can act like a 100-nF capacitor. The design uses two op-amps. The first op-amp works as a voltage follower, which helps isolate the generated capacitance from the loading caused by the second stage. The second op-amp...

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Measuring Sinusoid Phase on an Oscilloscope

Description

Transcript