Name: ac waveform basics and phase
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 18 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

HS-PS4-2

Sinusoidal Sources

Gleichstrom bezieht sich auf unidirektionalen Strom, während Wechselstrom sich auf Strom bezieht, der seine Richtung periodisch umkehrt.
Wechselströme sind für die Stromübertragung und -verteilung von entscheidender Bedeutung.
Die Stromversorgung in Haushalten erfolgt über sinusförmige Quellen, um Strom bereitzustellen. Diese Quellen erzeugen eine Spannung, die sinusförmig mit der Zeit variiert.
Mathematisch wird sie durch eine harmonische Funktion dargestellt, die als Sinuskurve bekannt ist und durch ihre Amplitude, Kreisfrequenz und Phase definiert wird.
Die Variation der Funktion wiederholt sich alle T Sekunden, und die Dauer eines vollständigen Zyklus wird als Periode bezeichnet. Sie hängt mit der Kreisfrequenz zusammen.
Die Anzahl der Zyklen pro Sekunde ist die Frequenz.
Betrachten Sie zwei Sinuskurven mit der gleichen Frequenz. Wenn eine Sinuskurve ihre Maxima und Minima früher erreicht als eine andere, dann führt die erste Sinuskurve die zweite.
Die beiden Sinuskurven werden dann als phasenverschoben bezeichnet, und die Verschiebung zwischen ihnen wird als Phasendifferenz bezeichnet.
Erreichen die beiden Sinuskurven gleichzeitig ihre Maxima und Minima, sind sie phasengleich und haben somit keine Phasendifferenz.

sinusförmige quellen

Unter Gleichstrom (DC) versteht man einen elektrischen Strom, der in eine Richtung fließt und dabei eine konstante Polarität beibehält. Dies steht im Gegensatz zum Wechselstrom (AC), der periodisch seine Richtung und Größe ändert. Wechselstrom bildet aufgrund seiner effizienten Fernübertragungsfähigkeiten das Rückgrat moderner Stromübertragungs- und -verteilungssysteme. In Privathaushalten nutzen die Netzteile sinusförmige Quellen zur Stromversorgung. Diese Quellen erzeugen eine Spannung, die sich im Laufe der Zeit sinusförmig ändert. Mit anderen Worten: Die Spannung schwankt in einem gleichmäßigen, wellenförmigen Muster zwischen einem Maximal- und einem Minimalwert. Mathematisch wird diese Variation durch eine harmonische Funktion dargestellt, die als Sinuskurve bekannt ist. Die Sinuskurve wird durch drei Hauptparameter definiert: ihre Amplitude (der Spitzenwert), ihre Winkelfrequenz (die Geschwindigkeit, mit der sie schwingt) und ihre Phase (ihre Position relativ zu einem Referenzpunkt). Die Sinuswellenform wiederholt ihr Muster alle T Sekunden, wobei T als Periode der Funktion bezeichnet wird. Die Periode steht im umgekehrten Verhältnis zur Kreisfrequenz und stellt die Dauer eines vollständigen Zyklus der Wellenform dar. Andererseits ist die Sinusfrequenz als die Anzahl der Zyklen definiert, die pro Sekunde auftreten. Sie ist der Kehrwert der Periode und wird typischerweise in Hertz (Hz) gemessen. Um das Konzept der Phase zu verstehen, betrachten Sie zwei Sinuskurven mit derselben Frequenz. Wenn eine Sinuskurve ihre Maxima und Minima früher erreicht als die andere, dann sagt man, dass die erste Sinuskurve der zweiten „voreilt“. In diesem Fall sind die beiden Sinuskurven phasenverschoben und die Verschiebung zwischen ihnen wird als Phasendifferenz bezeichnet. Wenn hingegen die beiden Sinuskurven gleichzeitig ihre Maxima und Minima erreichen, gelten sie als in Phase. Das bedeutet, dass sie eine Phasendifferenz von Null haben. Das Verständnis dieser grundlegenden Konzepte im Zusammenhang mit Wechselstrom ist für verschiedene Anwendungen von entscheidender Bedeutung, vom Entwurf elektronischer Schaltkreise bis zur Analyse von Energiesystemen. Die Prinzipien des Wechselstroms liegen vielen Technologien unseres täglichen Lebens zugrunde, darunter Haushaltsgeräte, Telekommunikationssysteme und Stromerzeugungsanlagen.

Sinusförmige Quellen

Gleichstrom bezieht sich auf unidirektionalen Strom, während Wechselstrom sich auf Strom bezieht, der seine Richtung periodisch umkehrt.
Abwechselnd...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

AC Circuit Analysis

Analyse von Wechselstromschaltungen

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

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 a harmonic function. The shape of the wave is described by three key parts: amplitude, angular frequency, and phase. Amplitude is the peak value. Angular frequency tells how fast the wave oscillates. Phase shows the wave’s position compared with a reference point.

A sinusoid repeats after a time called the period, or T. The period is the time for one complete cycle of the waveform. It is inversely related to angular frequency. Frequency is the number of cycles per second, and it is the reciprocal of the period. Frequency is measured in Hertz, or Hz.

Phase helps compare two sinusoids with the same frequency. If one wave reaches its maxima and minima earlier than the other, it leads the second wave. The waves are then out of phase, and the shift between them is called the phase difference. If both waves reach their maxima and minima at the same time, they are in phase. In that case, the phase difference is zero.

Understanding AC, sinusoidal sources, and phase is important in many settings. These ideas are used in electronic circuit design and in power system analysis. They also support technologies that shape daily life, including household appliances, telecommunications systems, and power generation facilities.

AC Waveform Basics and Phase

sinusoidal sources

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 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 AC sinusoidal sources work, including amplitude, frequency, period, and phase, plus why phase difference matters in power and circuits.

AC Waveform Basics and Phase | 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

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. ...

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be ...

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a ...

Graphing the Wave Function

Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the ...

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Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The ...

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Problem-Solving: Tuning of a Guitar String

In the case of stringed instruments like the guitar, the elastic property that determines the speed of the sound produced is its linear mass density or ...

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Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Propagation of Waves

When a wave propagates from one medium to another, part of it may get reflected in the first medium, and part of it may get transmitted to the second ...

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a ...

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

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Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. 

Clarification statement: Examples of data could include electromagnetic radiation traveling in a vacuum and glass, sound waves traveling through air and water, and seismic waves traveling through the earth. 

Assessment Boundary: Assessment is limited to algebraic relationships and describing those relationships qualitatively.

HS-PS4-1

Speed of Sound in Gases

The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. ...

Direct current refers to unidirectional current, whereas alternating current refers to current that reverses its direction periodically.
Alternating ...

Signal and System

Signals are sets of data or information.
One-dimensional signals include single-variable functions, such as the variations in air pressure over time in ...

reconstruction-of-signal-using-interpolation

Reconstruction of Signal using Interpolation

Consider a continuous signal and its sampled counterpart with a sampling period T.
Applying a zero-order hold to the sampled signal results in a piecewise ...

Classification of Signals

Signals are categorized as Continuous-time or discrete-time, Periodic or aperiodic, Analog or digital, and Causal or noncausal.
A continuous-time signal ...

Evaluate questions about the advantages of using a digital transmission and storage of information. 

Clarification statement: Examples of advantages could include that digital information is stable because it can be stored reliably in computer memory, transferred easily, and copied and shared rapidly. Disadvantages could include issues of easy deletion, security, and theft.

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Dual Nature of Electromagnetic (EM) Radiation

Electromagnetic (EM) radiation consists of electric and magnetic field components oscillating in planes perpendicular to each other and mutually ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Electromagnetic Waves

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

Generating Electromagnetic Radiations

The German physicist Heinrich Hertz (1857&#8211;1894) was the first to generate and detect certain types of electromagnetic waves in the laboratory. ...

Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other. 

Clarification statement: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect. 

Assessment Boundary: Assessment does not include using quantum theory.

HS-PS4-3

The Electromagnetic Spectrum

The electromagnetic spectrum consists of all the types of electromagnetic radiation arranged according to their frequency and wavelength. Each of the ...

Biological Effects of Radiation

All radioactive nuclides emit high-energy particles or electromagnetic waves. When this radiation encounters living cells, it can cause heating, break ...

Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter. 

Clarification statement: Emphasis is on the idea that photons associated with different frequencies of light have different energies, and the damage to living tissue from electromagnetic radiation depends on the energy of the radiation. Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias. 

Assessment Boundary: Assessment is limited to qualitative descriptions.

HS-PS4-4

Control Systems

Control systems influence many applications, from space shuttles to automated manufacturing. They exist naturally, such as our body&#39;s blood sugar ...

Electromagnetic waves are categorized according to their wavelengths and frequencies, giving the electromagnetic spectrum. These waves are classified as ...

Electromagnetic Wave Equation

Maxwell&#39;s equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose ...

Plane Electromagnetic Waves I

The existence of combined electric and magnetic fields that propagate through space as electromagnetic (EM) waves is the most significant prediction of ...

Plane Electromagnetic Waves II

Consider a plane wavefront traveling in position x-direction with a constant speed. This wavefront can be utilized to obtain the relationship between ...

propagation-speed-of-electromagnetic-waves

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


Consider a plane ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a ...

Standing Electromagnetic Waves

Electromagnetic waves can be reflected; the surface of a conductor or a dielectric can act as a reflector. As electric and magnetic fields obey the ...

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the ...

Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. 

Clarification statement: Examples could include solar cells capturing light and converting it to electricity; medical imaging; and communications technology. 

Assessment Boundary: Assessments are limited to qualitative information. Assessments do not include band theory.

HS-PS4-5

AC Waveform Basics and Phase

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