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

Die Analyse von zwei sinusförmigen Spannungen an einem Oszilloskop mit gleicher Amplitude und Periode, aber unterschiedlichen Phasen, umfasst drei Schritte.
Zuerst wird der Spitze-zu-Spitze-Wert gemessen, der doppelt so groß ist wie die Amplitude. Zweitens werden die Periode und die Kreisfrequenz bestimmt.
Drittens werden die Spannungswerte für beide Sinuskurven zu einem festen Zeitpunkt gemessen, um den Phasenwinkel zu bestimmen, der davon abhängt, ob die Sinuskurve eine positive oder negative Steigung hat.
Eine grafische Darstellung kann verwendet werden, um zwei Sinuskurven zu vergleichen, wobei die horizontale Achse die Größe des Kosinus und die vertikale Achse die Größe des Sinus darstellt.
Ähnlich wie bei Polarkoordinaten sind die Winkel, die gegen den Uhrzeigersinn und im Uhrzeigersinn von der horizontalen Achse gemessen werden, positiv bzw. negativ.
Subtrahiert man 90 Grad vom Kosinusargument, erhält man die Sinusfunktion.
Zwei Sinuskurven gleicher Frequenz - eine in Sinus- und die andere in Kosinusform - können mit Hilfe der grafischen Darstellung addiert werden.
Die Hypotenuse des rechtwinkligen Dreiecks stellt die resultierende Sinuskurve dar, und ihr Argument, von der horizontalen Achse aus gemessen, entspricht dem Kosinus-Kehrwert des Verhältnisses von Basis und Hypotenuse.

grafische und analytische darstellung von sinuskurven

Die Analyse zweier sinusförmiger Spannungen mit gleicher Amplitude und Periode, aber unterschiedlichen Phasen auf einem Oszilloskop, einem Instrument zur Anzeige und Analyse von Wellenformen, umfasst einen dreistufigen Prozess. Der erste Schritt besteht darin, den Spitze-zu-Spitze-Wert zu messen, der doppelt so groß ist wie die Amplitude der Sinuskurve. Dies liefert Informationen über den maximalen Spannungshub der Wellenform. Zweitens werden die Periode und die Kreisfrequenz bestimmt. Die Periode ist die Zeit, die für einen vollständigen Zyklus der Wellenform benötigt wird, während die Winkelfrequenz (oft mit dem griechischen Buchstaben Omega, ω bezeichnet) die Geschwindigkeit ist, mit der die Wellenform schwingt. Im dritten Schritt werden die Spannungswerte beider Sinuskurven zu einem festen Zeitpunkt gemessen. Damit wird der Phasenwinkel bestimmt, der davon abhängt, ob die Sinuskurve an diesem Punkt eine positive oder negative Steigung aufweist. Zum Vergleich der beiden Sinuskurven kann eine grafische Darstellung herangezogen werden. In dieser Darstellung repräsentiert die horizontale Achse den Betrag des Kosinus und die vertikale Achse den Betrag des Sinus. Diese Anordnung erinnert an Polarkoordinaten, bei denen Winkel, die gegen den Uhrzeigersinn von der horizontalen Achse gemessen werden, als positiv gelten, während solche, die im Uhrzeigersinn gemessen werden, als negativ gelten. Interessanterweise ergibt die Subtraktion von 90 Grad vom Argument einer Kosinusfunktion die Sinusfunktion. Diese Eigenschaft kann beim Umgang mit Sinuskurven genutzt werden. Um zwei Sinuskurven gleicher Frequenz zu addieren – eine in Sinusform und die andere in Kosinusform – kommt erneut die grafische Darstellung ins Spiel. Die Hypotenuse des durch diese Sinuskurven gebildeten rechtwinkligen Dreiecks stellt die resultierende Sinuskurve dar. Das Argument dieser resultierenden Sinuskurve, gemessen von der horizontalen Achse, entspricht dem Kosinus-Kehrwert des Verhältnisses der Basis zur Hypotenuse. Zusammenfassend lässt sich sagen, dass die Verwendung eines Oszilloskops in Verbindung mit einem fundierten Verständnis der trigonometrischen Prinzipien ein leistungsstarkes Werkzeugset zur Analyse sinusförmiger Spannungen bietet. Dieses Wissen hilft nicht nur beim Verständnis des Verhaltens von Wechselstromkreisen, sondern findet auch Anwendung in zahlreichen Bereichen wie Telekommunikation, Signalverarbeitung und Energiesystemen.

Grafische und analytische Darstellung von Sinuskurven

Die Analyse von zwei sinusförmigen Spannungen an einem Oszilloskop mit gleicher Amplitude und Periode, aber unterschiedlichen Phasen, umfasst drei Schritte.
Zuerst ist der Peak-to-Peak ...

graphical-and-analytic-representation-of-sinusoids

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

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...

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 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

Description

Transcript

Tags