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

Analyzing two sinusoidal voltages on an oscilloscope with equal amplitude and period but different phases involves three steps.
First, the peak-to-peak value is measured, which is twice the amplitude. Secondly, the period and angular frequency are determined.
Third, voltage values for both sinusoids are measured at a fixed time to determine the phase angle, which depends on whether the sinusoid has a positive or negative slope.
A graphical representation can be used to compare two sinusoids, where the horizontal axis represents the magnitude of cosine and the vertical axis represents the magnitude of sine.
Similar to polar coordinates, the angles measured counterclockwise and clockwise from the horizontal axis are positive and negative, respectively.
Subtracting 90 degrees from the argument of cosine yields the sine function.
Two same-frequency sinusoids- one in sine and the other in cosine form, can be added using the graphical representation.
The hypotenuse of the right-angled triangle represents the resultant sinusoid, and its argument measured from the horizontal axis equals the cosine inverse of the ratio of base and hypotenuse.

graphical and analytic representation of sinusoids

Analyzing two sinusoidal voltages with equal amplitude and period but different phases on an oscilloscope, an instrument used to display and analyze waveforms, involves a three-step process.
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while the angular frequency (often denoted by the Greek letter omega, &#969;) is the rate at which the waveform oscillates.
The third step involves measuring the voltage values for both sinusoids at a fixed point in time. This is used to determine the phase angle, which depends on whether the sinusoid has a positive or negative slope at that point.
A graphical representation can be employed to compare the two sinusoids. In this representation, the horizontal axis represents the magnitude of cosine, and the vertical axis represents the magnitude of sine. This arrangement is reminiscent of polar coordinates, where angles measured counterclockwise from the horizontal axis are considered positive, while those measured clockwise are deemed negative.
Interestingly, subtracting 90 degrees from the argument of a cosine function yields the sine function. This property can be leveraged when dealing with sinusoids.
To add two sinusoids of the same frequency - one in sine form and the other in cosine form - the graphical representation comes into play again. The hypotenuse of the right-angled triangle formed by these sinusoids represents the resultant sinusoid. The argument of this resultant sinusoid, measured from the horizontal axis, equals the cosine inverse of the ratio of the base to the hypotenuse.
In conclusion, the use of an oscilloscope coupled with a firm understanding of trigonometric principles provides a powerful toolset for analyzing sinusoidal voltages. This knowledge not only aids in understanding the behavior of AC circuits but also finds applications in numerous fields like telecommunications, signal processing, and power systems.

Graphical and Analytic Representation of Sinusoids

Analyzing two sinusoidal voltages on an oscilloscope with equal amplitude and period but different phases involves three steps.
First, the peak-to-peak ...

graphical-and-analytic-representation-of-sinusoids

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Electrical Engineering

Unit 1

AC Circuit Analysis

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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

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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.

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Measuring Sinusoid Phase on an Oscilloscope

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