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Remember that the phase of a sinusoid can be calculated after measuring the time location (or in the case of a discrete-time signal, the sample index) of a positive peak, if we know the frequency. (a) Make measurements of the "time-location of a positive peak" and the amplitude from the plots of x₁(t) and x₂(t). Then calculate (by hand) the phases of the two signals, x₁(t) and x2(t), by converting each time-shift tmi to phase. Note: when doing computations, express phase angles in radians, not degrees! (b) Measure the amplitude A3 and time-shift tm3 of x3(t) directly from the plot and then calculate the phase (93) by hand. Show how the amplitude and time-shift were measured, and how the phase was calculated.

Remember that the phase of a sinusoid can be calculated after measuring the time location (or in the case of a discrete-time signal, the sample index) of a positive peak, if we know the frequency. (a) Make measurements of the "time-location of a positive peak" and the amplitude from the plots of x₁(t) and x₂(t). Then calculate (by hand) the phases of the two signals, x₁(t) and x2(t), by converting each time-shift tmi to phase. Note: when doing computations, express phase angles in radians, not degrees! (b) Measure the amplitude A3 and time-shift tm3 of x3(t) directly from the plot and then calculate the phase (93) by hand. Show how the amplitude and time-shift were measured, and how the phase was calculated.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Theoretical Calculations Remember that the phase of a sinusoid can be calculated after measuring the time location (or in the case of a discrete-time signal, the sample index) of a positive peak, if we know the frequency. (a) Make measurements of the "time-location of a positive peak" and the amplitude from the plots of x₁(t) and x₂(t). Then calculate (by hand) the phases of the two signals, xi(t) and x2(t), by converting each time-shift tmi to phase. Note: when doing computations, express phase angles in radians, not degrees! (b) Measure the amplitude A3 and time-shift tm3 of x3(t) directly from the plot and then calculate the phase (93) by hand. Show how the amplitude and time-shift were measured, and how the phase was calculated. (c) Now use the phasor addition theorem. Carry out a phasor addition of complex amplitudes for x₁(t) and x₂(t) to determine the complex amplitude for x3(t). Use the complex amplitude for x3(t) to verify that your previous calculations of A3 and 03 were correct.
Transcribed Image Text:Theoretical Calculations Remember that the phase of a sinusoid can be calculated after measuring the time location (or in the case of a discrete-time signal, the sample index) of a positive peak, if we know the frequency. (a) Make measurements of the "time-location of a positive peak" and the amplitude from the plots of x₁(t) and x₂(t). Then calculate (by hand) the phases of the two signals, xi(t) and x2(t), by converting each time-shift tmi to phase. Note: when doing computations, express phase angles in radians, not degrees! (b) Measure the amplitude A3 and time-shift tm3 of x3(t) directly from the plot and then calculate the phase (93) by hand. Show how the amplitude and time-shift were measured, and how the phase was calculated. (c) Now use the phasor addition theorem. Carry out a phasor addition of complex amplitudes for x₁(t) and x₂(t) to determine the complex amplitude for x3(t). Use the complex amplitude for x3(t) to verify that your previous calculations of A3 and 03 were correct.
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