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Define x(t) as x(t)=5√√2 cos(20л+л/4)+ A cos(20лt+) where A is a positive number. In addition, assume that x(t) has a phase of zero, so that it may written as where B is a positive number. x(t) = B cos(20лt), (1) be (2) (a) What relationship must exist between A and in order for x(t) to have zero phase as indicated in Eq. 2? (b) If B = 10, what are the values for A and ø? (c) Now assume that B is unspecified. Find the values for A, B, and so that the value of A is minimized. Draw a plot of the complex amplitudes to prove using a geometrical argument that you have found the minimum for A. Hint: Recall the geometrical "theorem" that tells you how to find the shortest distance between a line and a point that is not on the line (have you heard the term "projection"?

Define x(t) as x(t)=5√√2 cos(20л+л/4)+ A cos(20лt+) where A is a positive number. In addition, assume that x(t) has a phase of zero, so that it may written as where B is a positive number. x(t) = B cos(20лt), (1) be (2) (a) What relationship must exist between A and in order for x(t) to have zero phase as indicated in Eq. 2? (b) If B = 10, what are the values for A and ø? (c) Now assume that B is unspecified. Find the values for A, B, and so that the value of A is minimized. Draw a plot of the complex amplitudes to prove using a geometrical argument that you have found the minimum for A. Hint: Recall the geometrical "theorem" that tells you how to find the shortest distance between a line and a point that is not on the line (have you heard the term "projection"?

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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Define x(t) as x(t)=5√√2 cos(20л+л/4)+ A cos(20лt+) where A is a positive number. In addition, assume that x(t) has a phase of zero, so that it may written as where B is a positive number. x(t) = B cos(20лt), (1) be (2) (a) What relationship must exist between A and in order for x(t) to have zero phase as indicated in Eq. 2? (b) If B = 10, what are the values for A and ø? (c) Now assume that B is unspecified. Find the values for A, B, and so that the value of A is minimized. Draw a plot of the complex amplitudes to prove using a geometrical argument that you have found the minimum for A. Hint: Recall the geometrical "theorem" that tells you how to find the shortest distance between a line and a point that is not on the line (have you heard the term "projection"?
Transcribed Image Text:Define x(t) as x(t)=5√√2 cos(20л+л/4)+ A cos(20лt+) where A is a positive number. In addition, assume that x(t) has a phase of zero, so that it may written as where B is a positive number. x(t) = B cos(20лt), (1) be (2) (a) What relationship must exist between A and in order for x(t) to have zero phase as indicated in Eq. 2? (b) If B = 10, what are the values for A and ø? (c) Now assume that B is unspecified. Find the values for A, B, and so that the value of A is minimized. Draw a plot of the complex amplitudes to prove using a geometrical argument that you have found the minimum for A. Hint: Recall the geometrical "theorem" that tells you how to find the shortest distance between a line and a point that is not on the line (have you heard the term "projection"?
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