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Example: Determine the power and the rms value of the following (a) x(t) = C cos (wot + 0) (b) x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂) W₁ W₂

Example: Determine the power and the rms value of the following (a) x(t) = C cos (wot + 0) (b) x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂) W₁ W₂

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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solve the Hw.

Example: Determine the power and the rms value of the following (a) x(t) = C cos (wot + 0) (b) x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂) Solution: (a) x(t) = C cos (wot + 0) It is a periodic signal with period To = 27/wo. The suitable measure of this signal is its power. 1 T/2 1 T/2 P == P = x² (t)dt -T/2 C² -T/2 2T P=2²23 = [1 + cos(2wot+20)] dt C² cos² (wot+0)dt = T/2 -T/2 1 dt + -T/2 W₁ W2 cos(2wot +20) dt -T/2 This show that a sinusoid of amplitude C has a power C²/2 regardless of the value of its frequency w(wo‡0) and phase 0. C Prms == HW: If the signal frequency is 0 (dc or a constant signal of amplitude C), show that the power is C².
Transcribed Image Text:Example: Determine the power and the rms value of the following (a) x(t) = C cos (wot + 0) (b) x(t) = C₁ cos (w₁t + 0₁) + C₂ cos (w₂t + 0₂) Solution: (a) x(t) = C cos (wot + 0) It is a periodic signal with period To = 27/wo. The suitable measure of this signal is its power. 1 T/2 1 T/2 P == P = x² (t)dt -T/2 C² -T/2 2T P=2²23 = [1 + cos(2wot+20)] dt C² cos² (wot+0)dt = T/2 -T/2 1 dt + -T/2 W₁ W2 cos(2wot +20) dt -T/2 This show that a sinusoid of amplitude C has a power C²/2 regardless of the value of its frequency w(wo‡0) and phase 0. C Prms == HW: If the signal frequency is 0 (dc or a constant signal of amplitude C), show that the power is C².
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