Explanation Given data: The given circuit diagram is shown in Figure 1. The given waveform is shown in Figure 2. Calculation: The conversion from mH to H is given as, 1 mH = 1 × 10 − 3 H The conversion from 5 mH to H is given as, L = 5 mH L = 5 × 10 − 3 H From figure 2 the time period T of the waveform is 2 s . The fundamental radian frequency ω 0 is given by, ω 0 = 2 π T Substitute 2 s for T in the above equation. ω 0 = 2 π 2 s = π rad / s The equation of the line passing through ( − 1 , 0 ) and ( − 0.5 , − 4 ) is given as, ( i s − 0 ) = − 4 − 0 − 0.5 + 1 ( t + 1 ) i s = − 8 ( t + 1 ) The equation of the line passing through ( − 0.5 , − 4 ) and ( 0.5 , 4 ) is given as, ( i s + 4 ) = 4 + 4 0.5 + 0.5 ( t + 0.5 ) i s + 4 = 8 ( t + 0.5 ) i s = 8 t The equation of the line passing through ( 0.5 , 4 ) and ( 1 , 0 ) is given as, ( i s − 4 ) = 0 − 4 1 − 0.5 ( t − 0.5 ) i s − 4 = − 8 ( t − 0.5 ) i s = − 8 ( t − 1 ) Thus, the mathematical representation of the waveform i s ( t ) given in figure 2 is, i s ( t ) = { − 8 ( t + 1 ) , − 1 ≤ t ≤ − 0.5 8 t , − 0.5 ≤ t ≤ 0.5 − 8 ( t − 1 ) , 0.5 ≤ t ≤ 1 (1) The Fourier series of the periodic function i s ( t ) of time period T can be written as, i s ( t ) = a 0 + ∑ n = 1 ∞ ( a n cos n ω 0 t + b n sin n ω 0 t ) (2) Here, a 0 , a n and b n are the Fourier series coefficients. Check the condition for odd symmetry of the function i s ( t ) . Substitute − t for t in the function given in equation (1). i s ( − t ) = { − 8 ( − t + 1 ) , − 1 ≤ − t ≤ − 0.5 8 ( − t ) , − 0.5 ≤ − t ≤ 0.5 − 8 ( − t − 1 ) , 0.5 ≤ − t ≤ 1 i s ( − t ) = − { − 8 ( t − 1 ) , 0.5 ≤ t ≤ 1 8 t , − 0.5 ≤ t ≤ 0.5 − 8 ( t + 1 ) , − 1 ≤ t ≤ − 0.5 The observed result from the above equation is writer as, i s ( − t ) = − i s ( t ) Therefore, it can be concluded that the function i s ( t ) is an odd function. It is observed that, i s ( t ) = − i s ( t − T 2 ) Therefore, the given waveform is half wave symmetric. Hence, the value of the Fourier coefficients a 0 and a n is 0 . The value of the b n is given by, b n = { 8 T ∫ 0 T 4 i s ( t ) sin n ω 0 t d t , for odd n 0 , for even n Substitute 2 for T and π for ω 0 in the above equation. b n = 8 2 ∫ 0 2 4 i s ( t ) sin n π t d t b n = 4 ∫ 0 0.5 i s ( t ) sin n π t d t Substitute the value of the function from equation (1) within the defined limits in the above equation

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

9th Edition

ISBN: 9781259989452

Author: Hayt

Publisher: Mcgraw Hill Publishers

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Chapter 17, Problem 26E

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Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

Ch. 17.1 - Let a third-harmonic voltage be added to the...Ch. 17.1 - A periodic waveform f(t) is described as follows:...Ch. 17.2 - Prob. 3P Ch. 17.2 - Prob. 4P Ch. 17.3 - Prob. 5P Ch. 17.3 - Prob. 6P Ch. 17.4 - Prob. 7P Ch. 17.5 - Prob. 8P Ch. 17.5 - Prob. 9P Ch. 17.6 - Prob. 10P

Ch. 17.6 - Prob. 11P Ch. 17.7 - Prob. 12P Ch. 17.7 - Prob. 13P Ch. 17.8 - Find (a) F5sin23t); (b) FAsin20t); (c)...Ch. 17.9 - Prob. 15P Ch. 17.10 - Prob. 16P Ch. 17 - Determine the fundamental frequency, fundamental...Ch. 17 - Plot multiple periods of the first, third, and...Ch. 17 - Calculate a0 for the following: (a) 4 sin 4t; (b)...Ch. 17 - Prob. 4E Ch. 17 - Prob. 5E Ch. 17 - Prob. 6E Ch. 17 - Prob. 7E Ch. 17 - With respect to the periodic waveform sketched in...Ch. 17 - Prob. 9E Ch. 17 - Prob. 10E Ch. 17 - A half-sinusoidal waveform is shown in Fig. 17.31,...Ch. 17 - Plot the line spectrum (limited to the six largest...Ch. 17 - Prob. 13E Ch. 17 - Prob. 14E Ch. 17 - Prob. 15E Ch. 17 - Prob. 16E Ch. 17 - Prob. 17E Ch. 17 - Prob. 18E Ch. 17 - The nonperiodic waveform g(t) is defined in Fig....Ch. 17 - Prob. 20E Ch. 17 - Prob. 21E Ch. 17 - Prob. 22E Ch. 17 - Prob. 23E Ch. 17 - Prob. 24E Ch. 17 - Prob. 25E Ch. 17 - Prob. 26E Ch. 17 - Prob. 27E Ch. 17 - Prob. 28E Ch. 17 - Prob. 29E Ch. 17 - Prob. 30E Ch. 17 - Prob. 31E Ch. 17 - Prob. 32E Ch. 17 - Prob. 33E Ch. 17 - Prob. 34E Ch. 17 - Prob. 35E Ch. 17 - Prob. 36E Ch. 17 - Use the Fourier transform to obtain and plot the...Ch. 17 - Prob. 38E Ch. 17 - Prob. 39E Ch. 17 - Prob. 40E Ch. 17 - For g(t) = 3etu(t), calculate (a) G(j); (b) ().Ch. 17 - Prob. 42E Ch. 17 - Prob. 43E Ch. 17 - Prob. 44E Ch. 17 - Prob. 45E Ch. 17 - Prob. 46E Ch. 17 - Find F(j) if f(t) is given by (a) 2 cos 10t; (b)...Ch. 17 - Prob. 48E Ch. 17 - Prob. 49E Ch. 17 - Prob. 50E Ch. 17 - Prob. 51E Ch. 17 - Prob. 52E Ch. 17 - Prob. 53E Ch. 17 - If a system is described by transfer function h(t)...Ch. 17 - Prob. 55E Ch. 17 - (a) Design a noninverting amplifier having a gain...Ch. 17 - Prob. 57E Ch. 17 - Prob. 58E Ch. 17 - Prob. 59E Ch. 17 - Prob. 60E Ch. 17 - Prob. 61E Ch. 17 - Prob. 62E Ch. 17 - Design an audio amplifier with gain of 10, using...

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