Responses to Periodic Inputs
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Responses to Periodic Inputs book
This chapter begins by presenting Fourier's theorem and deducing how the coefficients of the sine and cosine terms of the Fourier series expansion (FSE) can be obtained. The derivation of the FSE is significantly simplified if the given periodic function possesses some symmetry properties or if it's the sum, the product, the derivative, or the integral of functions whose FSE is already known. The chapter discusses these simplifications in considerable detail. This is followed by considering circuit responses to periodic signals and the average power involved, leading to the definition and derivation of the root-mean-square value of a periodic voltage or current. Circuit responses to periodic signals are of considerable practical interest, because these signals are very common. The steady state of any linear or nonlinear circuit, other than the dc steady state, is periodic. Thus, the outputs of free-running oscillators, the time bases of TV and computer displays, and continuous vibrations of all kinds are periodic signals.