Introduction to Steady State (AC)Analysis Sinusoidal Sources (Continued) Why are sinusoids important (Cont.)? Reason #3:Any periodic waveform can be represented as an infinite sum of sinusoids,with frequencies that are multiples of the fundamental frequency 0o>Fourier Series For any periodic waveform V(t),with fundamental frequency oo 00=(2π)/T v(t)=>E edino.),where j=v-1 The coefficients E are given by: T/2 E=1/T/V(t)e-inoot dt -T/2 n@o are the harmonic frequencies of v(t) Basic Electronics-Special Lecture for TIPP 2011 9 Gary Drake,Argonne National Lab-Session 2Basic Electronics – Special Lecture for TIPP 2011 9 Gary Drake, Argonne National Lab – Session 2 Introduction to Steady State (AC) Analysis  Sinusoidal Sources (Continued) • Why are sinusoids important (Cont.)?  Reason #3: Any periodic waveform can be represented as an infinite sum of sinusoids, with frequencies that are multiples of the fundamental frequency O  Fourier Series – For any periodic waveform V(t), with fundamental frequency O – The coefficients En are given by: t v(t) =  En e(jnot) , where j = S -1 n=-h +h T O = (2 ) / T En = 1/T f V(t) e-jnot dt -T/2 T/2 v(t)  n0 are the harmonic frequencies of v(t)