Sac State
EEE 102 -
Pulse Train Fourier Series Representation
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California State University, Sacramento
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Pulse Train Fourier Series RepresentationParameter DefinitionsPulse duration A Interpulse interval B Pulse period T = A + B Duty cycle D = A/TPulse frequency fo = 1/T Pulse radian frequency ωo = 2πfoPulse amplitude VoFourier Series Equationwhere the Fourier parameters are:The Fourier parameters for the Pulse TrainThe Fourier Series for the Pulse TrainVBTAmplitude in VoltsTime in secondsAo€ f(t) =ao2+ ancos(nωot)n=1∞∑+ bnsin(nωot)n =1∞∑€ ao=2Tf(t)dt0T∫€ an=2Tf(t)cos(nωo0T∫t)dt€ bn=2Tf(t)sin(nωot)dt0T∫€ ao=2AVoA + B€ an=Vonπsin(nωot)€ bn=Vonπ1- cos(nωot)[ ]€ f(t) =VoAA +B+Voπ1nsin(nωoA)[ ]cos(nωot) +1n1- cos(nωoA)[ ]sin(nωot) n=1∞∑Fotrr,'er.$niGf .. fLbcTe. :a S2ntloisPrF|sc 4rplJforls I lVr DuVC2cle *91f,,,
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