Post on 27-Mar-2020
Pulse Train Fourier Series Representation
Parameter Definitions
Pulse duration A Interpulse interval B Pulse period T = A + B Duty cycle D = A/TPulse frequency fo = 1/T Pulse radian frequency ωo = 2πfo Pulse amplitude Vo
Fourier Series Equation
where the Fourier parameters are:
The Fourier parameters for the Pulse Train
The Fourier Series for the Pulse Train
V
B
T
Amplitude in Volts
Time in seconds
A
o
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f(t) = ao2
+ ancos(nωot)n=1
∞
∑ + bnsin(nωot)n =1
∞
∑
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ao =2T
f(t)dt0
T∫
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an =2T
f(t)cos(nωo0
T∫ t)dt
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bn =2T
f(t)sin(nωot)dt0
T∫
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ao =2AVoA +B
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an =Vonπsin(nωot)
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bn =Vonπ
1- cos(nωot)[ ]
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f(t) = VoAA +B
+Voπ
1nsin(nωoA)[ ]cos(nωot)+
1n1- cos(nωoA)[ ]sin(nωot)
n=1
∞
∑