Pulse Train Fourier Series...
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Pulse Train Fourier Series Representation Parameter Definitions Pulse duration A Interpulse interval B Pulse period T = A + B Duty cycle D = A/T Pulse frequency f o = 1/T Pulse radian frequency ω o = 2πf o Pulse amplitude V o 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 f(t) = a o 2 + a n cos(nω o t) n=1 ∞ ∑ + b n sin(nω o t) n =1 ∞ ∑ a o = 2 T f(t)dt 0 T ∫ a n = 2 T f(t)cos(nω o 0 T ∫ t)dt b n = 2 T f(t)sin(nω o t)dt 0 T ∫ a o = 2AV o A+B a n = V o nπ sin(n ω o t) b n = V o nπ 1 - cos(nω o t) [ ] f(t) = V o A A+B + V o π 1 n sin(nω o A) [ ]cos(nω o t) + 1 n 1 - cos(nω o A) [ ]sin(nω o t) n=1 ∞ ∑
Transcript of Pulse Train Fourier Series...
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
∞
∑
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