Fourier en orcad
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Publicado: 5 de junio de 2011
EGR 261 Signals and Systems File: FourierPulse.doc
Fourier Analysis of a Pulse Waveform using PSPICE
A Fourier Analysis can be performed in PSPICE as part of a Transient Analysis. The pulsewaveform shown below was placed in parallel with a resistor and a Transient Analysis and Fourier Analysis was performed for three periods of the waveform. PSPICE generated the Fourier seriescoefficients for each harmonic and they were compared to those calculated using the Fourier series shown below. ∞
v(t) = 5 +
v(t)
10 V
20 1 ∑5,... n sin(2000nπt) π n =1,3,
t(ms) 0.0 PSPICESchematic:
EGR 261 Signals and Systems File: FourierPulse.opj
0.5
1.0
1.5
2.0
2.5
Fourier Analysis of a Pulse Waveform using PSPICE
A
V1 = 0V V2 = 10V TD = 0 TR = 1ns TF =1ns PW = 0.5ms PER = 1ms
V1 R1 1k
0
T = 1ms, so wo = 2pi/T = 2000pi = fundamental frequency (in rad/s) fo = 1/T = 1000 = fundamental frequency (in Hz) The Fourier Series for the waveformshown is v(t) = Av + 4Vm/pi*Sum[(1/n)sin(nwot) or v(t) = 5 + 6.366*Sum[(1/n)sin(2000npit)] (odd harmonics only) or v(t) = 5 + 6.3662sin(2000pit) + 2.1221sin(6000pit) + 1.2732sin(10000pit) +0.9095sin(14000pit) + 0.7074sin(18000pit) + 0.5787sin(22000pit) + ...
Page 2 PSPICE Output Waveform:
12V
8V
4V
0V 0s V(A) Time 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms
PSPICE SimulationSettings:
Page 3 PSPICE Output File: **** 03/28/ 15:06:44 ************** PSpice Lite (Mar 2000) ***************** ** Profile: "SCHEMATIC1-FourierPulse" [ C:\ProgramFiles\OrcadLite\Capture\Library\fourierpulse-SCHEMATIC1-FourierPulse.sim ] **** CIRCUIT DESCRIPTION ****************************************************************************** *Analysis directives: .TRAN 0 3ms 0 .FOUR 1000 11V([A]) .PROBE V(*) I(*) W(*) D(*) NOISE(*) * source FOURIERPULSE V_V1 A0 +PULSE 0V 10V 0 1ns 1ns 0.5ms 1ms R_R1 0 A 1k **** RESUMING fourierpulse-SCHEMATIC1-FourierPulse.sim.cir **** .END...
Fourier Analysis of a Pulse Waveform using PSPICE
A Fourier Analysis can be performed in PSPICE as part of a Transient Analysis. The pulsewaveform shown below was placed in parallel with a resistor and a Transient Analysis and Fourier Analysis was performed for three periods of the waveform. PSPICE generated the Fourier seriescoefficients for each harmonic and they were compared to those calculated using the Fourier series shown below. ∞
v(t) = 5 +
v(t)
10 V
20 1 ∑5,... n sin(2000nπt) π n =1,3,
t(ms) 0.0 PSPICESchematic:
EGR 261 Signals and Systems File: FourierPulse.opj
0.5
1.0
1.5
2.0
2.5
Fourier Analysis of a Pulse Waveform using PSPICE
A
V1 = 0V V2 = 10V TD = 0 TR = 1ns TF =1ns PW = 0.5ms PER = 1ms
V1 R1 1k
0
T = 1ms, so wo = 2pi/T = 2000pi = fundamental frequency (in rad/s) fo = 1/T = 1000 = fundamental frequency (in Hz) The Fourier Series for the waveformshown is v(t) = Av + 4Vm/pi*Sum[(1/n)sin(nwot) or v(t) = 5 + 6.366*Sum[(1/n)sin(2000npit)] (odd harmonics only) or v(t) = 5 + 6.3662sin(2000pit) + 2.1221sin(6000pit) + 1.2732sin(10000pit) +0.9095sin(14000pit) + 0.7074sin(18000pit) + 0.5787sin(22000pit) + ...
Page 2 PSPICE Output Waveform:
12V
8V
4V
0V 0s V(A) Time 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms
PSPICE SimulationSettings:
Page 3 PSPICE Output File: **** 03/28/ 15:06:44 ************** PSpice Lite (Mar 2000) ***************** ** Profile: "SCHEMATIC1-FourierPulse" [ C:\ProgramFiles\OrcadLite\Capture\Library\fourierpulse-SCHEMATIC1-FourierPulse.sim ] **** CIRCUIT DESCRIPTION ****************************************************************************** *Analysis directives: .TRAN 0 3ms 0 .FOUR 1000 11V([A]) .PROBE V(*) I(*) W(*) D(*) NOISE(*) * source FOURIERPULSE V_V1 A0 +PULSE 0V 10V 0 1ns 1ns 0.5ms 1ms R_R1 0 A 1k **** RESUMING fourierpulse-SCHEMATIC1-FourierPulse.sim.cir **** .END...
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