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Fourier Simulation Tool
Any complex waveform can be broken down into a (possibly infinite) series of sine and/or cosine terms, called harmonics. The series is called a Fourier Series. In theory, the waveform must be a periodic or repetitive one, but approximations can be valuable even for those waveforms that are not. The Fourier series approach is valuable in electronics because (in general) the impact of a circuit on a waveform is a function of frequency. By breaking the waveform down into a series of single frequency harmonics, the system can be analyzed for each individual harmonic and the components then summed back together. In concept, then, the impact of a circuit on any waveform can be determined.
This simulation shows the Fourier decomposition for several common waveforms found in electronic systems: square waves, triangle waves, trapezoidal waves, and sawtooth waves. It shows how the accuracy of the underlying waveform improves as we add harmonics and what happens if we filter out specific harmonics.
Operation is straightforward:
1. Select the waveform.
2. Enter the number of harmonics to use in the simulation.
3. Select the harmonics to include or exclude. The options are:
a. Include all harmonics
b. Exclude a specific harmonic and see the impact if that harmonic is
somehow filtered out by the circuit.
c. Exclude all except one specific harmonic to visualize the impact of
that one harmonic.
The "See Examples and Formulas" button opens a second form that illustrates the common waveforms and the formulas used in the simulation.
UltraCAD's universal license is required for this calculator. The calculator is included in the download "ucad-universal.zip." |
Download "ucad-universal.zip" here. |
This calculator is designed to run on Windows 98/ME/NT/2K/XP/VISTA/Win7, 32 bit and 64 bit versions.
On most systems, Microsoft's chart control must be added. It (mschart.exe) is included in the download. Execute it on your system.
Click on logo to return to UltraCAD's Calculator page.