Attached are images for questions regarding Fourier Analysis.
Techniques involving the electronic control of power to a load such as controlled rectification and variable frequency drives are widely used by industry. There can be, however, serious problems with these techniques because of the generation of harmonics and the consequential harmonic distortion. Harmonics, when fed back to the supply, can have adverse effects on other electrical equipment. It can increase the current in power lines resulting wasted power that causes higher temperatures in neutral conductors and distribution transformers. High order harmonics may cause excessive heating in the core of a.c motors and can also interfere with communication systems. Increased temperatures can damage power systems and shorten the life of electronic equipment.
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The Fourier Analysis tool solves problems in linear systems and analyzes periodic data by using the Fast Fourier Transform (FFT) method to transform data. This tool also supports inverse transformations, in which the inverse of transformed data returns the original data.
The Fourier Analysis Toolpack is available under the "Tools" tab then selecting "Analysis Toolpak". Most bare versions of Excel will by default not contain the "Analysis Toolpak" in the first instance so you may need to initially install this so follow the steps below.
Installation of Excel "Analysis Toolpak"
• Open Excel spreadsheet and hit the "Tools" tab and then select "Add Ins" from the drop down options.
• Tick the "Analysis Toolpak" option and then OK
To carry out Fourier Analysis with Excel
• Open Excel and hit the "Tools" tab
• Select and hit the "Data ...
The solution provides an analysis of given time domain waveform into fourier components using Excel Fourier analysis tools and then identification of main frequency components. Further from this information the total harmonic distortion (% THD) is determined
Fourier analysis using Excel
The supply current was sampled 1024 times over a very short time interval. The data so obtained is given in column B of the accompanying Excel worksheet (see attached).
This worksheet has been set up to give a graph showing the spectral components of the data.
i) Obtain the Fourier Transform for the data using the Fourier Analysis tool of Excel. The transformed data should commence in cell D2.
ii) Identify the principal frequencies in the current waveform.
iii) Estimate the total harmonic distortion [THD] present in the current waveform using the formula:
(See attached file for equation)
Where I1 is the r.m.s. value of the fundamental current, In the r.m.s value of the nth harmonic and n(max) is the number of the highest measurable or significant harmonic.
[Note the vertical axis of the spectrum graph is scaled in (current)^2.]
iv) Attempt to synthesise the shape of the original waveform from its principal harmonics [e.g. sketch the waveforms of the harmonics on the same time axis and add them together].
Q4. Sketch, on a set of common axes, waveforms to represent the transient response of circuits having transfer functions with the following parameters:
(see attached file for more information)