Fourier Transform

Principles

A very important mathematics tool is used in EMC, called the Fourier transform. It converts time domain voltage waveform into frequency domain energy contents. Usually we plot frequency domain waveforms in log for frequency and log for volts.

Time domain
measurement

Fourier transform

Frequency
measurement

Invert Fourier transform

Why freauency domain is so important

Time domain aspect is dominated by the major frequency harmonics. Small noise contribution may hardly be seen. As most users specification only tolerate very low levels of energy in some critical frequency bands, we need to know if low energy signals exist in such bands. Time domain analysis is not an appropriate approach.

The time domain wave form on the left part of the slide looks like a noise. However, the spectrum reveals a small sinusoidal wave above the noise, which appears as a random energy distribution.

Exercise: Find the Fourier Transform of basic signals

In this slide, we propose some basic signals and ask the reader to use Microwind, invoke the FFT in order to find the corresponding spectrum. The user may also investigate the role of parameters such as the simulation length and FFT resolution.

Internal current peaks in integrated circuits produce the highest amount of harmonics

Considering a triangular signal of 1A, at a rate of 1GHz. The Fourier Transform of this signal is an infinite sum of pure sinusoidal waves, called harmonics). Notice that the harmonic energy is still high at 30GHz.