[Utility Guide] teaches you to use FFT and oscilloscope

This article discusses some of the important FFT features and explains how to use these features to set up the FFT for efficient analysis. I hope you will be able to help you the next time you want to use the FFT in an oscilloscope.

This article discusses some of the important FFT features and explains how to use these features to set up the FFT for efficient analysis.

The Fast Fourier Transform (FFT) was first introduced in the 1970s when microprocessors entered commercial design. From expensive lab models to the cheapest amateur models, almost every oscilloscope now offers FFT analysis. FFT is a powerful tool, and efficient use of FFT requires some research on FFT. This article will introduce how to set up the FFT and use the FFT efficiently. The technical principle of the FFT is not repeated here.

FFT is an algorithm that can shorten the time of discrete Fourier transform (DFT) calculation. It is also used to view the acquired time domain (amplitude and time) data in the frequency domain (the relationship between amplitude and phase and frequency). analyzing tool. The FFT adds spectrum analysis to the digital oscilloscope.

Looking at the upper half of the curve in Figure 1, you see an amplitude modulated carrier that uses a trapezoidal pulse as the modulation function. When you look at the time domain diagram in Figure 1, if you tell me the bandwidth of the signal, you may not be able to answer it for a while. But if you FFT the signal, you get another perspective. This signal has a linear sweep frequency, and the bandwidth is marked with a cursor, which is 4.7MHz. This is the principle of adding FFT function to the oscilloscope. It is the same data from another perspective.

Figure 1: The upper time-domain diagram shows the pulse-modulated RF carrier, and the lower frequency-domain diagram shows the carrier frequency evenly distributed between 997MHz and 1002MHz.

FFT bandwidth and resolution bandwidth

In the earliest circuit courses, you should learn that the frequency (frequency domain) of the periodic signal is the reciprocal of the period (time domain). Again, this relationship runs through the entire FFT setup process.

Setting the FFT is best done by selecting the resolution bandwidth (RBW) as it relates to single parameter adjustment. RBW (Δf) is the incremental step size for displaying the FFT frequency axis. In the time domain, the sampling period determines the time interval between samples. In the frequency domain, RBW is the frequency difference between adjacent "cells" in the spectrogram. RBW is the reciprocal of the time domain record length (also known as acquisition time), as shown in Figure 2. You can control the RBW with the oscilloscope's horizontal scale or time/division parameter settings. The acquisition duration in Figure 1 is 20 μs, and the RBW in the spectrogram is its reciprocal, 50 kHz.

Figure 2: The resolution bandwidth of the spectrum is the reciprocal of the time domain record length or acquisition time.

The next step in setting up the FFT is to determine the width of the frequency domain plot - the difference between the highest frequency and the lowest frequency in the FFT. Note that the FFT usually starts at 0 Hz and continues to the entire bandwidth. This is very different from the RF spectrum analyzer, I will talk about it right away.

The bandwidth of the FFT is half the effective sampling rate of the oscilloscope (Figure 3). The shortest time increment in the time domain - the sampling period - determines the largest component in the frequency domain. Again, the smallest increment in the frequency domain is a function of the longest duration in the time record. This is consistent with the inverse relationship between the time domain and the frequency domain.

Figure 3: Spectrum width is half the effective sampling rate of the oscilloscope

In order to achieve higher resolution in the frequency domain, the amount of data collected must be increased by increasing the time/div setting. This is exactly the opposite of adding time resolution to the time domain map of the oscilloscope.

From a practical point of view, the time domain record length is controlled by the oscilloscope's time/division parameter values. Once you have selected the time/division parameter values ​​to achieve the desired resolution bandwidth, the only way to control the sample rate to the desired bandwidth is to modify the oscilloscope's acquisition memory length. Things seem complicated now, and it is.

Recently, most high-end oscilloscope manufacturers have modified the FFT user interface to make it more similar to a standard RF spectrum analyzer, with resolution bandwidth as a parameter when setting the center frequency and bandwidth. Although this type of interface makes the FFT easier to use, it does hide the basic functions of the FFT, resulting in the need to accept the time/division, sample rate, and memory length combinations set by the oscilloscope. Based on some of the rules discussed in this section, you can manually set the FFT and get more freedom in the settings.

Vertical zoom

Depending on the oscilloscope, the FFT may have a vertical scale, perhaps a fixed single vertical format. The most common vertical format is the power spectrum, which displays the vertical amplitude in power, commonly expressed in decibels (dBm) relative to 1 milliwatt and displayed on a logarithmic vertical scale. This choice is also a feature of the RF spectrum analyzer function. Lab-level oscilloscopes can provide more data, including power spectral density (PSD), linear amplitude, squared amplitude, phase, or real/imaginary components.

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