Oscilloscope helps measure harmonic content calculation

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Oscilloscope helps measure harmonic content calculation [Copy link]

Recently, a user of a Macosin oscilloscope asked how to use an oscilloscope to calculate the harmonic content of a signal. So today we will systematically learn how an oscilloscope measures the harmonics of a signal and how to calculate the specific operations of the harmonic content.

Harmonic interference in the power system will affect the quality of power supply, causing energy waste, and will also cause electrical equipment and wires to overload, resulting in heat generation, increased losses, shortened service life, and even failure or burnout, causing significant economic losses. In signal transmission, it will also interfere with the communication system and reduce the quality of signal transmission.

Harmonic content is the quantity obtained by subtracting the fundamental component from the AC quantity, and is one of the important indicators for evaluating power quality. So how can we use an oscilloscope to find the harmonics in the signal?

Let's review the FFT (Fast Fourier Transform) function of the oscilloscope. Fourier transform believes that any complex signal is the superposition of multiple sine waves.

For example, we can regard this red signal as the superposition of multiple blue sine waves on the vertical vector. The blue sine wave with the smallest frequency and the largest voltage is called the fundamental wave, and the blue sine wave with a frequency twice that of the fundamental wave is called the second harmonic. Similarly, the blue sine wave with a frequency three times that of the fundamental wave is called the third harmonic, and so on.

Here, each separated blue signal has a different frequency, and each signal has a different voltage value. If we take the frequency of these signals as the X-axis and the voltage value as the Y-axis, it will be as follows:

The red histogram in the figure below is what the calibration square wave of the oscilloscope looks like after FFT (Fast Fourier Transform). It can be seen from the red histogram that the voltage of the signal component with a frequency of 0Hz is 0, which means that the signal does not contain a DC component. The first red line is the fundamental wave of the signal, with a frequency of 1KHZ and an amplitude of 896.6mV. Through the difference between the X-axis cursors X1 and X2, we find that the frequency of the fifth straight line is 9KHz, which is 9 times the fundamental wave, that is, the ninth harmonic. Through the difference between the Y-axis cursors Y1 and Y2, we can know that the amplitude of this harmonic is 104mv.

So how do we calculate the content of this harmonic? Here is the formula:

The content of a certain harmonic = the size of a certain harmonic ÷ the root mean square value of the entire waveform x 100%

Using this method, let's calculate the 7th harmonic voltage content of a 1MHz square wave.

As shown in the figure, the yellow one is a square wave with a frequency of 1MHz and an effective value of 2.369V, and the red one is the histogram after FFT (line). The frequency of the fundamental wave is 1MHz, and the harmonic frequency selected by the cursor is 7MHz, that is, the seventh harmonic, and its voltage value is 188mV.

Therefore, the seventh harmonic content of the signal is (0.188 ÷ 2.369) X 100% ≈ 7.936%