LLC Power Conversion Explained, Part 2: Sine Wave from a Square Wave

In LLC Power Conversion Explained, Part 1: Introduction of this series, it was learned that the operation of the LLC requires the creation of a primary side sine wave current that is converter to a secondary side sine wave and then rectified and filtered by a large capacitor as shown.

This blog explains how to convert the square wave into a sine wave by using a low pass filter. A square wave can be created by adding the sum of the odd harmonics of a sine wave.

This is better explained for odd harmonics as follows.

For the LLC, a higher switching frequency of 90 kHz is used in place of the 50Hz fundamental frequency in the aforementioned example. Individual harmonics for a 90 kHz sine wave made into a square wave will then look something like sine waves that are increasing in frequency and decreasing in amplitude.

The summation of these waveforms shows how a series of sine waves can be summed together to create a square wave.

The higher the number of harmonics, the closer the summation comes to a square wave.

Little changes beyond the 11th harmonic as the amplitudes have been divided by the harmonic number. By the time you get to the 19th harmonic, the waveform shows little impact from the higher harmonics.

However, adding a low pass filter to the waveform, the individual harmonics look like this.

The summation of these waveforms begins to look like the original sine wave as follows.

Thus far we have established the basic operation of the LLC converter along with the method by which a traditional Switched Mode Power Supply is used to create a sine wave. There is a lot more to cover on the LLC as it is a complex converter with many operating modes. Future blogs will address these segments of the design.

References

• “Design Considerations for an LLC Resonant Converter” Fairchild Semiconductor Power Seminar 2007 Appendix A: White Papers; couldn’t get a website URL; suggest you Google the text in brackets [“Design Considerations for an LLC Resonant Converter” Fairchild Semiconductor Power Seminar 2007 Appendix A: White Papers]
• Square Wave Signals”, Chapter 7 – Mixed-Frequency AC Signals, All About Circuits website

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