The LLC Resonant Power Converter is a very complex circuit. This blog is the fourth in a series of blogs that attempts to simplify the circuit in order to understand the basics. This series is written in a manner that explains a popular circuit without the need of having a background in advanced electrical engineering, Switched Mode Power Supply (SMPS) or SMPS modeling and analysis. Note that the list of references expands with each blog. Only the references relevant to this discussion will contain links in the text. The full list of references helps to further piece together the complicated operation of this circuit. That full list has relevance throughout the various blogs where the links are present in the text of each individual blog.

Thus far the LLC converter has been presented as a converter that creates a DC output by rectifying and storing an AC waveform in a capacitor in LLC Power Conversion Explained, Part 1: Introduction. LLC Power Conversion Explained, Part 2: Sine Wave from a Square Wave went on to explain how to create a sine wave using SMPS switching of a DC voltage. LLC Power Conversion Explained, Part 3: Understanding transformers introduced the role of the transformer in the LLC circuit. Part 3 also showed how the LLC circuit could be simulated by reflecting the output load back through the transformer.

It takes a three-part introduction in order to get to the gain equation of the LLC circuit and explain the operating modes. In summary, the goal is to operate the LLC at a resonant frequency to create a sine wave current and keep the rectifier diodes in constant current mode. As stated previously, this is a departure from the traditional SMPS desire to store energy in an inductor. The typical SMPS will have a reduced ripple current if the inductor is operated in continuous current mode or CCM. To avoid confusion, CCM in an LLC refers to rectifier diode current.

The following figure shows the desired sine wave output of the LLC circuit from a basic voltage divider. In a true LLC circuit, the input waveform is a square wave and not the sine wave shown. Part 2 of this series explained how the sine wave is a result of filtering a square wave with the resonant tank circuit. The square wave is created by using a half bridge circuit to switch a DC input voltage as stated in Part 1. Finally, Part 3 explained the various impedances of the transformer’s leakage inductance, magnetizing inductance, and load resistance as reflected through the transformer and massaged for AC analysis.

**Image courtesy of On Semiconductor **

The gain is found using the impedance of a voltage divider in the figure above where

Vo = (Vin x X2) / (X1 + X2)

**(Note that this is a correction from part 2 which erroneously left out the division sign.)**

Where X2 = XLm||Rac and X1 = XCr + XLr when combining the impedances of the resonant tank circuit components in the last figure.

The majority of the application notes jump right into the gain equation of the LLC converter and how it sets the switching frequency. This blog has a somewhat different approach as it explains how the converter actually transfers AC current to the secondary while enabling the transformer to function properly. In the following figure, there is shown transformer T1 with magnetizing inductance Lm. This creates one of the difficulties in understanding the LLC’s various operating forms. Here are two simple concepts that will help the explanation.

- In order for the transformer to operate properly, there has to be enough magnetizing current flowing through Lm.
- The AC current for the secondary flows through the primary of T1

**Image courtesy of On Semiconductor **

Let this sink in for a minute. Lm is the magnetizing current. The transformer primary current is an AC current from a resonant tank circuit. As it turns out, these currents are crucial to the operation of the LLC current yet they are very different from each other. The magnetizing current is actually a triangular current that is of the traditional SMPS calculation where:

Magnetizing Current di/di =Vprim/Lm, Vprim is the reflected DC output voltage

This takes a some understanding of current flow and transformer operation. The transformer needs magnetizing current to properly transfer energy. When the output diode is conducting, the output voltage is clamped across the secondary and thus the DC output voltage is reflected to the primary and magnetizing inductance causing a triangular current through Lm. The resonant tank circuit is trying to create an AC current. This AC sine wave current is flowing in the transformer primary. Each of these currents plays a role in the LLC circuit with the AC current relating to the output voltage and the magnetizing current relating to basic transformer operation.

This point is often misunderstood because the output voltage dictates the transformer magnetizing current. It is easier to base the magnetizing current of the transformer on a steady DC voltage of the output from an analysis standpoint rather than the traditional method of using a hard-switched SMPS input voltage due to the filtering out of the square wave on the primary side of the transformer. The following waveforms show how this division of current occurs in the LLC.

**Image courtesy of On Semiconductor **

Note that the magnetizing current is much lower than the resonant current. By choosing to ignore the magnetizing current, the majority of LLC operating explanations jump right into focusing on the resonant current and then mention the magnetizing current as an afterthought. After reading several of the articles on LLC converters, I would have preferred that this point be mentioned up front. I believe that it provides a little better insight for understanding the operation of the converter.

This blog will end with the added concept of operating modes for the LLC. The majority of the operation of the LLC can be viewed as a tuned AC circuit with resonance based on the Lr = leakage inductance, Lm = magnetizing inductance, and C = added series capacitor. These are the three elements of the LLC circuit. As we shall see in future blogs, the operating point of the LLC requires one to consider the magnetizing inductance as a tuned circuit component as well as a part of the transformer model. If that isn’t confusing enough, the gain equation has three AC operating modes to consider as we shall see in future blogs.

**References**

- “Topology Investigation for Front End DC/DC Power Conversion for Distributed Power Systems”, Bo Yang Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering Fred C. Lee, Chairman Dushan Boroyevich Jason Lai Guo-Quan. Lu Alex Q. Huang September 12, 2003 Blacksburg, Virginia

- “Basic Principles of LLC Resonant Half Bridge Converter and DC/Dynamic Circuit Simulation Examples”, On Semiconductor LLC Application Note AND9408/D

- “RLC Resonant Circuits”, Andrew McHutchon April 20, 2013

- “Resonant LLC Converter: Operation and Design 250W 33Vin 400V out DesignExample“, AN2012-09, Sam Abdel-Rahman, Infineon Technologies North America (IFNA) Corp.

- “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]

- “SIMULATION OF A SERIES HALF BRIDGE LLC RESONANT CIRCUIT”, ECE562: Power Electronics I COLORADO STATE UNIVERSITY Fall 2011

- “230-V, 400-W, 92% Efficiency Battery Charger w/PFC and LLC for 36-V Power Tools” Texas Instruments Reference Design, TIDA-00355

- Can you turn a square wave into a sine wave using a low-pass filter?, Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing

- “Square Wave Signals”, Chapter 7 – Mixed-Frequency AC Signals, All About Circuits website

- “Chapter 14 Transformers” C. Y. Lee, ISU EE

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