LLC Power Conversion Explained, Part 1: Introduction

Recently I had the privilege of dissecting the Half Bridge LLC circuit. I thought that this would make for a good series of blogs starting with the basics and working forward. I will say that it took some time and reading several articles, chapters, dissertations, and application notes in order to grasp the true operation of this circuit. It took more time to assemble and address the references for this blog than it did to write the actual blog. Note that no single reference can actually give you the full analysis of this converter as there are many operating modes and situations occurring. Hopefully you can get a general idea of the overall circuit operation with a little help from me filtering out the references and pointing out the key relevance of each (Please ignore the Figure numbers in all the following images—these are being presented in the order that is needed in this tutorial blog series) .

(Image courtesy of Reference 2)

The LLC circuit is in the Switched Mode Power Supply (SMPS) family of power converters. Most of the literature starts by describing the basic LLC operating principles. I’m starting differently by explaining how the LLC differs from other SMPS designs.

  • Typical SMPS operation is to store energy by building up a voltage across an inductor and then dumping the energy as the inductor “flies back” trying to keep its current flowing. You may remember that the basic operation of an inductor states that inductor current cannot change instantaneously nor can capacitor voltage. This is the premise for many SMPS designs with the latter being a switched capacitor design principle.
  • LLC operation is based on creating a sine wave current that is half-wave rectified and stored in a large capacitor. The inductors do not store volt-seconds but instead act as a resonant tank storage component of sorts. The inductors are actually more of a filter helping turni a square wave into a sine wave….while the magnetizing inductor still clamps to a voltage with the traditional triangular rise in current. That’s one of the confusing points that will be explained.

Operating modes are even more complex in the LLC as everything seems to be different

  • Instead of fixing the frequency and varying the pulse width, the frequency is varied and the switches are fixed at a 50% duty cycle.
  • Energy transfer in the LLC is based on the operating point of the magnetizing inductance.
  • The LLC has varying voltage gains based on load current.
  • There are two resonant frequencies in the LLC and they affect each other.
  • Continuous current mode (CCM) for the LLC is based on rectifier current, not inductor current as there is no traditional inductor present.

Much of this may seem a bit foreign especially to those that are new to power electronics. The second part of this blog will explain the references as well as the key points I found to be useful. First however, realize that resonant power conversion needs some introduction.

The SMPS technology presented a revolutionary improvement for DC voltage conversion and power conversion in general. Engineers quickly discovered that a hard switched combination of a switch, rectifier, inductor, and capacitor could overcome large differentials between input and output levels with dramatic increases in efficiency. Furthermore, transformers could solve the problem of isolation, large voltage level differentials, and enable topologies that created negative voltages to produce positive voltages.

All was well in the world of power conversion; however, as with life itself, the solution to one problem eventually created problems in other areas. Switching frequency dictated SMPS size so the desire to shrink electronics forced an increase in frequencies. Furthermore, power levels were increasing. The faster switching frequencies combined with the higher voltage and current peaks of increased power were causing havoc due to the ringing that resulted from the circuit parasitics in these abrupt-edged, squared-wave type of switching methods.

As a result, tuned resonant circuits were being looked at in order to enable Zero Current Switching (ZCS), and Zero Voltage Switching (ZVS), as a means by which to lower the impact from parasitics. The problem with tuned circuits is the resonance is confined to a certain frequency which equated to a portion of the pulse width or turn on/off time of an SMPS. Large input voltage and load current swings would require operation outside the tuned resonant frequency.

Furthermore, the tuned components were parasitics which could vary based on component construction, operating point, and layout. In a way, the LLC allows a bit more freedom in this tuning variance although it does have a limited operating frequency range and loses its switching loss benefits when operated at a frequency other than the f1 tuned frequency. What is the f1 tuned frequency you might ask?

As it turns out, the two “L’s” in LLC result in two resonant frequencies in the operation range. We will get to that in more detail in a later blog. For now, realize that certain operating points of the LLC circuit provide both ZVS and ZCS in the MOSFET switches as well as ZCS in the rectifier diodes. This overcomes the issues associated with rectifier diode reverse recovery.

Now that the basic resonant SMPS operation has been introduced, here’s a rundown of the references and their key points.

The best way to ease into the complex operation of the LLC circuit is to read the ON Semiconductor application note in Reference 2 first. This note starts with the basic voltage divider equation, thus explaining the LLC theory of circuit operation based on the impedances of the two inductors, LL, and the capacitor C in combination with the load resistance. Note that the two inductors are the leakage and magnetizing inductance of the transformer that form a resonant tank circuit with an additional series capacitor component. In the case of the LLC circuit, the MOSFET parasitic output capacitance, or Coss, does not play a role in the resonant tank circuit like it does in typical ZVS and ZCS converters.

(Image courtesy of Reference 2)

Reference 1 is actually a series of references to help you get to the master document which is Bo Yang’s PhD dissertation entitled “Topology Investigation for Front End DC/DC Power Conversion for Distributed Power Systems”. Note that there are sub-references to Chapter 4 the LLC part of the dissertation as well as Appendix B where the elusive voltage gain graph is developed (This link actually has Appendices A through D and References). Although most of the references show this graph, producing it was another story as it took me a lot of work and some searching of my engineering education to duplicate.

Reference 3 and Reference 4 were crucial in assisting my graphing of the converter gain as they called attention to the capacitive operating portion of the gain and why the negative impedance was messing up the graphs. More on that in a later blog.

Infineon Reference #5 has a detailed set of design steps that are most useful. This reference also compares full-bridge and half-bridge switching as well as rectification and the associated tradeoffs. I used to explain full- and half-bridges to my audience as voltage and current related. Bridges mean you stack the MOSFETs for voltage withstanding. Full bridges parallel the MOSFETs for current withstanding. This was usually the SMPS requirement for using the full portion of the transformer volt-seconds while avoiding having to insert a reset network so the transformer wouldn’t saturate. As mentioned before, the LLC differs as it needs a bridge to create a positive and negative square wave that is filtered into an AC sine wave.

Fairchild Reference #6 is the only reference I found that also included the secondary leakage inductance in the gain equation. Note that the secondary leakage inductance as well as load resistance are reflected through the transformer and thus adjusted by the turns ratio. I didn’t include a URL for this because it goes to a direct pdf download rather than a website. Reference 6 has instructions for finding this pdf file. The Infineon/Fairchild white paper also details the transformer design. Because resonance tuning of the LLC relies on both the leakage inductance and magnetizing inductance of the transformer this information is beyond useful.

Once again, our university friends in Colorado come forward with some whiz bang information on power conversion. This time however, it’s not the Erickson crew in the Republic of Boulder. Instead, it’s from ‘up the Front Range a piece’ at Colorado State in Fort Collins. Gotta keep my Rams separate from my Buffalos if I’m to remain in Colorado. The ECE 562 Colorado State electrical engineering course has a lot of MATLAB simulations in it.

The reference design I am evaluating is from Texas Instruments. This note also has a number of key design hints to assist with the development of an actual circuit. By having a power factor correction front end, this design provides a stable input voltage of 400 VDC thus emphasizing more of the load current variations and their effect on the operating point and switching as well as resonant frequencies.

Speaking of simulations, there are a number of references to SPICE models as well as sample waveforms throughout the references. I’m not putting any one reference over another for these aspects of the explanation. I believe that by looking at them all and the key points they represent, one can come away with confidence in the various operating modes of the LLC converter. Again, there’s a lot going on in the LLC that is beyond the typical SMPS.

As a final note, if you think you are going to find commonality among the gain equations of the various articles–you won’t. The use of the common variable M for gain means different things depending on the article/application note/dissertation/course chapter you are reading. In fact, if I get the time, I might just do an Excel matrix comparison of these to see how they differ based on circuit components and presentation of the gain over various operating points.

This was a rather long winded blog and it’s only just begun to explain the LLC circuit. For now, you have some reading to do on this complex circuit with ‘oh so many’ benefits mostly due to the reduction and sometimes elimination of switching losses. You can also leave out that huge, honking inductor as it’s already included in the transformer. It will take several blogs to ‘splain’ all of these advantages, Lucy. Read up and check back in for part 2.


  1. 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
    1. Chapter 4 LLC Resonant Converter
    2. Bo Yang Dissertation Appendices
  2. Basic Principles of LLC Resonant Half Bridge Converter and DC/Dynamic Circuit Simulation Examples”, On Semiconductor LLC Application Note AND9408/D
  3. RLC Resonant Circuits” Andrew McHutchon April 20, 2013
  4. 11 The Series RLC Resonance Circuit
  5. 'Resonant LLC Converter: Operation and Design 250W 33Vin 400V out Design Example'AN2012-09 Sam Abdel-Rahman, Infineon Technologies North America (IFNA) Corp.
  6. “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]
  8. 230-V, 400-W, 92% Efficiency Battery Charger w/PFC and LLC for 36-V Power Tools ” Texas Instruments Reference Design, TIDA-00355

3 comments on “LLC Power Conversion Explained, Part 1: Introduction

  1. thelyonnais
    August 13, 2017

    Great ! thanks a lot for share

  2. D Feucht
    August 15, 2017


    Recommendation of another reference on resonant converters:

    Resonant Power Converters, Second Edition, Marian K. Kazimierczuk, Dariusz Czarkowski, Wiley, 2011; ISBN 978-0-470-90538-8

  3. sby
    August 17, 2017

    Design of Resonant LLC converters by scaled cloning

    posted as a video on YouTube

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