LLC Power Conversion Explained, Part 3: Understanding transformers

In LLC Power Conversion Explained, Part 2: Sine Wave from a Square Wave, a basic square wave Switched Mode Power Supply was shown to be filtered from a square wave into a sine wave. This resulted in a filtered version of the square wave as shown below.

The actual filtering of the harmonics is due to the LLC circuit where Vo is a filtered version of square wave Vin as shown in the simplified circuit on the right of the following figure.

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

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

Where X2 = XLm||Rac and

X1 = XCr + XLr when combining the components in the last figure into the impedances of the next figure.

When reading the variety of application notes, one can easily get confused as there are several references to impedances (X1 and X2), resonant components (Lr, Cr, Lm), load resistance (Ro), and reflected resistances (Rac). The following figure shows these components as they exist in a half bridge, transformer isolated converter. Understanding these components is crucial to understanding the operation of the LLC converter.

In this figure, the following resonant tank converter components are explained.

  • Lr = the resonant inductor of the tank circuit and is the combination of the transformer primary leakage inductance, Llkp and the transformer secondary leakage inductance Llks (Fairchild, reference 6 is the only application note that includes the secondary leakage inductance)
  • Lm is the magnetizing inductance of the transformer
  • Cr is the resonant capacitor
  • Ro is the DC load resistance (the output voltage Vo divided by the output current Io)

Understanding the LLC circuit requires understanding a transformer where

  • The magnetizing inductance of the transformer is related to the magnetizing flux of a transformer. The magnetizing inductance is often a high value.
  • The leakage inductance of a transformer is related to the leakage flux of a transformer. The leakage inductance is often several magnitudes lower than the magnetizing inductance.

Whereas power inductors are meant to store energy in an air gap, transformers are meant to transfer energy via a flux linkage to a secondary. The efficiency of a transformer is based on its ability to transfer energy thus requiring as much magnetizing flux as possible. This flux is “steered” by the transformer core from the primary to the secondary. Because a transformer winding has some air gap between it and the core, leakage flux is also created. This flux stores energy in a manner similar to a power inductor.

Storing energy in a transformer is an undesired occurrence that reduces the amount of energy that is transferred. In non-resonant topology with abrupt switching waveforms, this energy will create voltage spikes when current levels change rapidly. As mentioned in LLC Power Conversion Explained, Part 1: Introduction of this series, using the leakage inductance as a resonant tank component allows a transfer of the leakage inductance energy therefore turning a parasitic element into a beneficial circuit component.

The next part of the transformer that needs to be understood is the turns ratio and how to use it to simplify the LLC circuit. It takes a bit of searching to get a basic explanation of how an output load can be reflected to the primary side of a transformer. Fortunately, Reference 11 provided a slide with the information.

We have now established that reflecting the load into the primary from the secondary is a function of the turns ratio squared. In order to compute Rac, some AC massaging of the rectified sine wave requires a factor of 8/ π 2 .

Note that Ro and RLOAD are the same parameter of the DC load voltage divided by the DC load current.

The major components of the LLC converter have been identified. The actual circuit components of the half bridge transformer based design have been linked to their roles in the resonant tank circuit. The resonant tank circuit has been shown to perform two tasks in the LLC topology; first it filters the square wave into a sine wave. Second, the resonant tank stores energy in the circuit components. This basic understanding is crucial to the creation of the sine wave on the secondary of the LLC circuit.

Again, the sine wave is rectified and stored in a capacitor rather than the traditional power transfer method of a Switched Mode Power Supply. Energy transfer in the LLC circuit has many different and complicated operating modes that are based on the resonant frequencies of the components as well as the load resistance of the converter. Therefore, developing the gain equation is not a trivial calculation as we shall see in the next few blogs that are parts of “LLC Power Conversion Explained”.


  • “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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