# LLC resonant topology lowers switching losses, boosts efficiency

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With the current global energy crisis, the focus is on efficiency and electronic products are facing the daunting challenge of delivering high performance, while consuming less power. As a result of this crisis, various governmental agencies around the world have or are looking to increase their efficiency standards for numerous products in their respective specifications. It will be difficult to meet these efficiency specifications with conventional hard switched converters. Power supply designers will need to consider soft switching topologies to improve the efficiency as well as to allow for higher frequency operation.

One such topology is the LLC resonant converter. The LLC resonant topology allows for zero voltage switching of the main switches thereby dramatically lowering switching losses and boosting efficiency. Efficiencies of 93 to 96% can be achieved with LLC resonant converters. This paper will describe the operation of the LLC resonant topology and illustrate how such high efficiencies can be attained.

Resonant converters have been around for a long time. However, only now are they seeing increased acceptance as controllers become more available and there is an absolute need to improve efficiency. Perhaps the best way to understand the LLC resonant converter is to first study the conventional series resonant converter as shown in Figure 1.

**Figure 1: Series resonant converter (1)**

In Figure 1, the series resonant converter is shown in a half bridge configuration. In an offline application, Vin is typically the output of an upstream power factor correction (PFC) circuit of approximately 400 V. The resonant network is made up of Lr and Cr. The primary inductance of the transformer is considered to be so large as to not affect the resonant network. It is referred to as a series resonant converter because the load resistance, as well as the impact of the rectifier and filter circuitry, can be reflected back into the primary circuit through the turns ratio of the transformer. This action effectively puts the load in series with the resonant network. The resonant network and reflected load resistance form a voltage divider. Recall that in a general series resonant circuit, the impedance of the resonant network is at a minimum at the resonant frequency. This is shown in Figure 2.

**Figure 2: Series RLC impedance characteristic**

Since the converter is controlled through frequency modulation, the impedance of the resonant network will be changed by changing the switching frequency in response to load changes. Consequently the output voltage can be regulated by changing impedance of the resonant tank circuit. For example, if the load current increases the output voltage will have a tendency to decrease. The feedback circuit will sense this decrease and move the switching frequency of the converter toward resonance such that more voltage applied to the resonant network will be dropped across the load thereby increasing the output voltage.

Conversely, if the load current decreases, the feedback circuit will move the frequency away from resonance such that more voltage is dropped across the tank circuit. The fact that the converter works as a voltage divider means that the maximum gain that can be achieved in the power train of the converter is one. The advantage of the series resonant converter is that it can zero voltage the main switches, Q1 and Q2, in Figure 1. This improves the efficiency of the converter particularly as higher switching frequencies are used.

Additionally, when operated near the resonant frequency the power will be processed through the power train in a sinusoidal manner (9). The gain characteristic of the series resonant converter is shown in Figure 3. Notice that the series resonant converter, as well as the LLC, will be operated above resonance. Above resonance the primary current lags the applied voltage and allows Q1 and Q2 to be zero voltage switched.

**Figure 3: The dc gain characteristic of the series resonant converter (2)**

One of the drawbacks to a series resonant converter is illustrated in Figure 3. As the load decreases, the Q decreases and the result is that the frequency needs to increase significantly to keep the output regulated. The large frequency change to maintain output regulation becomes a serious drawback of the series resonant converter. In fact, in the limit of a no load condition, it would take an infinite frequency to keep the output voltage in regulation.

Although the series resonant converter offers the advantage of increased efficiency through zero voltage switching, the large frequency change to maintain regulation and the inability to regulate under a no load condition highlight the need for something better. The LLC resonant converter overcomes the disadvantages of the series resonant converter.

**Figure 4: LLC resonant converter (3)**

As can be seen in Figure 4, the LLC resonant converter schematically looks very similar to the series resonant converter. The main difference is that in the series resonant converter the primary inductance of the transformer was so great as to not factor in the characteristics of the resonant network. However, in the LLC converter the primary inductance of the transformer is reduced in value such that it now impacts the resonant network. In fact, an LLC resonant converter has two resonant frequencies as can be seen in Figure 5.

**Figure 5: Gain characteristics of the LLC resonant converter (4)**

Right away the advantages of the LLC converter become evident. As can be seen in Figure 5, when the converter is operated at the upper resonant frequency, fo, as is usually the case, all the load (Q) curves converge. What this means is that for an extremely wide load range, there is very little frequency change. In fact, the LLC converter can keep the output voltage regulated even under a no load condition. Additionally, notice that at fo the power train of the LLC converter exhibits a gain greater than one. In other words, the LLC resonant converter overcomes the disadvantages that are characteristic of the series resonant converter.

As mentioned above, the lower valued primary inductance of the LLC resonant converter impacts the resonant network. The resonant inductor can be comprised of the leakage inductance of the transformer. In many cases this eliminates another magnetic component thereby saving cost and printed-circuit-board space. The schematic of the LLC shown in Figure 4 can be simplified as shown in Figure 6.

**Figure 6: Simplification of the LLC converter power train (5)**

Although a square wave voltage is applied to the resonant network, the filtering action of the resonant network forces the current through the network to be sinusoidal. This means that the power is processed sinusoidally. This allows for the mathematical analysis to be greatly simplified since only the fundamental frequency needs to be considered. In Figure 6, the leakage inductance of the primary as well as the secondary side is taken into account when analyzing the circuit. If it is assumed that the primary side leakage inductance equals the reflected secondary side leakage inductance the circuit can be simplified further as shown in Figure 7 (10).

**Figure 7: Equivalent LLC circuit with Llkp = n2Llks (6)**

As shown in Figure 5, the gain at the resonant frequency simplifies to:

Since in a LLC resonant converter Lp will still be larger than Lr, by typically 3-8 times, the power train will experience gain at the resonant frequency.

The resonant frequencies can be expressed mathematically as:

and:

Lm represents the magnetizing inductance and Lp is the primary inductance which includes the primary side leakage inductance. In a practical transformer measuring the primary inductance with the secondary open will give the Lp value. When the secondary is shorted, measuring the primary inductance will yield the Lr value. In a typical LLC converter the Lr value will calculate to be relatively large. In order to eliminate an extra magnetic component the leakage inductance will need to be incorporated inside the main transformer to achieve the desired Lr value. One way to build in the proper amount of leakage inductance is to wind the primary and secondary windings side by side on the bobbin as shown in Figure 8. Of course the bobbin must incorporate the proper spacing to meet the relevant safety specifications.

**Figure 8: Side by side wound LLC transformer (7)**

As mentioned before, a critical advantage of resonant converters including the LLC, is the soft switching of the FETs and the sinusoidal power processing. Figure 9 illustrates typical waveforms characteristic of an LLC converter.

**Figure 9: Typical waveforms of an LLC converter (8)**

Notice in Figure 9 that the FET drain current, Ids2, swings negative before becoming positive. The negative current is indicative of the body diode conducting. When the body diode of the FET is conducting there is very little voltage (a diode drop) across the drain-source of the FET. The FET is activated during body diode conduction leading to zero voltage switching and greatly reduced switching losses. Converter efficiencies in the mid-90s can be attained. Also notice the sinusoidal primary current. The sinusoidal waveform will lead to a reduced EMI signature.

As efficiency of electronic products becomes ever more important, alternative power supply topologies need to be considered. With greatly improved efficiency through zero voltage switching and reduced EMI with sinusoidal current waveforms, the LLC resonant converter can be an excellent topology choice for many applications.

References:

1-8: Choi, HS; Fairchild Semiconductor Power Seminar 2007 PowerPoint slides

9: Robert L. Steigerwald "A Comparison of Half Bridge Resonant Topologies," IEEE Transactions on Power Electronics, Vol. 3, No. 2, April 1988

10: Choi, HS; Fairchild Semiconductor, AN-4151, Half Bridge LLC Resonant Converter Design Using FSFR-series Fairchild Power Switch