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Consideration of Gain Distortion Under Light Load Conditions In An LLC Resonant Converter Jintae, Kim / Fairchild Korea Semiconductor Abstract In an LLC resonant converter, it is well known that input to output voltage conversion ratio decreases as operating frequency increases under ZVS (Zero Voltage Switching) operating region. However, practical gain of the converter could be increased under light load conditions as the operating frequency increases due to stray capacitance existing parallel with the primary side winding of a high frequency transformer. Power supply designers can be confronted with the phenomenon of output voltage increase under light load condition and especially no load condition even though the operating frequency increase to regulate output voltage. In this paper, root cause the phenomenon will be analyzed and solutions to avoid will be suggested. Introduction Recently, the LLC resonant converter has received a lot of attention as a result of some outstanding advantages, such as achieving high efficiency through Zero Voltage Switching (ZVS) and having a narrow operating frequency variation under overall load conditions - despite the fact that the design of the converter is somewhat complicated. The LLC resonant converter is widely used in home appliances, street lamps chargers, and various other electric devices. It is well known that the LLC resonant converter regulates output voltage with adjusting the operating frequency. Generally, voltage conversion ratio, namely a gain values under ZVS operating region theoretically decreases as the operating frequency increases. However, practical a gain value can be increased at light load conditions unlike the ideal gain curve even though operating frequency increases. This gain distortion is mainly caused by parasitic components, i.e. resonant inductances and stray capacitances distributed to the high frequency transformer. In order to avoid undesirable output voltage increases in the light load condition, the parasitic components have to be taken into account in the design phase. In this paper, the cause of gain curve distortion by the parasitic components will be discussed in detail and solutions will be suggested. Operation Principle of an LLC Resonant Converter Figure 1 shows a basic circuit of an LLC resonant converter. Generally, the LLC resonant converter consists of a controller with MOSFETs, a resonant network and a rectifier network. The controller delivers a gate signal with 50% duty ratio to two MOSFETs alternatively and changes operating frequency of load variations to regulate the output voltage, Vout, which is called PFM (Pulse Frequency Modulation). The resonant network is comprised of two resonant inductors and one resonant capacitor (L-L-C). Basically, the resonant inductances, Lr and Lm and capacitor, Cr act as a voltage divider whose impedance is varied by the operation frequency so that the desirable output voltage can be obtained, as shown in Equation 1. For a practical design, the resonant network can be made of a magnetizing inductance, Lm and leakage inductance, Llk of a high frequency transformer with general bobbin or a sectional one as shown in Figure 2. Finally, the rectifier network rectifies sinusoidal waveforms from the resonant network and delivers to the output stage. n Vout Rac || Lm 1 Cr Lr Rac || Lm Vd … Equation 1 where Vd is input voltage and Rac is load resistance. Even though the input voltage, Vd is a square waveform controlled by two MOSFETs, it could also be considered as a sinusoidal waveform by the fundamental approximation. With this approximation, the voltage conversion ratio can be expressed as shown in Equation 2. 2 M 2n Vo Vin m 1 r 2 … Equation 2 2 2 2 2 1 1 (m 1) Q p r r 2 Where, Lp m , Lr r 1 , p Lr Cr 1 1 , and Q Rac L p Cr Lr and Rac and Vd can be expressed Cr V 8 n 2 Vout and in respectively. 2 2 I out As can be seen in Equation 2, there are two resonant frequencies. One is ωp which is determined by (Lm + Lr) and Cr and the other is ωr which is determined by Lr and Cr. By using this equation, a voltage conversion ratio of the converter, namely gain curve, can be plotted with according to the variation of operating frequency & load as shown in Figure 3. In Figure 3, the highest value indicated with ‘+’ for each curve is called ‘peak gain’ and is placed between two resonant frequencies, ωp and ωr. As output load increases more and more, a value of the peak gain lessens and the position of peak gain moves to a higher frequency. Meanwhile, it can be seen that the resonant gain indicated with ‘×’ at ωr is fixed even though the output load varies. The gain curve demonstrates that the gain decreases and output voltage reduces when the operating frequency applied to the resonant network increases in the ZVS region. Practical Voltage Conversion Ratio of an LLC resonant Converter Figure 4 shows a practical circuit of an LLC resonant converter with stray capacitance. The stray capacitance is usually dependant upon the transformer winding structures and the output capacitance of rectifiers on the secondary side. Generally these parameters will not affect a gain curve under some load on the output, however influence for a gain distortion could become more as the load resistance, Rac increases, which finally makes the converter operate undesirably. Considering the stray capacitance, especially one distributed to the primary side winding of a high frequency transformer, a voltage divide equation of L-L-C impedance can be expressed by the following: Cr || Rac || Lm 1 n Vout 1 Cr Lr Cr || Rac || Lm 1 Vd …Equation 3 And the voltage conversion ratio of the converter can be also calculated with the fundamental approximation: 2 M m 1 r 2n V o Vin 2 2 2 2 m 1 1 (m 1) Q 1 r r s r p 2 … Equation 4 where, m Lp Lr , r 1 , p Lr Cr 1 , s L p Cr 1 1 , and Q Rac Lr Cs Lr and Rac and Vd can be Cr V 8 n 2 Vout expressed and in respectively. 2 2 I out In Equation 4, three resonant frequencies can be observed. Two resonant frequencies are same as one of the ideal voltage conversion ratios; ωp and ωr are determined by {(Lm + Lr) & Cr} and {Lr & Cr} respectively. The rest is ωs, and this is formed by the resonant inductance and stray capacitance (Lr + Cs). A voltage conversion ratio of the equation can be plotted according to load conditions of 20%, 10% and no-load as shown in Figure 5. In figure 5, it can be observed that while operating frequency increases, the voltage gain decreases, but increases slowly after the operating frequency passes the resonant frequency formed by Lr and Cr. The rate of gain increases more and more as the load of the output reduces. If this practical fact isn’t taken into account, the designed converter will not control the output voltage. Overcoming the Gain Distortion in an LLC resonant converter Stray capacitance causing gain distortion is usually dependant upon the stray capacitance that is distributed to the high frequency transformer, especially primary side winding so that it is impossible to avoid the gain distortion unless it is removed. Stray capacitance in high frequency transformers usually increases as the distance between each winding layer decreases, and / or the number of winding layers increases. Simple ways to reduce stray capacitance are to lengthen the distance between the layers of the primary side winding, add more insulation tape between each layer, and reduce the number of winding layers. Unfortunately, these ways cannot remove the parasitic capacitance completely; therefore, it needs an easy way to avoid it rather than to remove it. Some ways to avoid gain distortion include: a) Burst Mode Operation The burst mode function is one of the well-known ways to regulate the output voltage in a conventional converter controlled by PWM (Pulse Width Modulation) when a controller is under a range not to regulate an output voltage at no load condition due to a saturation voltage of transistor built in photo-coupler. This function is traditionally used not only to increase efficiency under light load conditions but to also avoid the case of not controlling an output voltage. It can be also implemented in an LLC resonant converter. Figure 6 shows a typical LLC resonant converter using FSFR-series designed especially for a resonant converter by Fairchild Semiconductor and its burst mode operating waveforms. A maximum & minimum operating frequency can be easily set by the resistors, Rmax & Rmin. When the operating frequency increases up to maximum frequency set by Rmax and a voltage on ‘CON’ pin decreases to the burst-on-threshold level, the controller goes into the burst mode operation. Therefore, a maximum frequency is set at front of a frequency of starting to increase gain by the parasitic capacitance and leakage inductance and then if the load condition becomes light and the operating frequency increases to the maximum frequency, the controller can regulate the output voltage under the burst mode operation without any gain distortion. b) Increasing M Factor Table 1 shows an example of designed L-L-C parameters for 4 and 10 of m factor, with the same input & output voltage and current electrical specifications. As shown in the Table 1, the resonant inductance, Lr of m for 4 is relatively higher than one of m for 10. As mentioned above, the resonant frequency, ωs which generates the gain distortion is formed by Lr and Cs. If either Lr or Cs decreases, it can push up ωs to higer frequency. Hence, it could prevent the increase of the output voltage of the LLC converter under no load condition. Table 1. An example of designed key LLC parameters with m factor of 10 & 4 4 m factor 10 Required Maximum Gain 1.33 Turn-ratio (n1) 8.0 AC Resistor (Rac) 169 [ohm] Q factor 0.28 0.6 Resonant Frequency 100 [kHz] Resonant capacitor, Cr 33.6 [nF] 16.2 [nF] Resonant Inductance, Lr 75.36 [uH] 156.1[uF] c) Adding Dummy Resistor Adding a dummy resistor is the best simple way to remove the gain distortion. As mentioned above, the gain distortion occurs with light or no load condition. By adding a dummy resistor, a required maximum operating frequency of the LLC resonant converter is put at the front of a frequency of the beginning of gain distortion. However, this way cannot be applied to applications in which stand-by power is prioritized due to power dissipation by the dummy resistor. It is usually used at power supplied for the LCD TV which is composed with an auxiliary power supply and LLC resonant converter. An LLC resonant converter attracts a lot attention due to its many outstanding advantages, including optimal design procedure. However, the gain distortion generated by parasitic capacitance and leakage inductance are barely known. Many engineers - when confronted with the case of not regulating an output voltage, which is increased under no load condition - are embarrassed. The proposed solutions in this paper prevents gain distortion and allows the controlling of an output voltage in spite of no load condition. Q1 Rectifier network Resonant network n:1 Controller Vin Iout Vd + Lr Q2 Rout Lm Vout - Controller & MOSFETs Cr Transformer Lr Lm Rac Cr Figure 1. A basic circuit of an LLC resonant converter Inductor Transformer n:1 Lr Integrated Transformer n:1 Llk,se Llk,pri c Lm Lm Cr Cr (a) (b) gain Figure 2. A high frequency inductor & transformer with general bobbin (a) and an integrated transformer with a sectional bobbin (b) ZVS region Below region Above region Load increase peak gain ZCS region ωp ωr frequency Figure 3. Voltage conversion ratio of an LLC resonant converter according to the operating frequency & load variation Controller Q1 Vin n:1 Iout Vd Cstray Lr + Q2 Cstray Rout Lm Vout - Cstray Cr Transformer Lr Lm Cstray Rac Cr gain Figure 4. A practical LLC resonant converter with stray capacitance No load @ Ideal 20% Load @ Practical 10% Load @ Practical No load @ Practical rease to inc s t r a st Gain ωp ωr ωs frequency Figure 5. Ideal & practical voltage conversion ratio of an LLC resonant converter according to the operating frequency & load variation Cr VIN iCr Vcc LVCC vCON vCTR VDL vCON RT Rmax Rmin CON FSFR-series HVCC iCr CTR vCTR CS SG PG Figure 6. Typical LLC resonant converter using FSFR-series and its burst mode operating waveforms