Dealing with gain distortion in an LLC resonant converter under light load conditions

The LLC (inductor-inductor-capacitance) resonant converter – which is finding applications in home appliances, street lamps, chargers and other electric devices – regulates the output voltage by adjusting the operating frequency. Generally, the voltage conversion ratio decreases as the operating frequency increases. However, gain can increase under light loads, even though operating frequency increases. This gain distortion is mainly caused by parasitic components, such as resonant inductances and stray capacitances distributed to the high frequency transformer. In order to avoid undesirable increases in output voltage under light loads, the parasitic components have to be taken into account in the design phase. 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 a 50% duty ratio to two mosfets alternatively and changes the operating frequency with load to regulate the output voltage, V_out. The resonant network is comprised of two resonant inductors and one resonant capacitor. The resonant inductances, L_r and L_m, and capacitor, C_r, act as a voltage divider whose impedance is varied by the operating frequency. For a practical design, the resonant network can be made of a magnetising inductance, L_m, and leakage inductance, L_lk, of a high frequency transformer with a general bobbin or a sectional one. Finally, the rectifier network delivers sinusoidal waveforms to the output stage. Even though the input voltage, Vd, is a square waveform controlled by two mosfets, it could also be considered as a sinusoidal waveform by fundamental approximation. It can be shown there are two resonant frequencies: ω_p, which is determined by (L_r and L_m) and C_r; and ω_r, which is determined by L_r and C_r. Knowing these values, it is possible to plot the converter's voltage conversion ratio – or gain curve – which shows the variation of operating frequency and load (see fig 2). In Figure 2, the highest value for each curve is known as peak gain and falls between the two resonant frequencies, ω_p and ω_r. As output load increases, the value of the peak gain decreases and the position of peak gain moves to a higher frequency. Meanwhile, it can be seen that the resonant gain, ω_r, is fixed, even though the output load varies. The gain curve shows that gain and output voltage decrease when the operating frequency applied to the resonant network increases in the ZVS region. Figure 3 shows a practical LLC resonant converter circuit with stray capacitance. This stray capacitance is usually dependent 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, gain distortion could become more apparent as the load resistance, R_ac, increases, eventually making the converter operate undesirably.# Three resonant frequencies can be observed: two of these are same as one of the ideal voltage conversion ratios; ω_p and ω_r are determined by {(L_m + L_r) and C_r} and {L_r and C_r} respectively. The other one is ω^s, formed by the resonant inductance and stray capacitance (L_r + C_s). A voltage conversion ratio can be plotted and this will show that, while operating frequency increases, the voltage gain decreases, the increases slowly once the operating frequency passes the resonant frequency formed by L^r and C^r. The rate of gain increases as the output load reduces and if this isn't taken into account, the designed converter will not control the output voltage. Stray capacitance causing gain distortion is usually dependent upon the stray capacitance distributed to the high frequency transformer, especially the primary side winding, so it is impossible to avoid the gain distortion unless this stray capacitance 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 include increasing the distance between the layers of the primary side winding, adding more insulation between the layers and reducing the number of winding layers. Unfortunately, these steps will not remove the parasitic capacitance completely, so an easy way is needed to avoid stray capacitance, rather than remove it. Ways to avoid gain distortion • Burst mode operation The burst mode function is a well known way to regulate the output voltage in a conventional pwm controlled converter. This function is used not only to increase efficiency under light load conditions, but to also avoid not controlling an output voltage. It can be also implemented in an LLC resonant converter. Fig 4 shows a typical LLC resonant converter using FSFR series device designed especially for the application by Fairchild. Maximum and minimum operating frequencies can be set using resistors R_max and R_min. When the operating frequency increases to the maximum set by R_max and a voltage on the 'CON' pin decreases to the burst on threshold level, the controller enters burst mode operation. Therefore, the maximum frequency is set so that it is less than that at which gain increases due to parasitic capacitance and leakage inductance. If the load becomes light and the operating frequency increases to the maximum, the controller can regulate the output voltage under burst mode operation without gain distortion. •Increasing the M factor The resonant inductance, L_r, for an M factor of 4 is relatively higher than one for and M of 10. The resonant frequency ω^s, which generates gain distortion, is formed by L_r and C_s. If either L_r or C_s decreases, it can push ω_s to a higher frequency and prevent the converter's output voltage increasing under no load conditions. •Adding a dummy resistor Adding a dummy resistor is the simplest way to remove the gain distortion. Because gain distortion occurs under light or no load conditions, a dummy resistor imposes maximum operating frequency for the LLC resonant converter which is less than the frequency where gain distortion begins. However, because of the dummy resistor's power dissipation, this approach cannot be used in applications where stand by power is prioritised. An example application is in lcd tv power supplies, which comprise an auxiliary power supply and an LLC resonant converter. Many engineers can be confused when confronted with a power supply that is not regulating an output voltage when under no load conditions. The solutions proposed above prevent gain distortion and allow the output voltage to be controlled, even when there is no load. The full article can be downloaded in Word format below. Jin-tae Kim is a senior engineer with Fairchild Korea.