This power tip focuses on key parameters that affect switching component selection, as well as the effect of transformer intrawinding capacitance in a high-frequency resonant converter.

High-frequency resonant converter design considerations include component selections, design with parasitic parameters, synchronous rectifier design, and voltage gain design. This power tip focuses on key parameters that affect switching component selection, as well as the effect of transformer intrawinding capacitance in a high-frequency resonant converter.

The commercialization of wide bandgap (WBG) devices over the past decade has enabled the operation of power converters at much higher frequencies for higher power density. High-performance power supplies are just starting to include WBG devices – especially silicon carbide and gallium nitride field-effect transistors (FETs) – because of their output capacitance (C_{oss}), gate charge (Q_{g}), on-resistance (R_{DS(on)}), and reverse-recovery charges (Q_{rr}), all lower (or nonexistent) than silicon or silicon super-junction FETs at the same breakdown voltage level. A lower Q_{g} reduces the driving power needed – P_{drive }= V_{drive}Q_{g}F_{sw} – and a lower R_{DS(on)} reduces the conduction loss, where V_{drive} is the driving voltage and F_{sw} is the FET switching frequency. Other than Q_{g} and R_{DS(on)}, it’s also important to consider C_{oss} and Q_{rr} when selecting components in high-frequency converters.

In a resonant converter like the inductor-inductor-capacitor-series resonant converter (LLC-SRC) shown in **Figure 1**, the current in the resonant tank charges/discharges the C_{oss} of the FETs (state 1 in Figure 2) in order to achieve zero voltage switching (ZVS). ZVS means that the FET drain-to-source voltage (V_{DS}) reaches zero before its gate voltage goes high. Therefore, a lower C_{oss} enables a shorter dead time under the same resonant tank current level to achieve ZVS. A shorter dead time means a larger duty cycle and a lower root-mean-square (RMS) current on the primary-side resonant tank and FETs, which means higher efficiency and the ability to operate the converter at a higher switching frequency.

**Figure 1 **LLC-SRC

To achieve ZVS, there is always a period during which the body diode of the FET conducts current – state 2 in **Figure 2**. If the FET has Q_{rr} and is turned on again when the body diode still conducts current, the FET itself will create a reverse current to discharge Q_{rr} and cause hard switching and high voltage stress – potentially damaging the FET.

**Figure 2 **Switching transitions of an LLC-SRC

**Figure 3** illustrates this hard switching phenomenon during the startup process of an LLC-SRC as illustrated in Figure 1. When FET Q_{2} first conducts current, inductor current I_{PRI} is built up. The current I_{PRI} then conducts through FET Q_{1} channel and body diode. Without allowing the current to go in the reverse direction, FET Q_{2} turns on again. Because of the Q_{rr}, FET Q_{1} self-generates a reverse current to discharge Q_{rr}, which results in high voltage stress.

**Figure 3 **Hard switching due to Q_{rr}

In a high-frequency resonant converter, the resonant tank impedance is generally much lower than that in a low-frequency resonant converter. Therefore, the startup inrush current in a high-frequency resonant converter is expected to be higher. Using the LLC-SRC in Figure 1 as an example, when the output voltage is zero (the initial condition at startup), the only impedance limiting the startup current when Q_{2} first conducts is L_{r }– the series resonant inductor in the LLC-SRC. High-efficiency and high-frequency resonant converter designs, especially bus converters, generally minimize L_{r} in order to improve efficiency. A smaller L_{r} value makes the startup current higher under the same startup frequency and thus more vulnerable to Q_{rr}-related hard switching. Therefore, it is essential to use low Q_{rr} FETs in high-frequency resonant converters.

Harnessing the aforementioned benefits of WBG devices, it is possible to operate isolated resonant converters in the megahertz range, which is 5 to 10 times faster than traditional isolated power supplies. In this “higher frequency” domain, many parameters once considered “negligible” during the converter design process are no longer negligible, such as the transformer intrawinding capacitor.

In the traditional resonant converter design process, the designer must ensure that the energy stored in the resonant tank is higher than the energy stored in the FET C_{oss} so that C_{oss} depletes the energy stored in the resonant tank to achieve ZVS. Taking the LLC-SRC shown in Figure 1 as an example, Equation 1 ensures the validity of this inequality:

where I_{Lm} is the peak current of the magnetizing inductor L_{m} and V_{in} is the input voltage of the LLC-SRC. Equation 1 can be rewritten as Equation 2 by applying Ohm’s law for the inductor to L_{m}:

where n = N_{p}:N_{s1} (assuming N_{s1} = N_{s2}) is the transformer turns ratio and V_{out} is the output voltage.

When resonant converter designs need to cover a wide operation range and holdup time, L_{m} is generally much smaller than the value on the right side of Equation 2 in order to keep L_{n }= L_{m}/L_{r} low (applying L_{n} values from 4 to 10 in a closed-loop LLC-SRC design). When resonant converter designs such as bus converters require high converter efficiency, maximizing L_{m} lowers the primary RMS current for a lower conduction loss. In this case, the L_{m} value will be closed to the value on the right side of Equation 2. Equation 2 only represents the ideal condition with an ideal transformer, however. In a real transformer, many parameters could affect the C_{oss} charge and discharge capability. The most critical parameter is the intrawinding capacitance.

**Figure 4** shows a simplified circuit model during a switching transient in an LLC-SRC, where current on L_{m} (I_{Lm}) discharges C_{eq} (the C_{oss} of two FETs in series with resonant capacitor C_{r}), assuming C_{r} as a voltage source. Without the transformer intrawinding capacitance (C_{TX}), all of I_{Lm} goes to C_{eq} and Equation 2 is valid. But with the presence of C_{TX}, some of I_{Lm} has to go to C_{TX} to change the transformer winding polarity, which reduces the C_{oss} discharge capability and creates the possibility of losing ZVS. Therefore, it is essential to keep C_{TX} lower by keeping layers of primary winding apart from each layer with distance as well as layers distance of secondary windings.

**Figure 4 **The effect of a transformer intrawinding capacitor

A rule of thumb in determining the L_{m} value is to use just half of the maximum L_{m} value calculated using Equation 2, as it is generally difficult to predict the C_{TX} value before actually building a transformer. C_{TX} generally falls inside the range of 22 pF to 100 pF in a converter with a 400-V input. It is also very useful to model C_{TX} in a circuit simulation once the transformer structure is fixed, in order to ensure a low-enough L_{m} with margin.

In the next installment of this series, I will focus on synchronous rectifier design challenges in high-frequency resonant converter designs.

*Sheng-Yang Yu is an applications engineer at Texas Instruments.*

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- Power Tips #84: Think outside the LLC series resonant converter box
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- Design considerations when selecting half bridge resonant LLC converters and primary side MOSFETs
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