8.1.1 Principal of Operation

The soft-switching capability, high efficiency, and long holdup time make the LLC resonant converter attractive for many applications, such as digital TV, ac-to-dc adapters, and computer power supplies. Figure 14 shows the schematic of the LLC resonant converter.

Figure 14. LLC Resonant Converter

The LLC resonant converter is based on the series resonant converter (SRC). By using the transformer magnetizing inductor, zero-voltage switching can be achieved over a wide range of input voltage and load. As a result of multiple resonances, zero-voltage switching can be maintained even when the switching frequency is higher or lower than resonant frequency. This simplifies the converter design to avoid the zero-current switching region which can lead to system damage. The converter achieves the best efficiency when operated close to its resonant frequency at a nominal input voltage. As the switching frequency is lowered, the voltage gain is significantly increased. This allows the converter to maintain regulation when the input voltage falls low. These features make the converter ideally suited to operate from the output of a high-voltage, boost PFC pre-regulator, allowing it to hold up through brief periods of ac line-voltage dropout.

Due to the nature of resonant converter, all the voltages and currents on the resonant components are approximately sinusoidal. The gain characteristic of the LLC resonant converter is analyzed based on the first harmonic approximation (FHA), which means all the voltages and currents are treated as a sinusoidal shape with the frequency the same as the switching frequency.

According to the operation principle of the converter, the LLC resonant converter can be drawn as the equivalent circuit shown in Figure 15.

Figure 15. LLC Resonant Converter Equivalent Circuit

In this equivalent circuit, the V_ge and V_oe are the fundamental harmonics of the voltage generated by the half-bridge and the voltage on the transformer primary side, respectively. These voltages can be calculated through Fourier analysis. The load resistor R_e is the equivalent resistor of the load, and it can be calculated as:

Equation 9.

Based on this equivalent circuit, the converter gain at different switching frequencies can be calculated as:

Equation 10.

In this equation V_DC/2 is the equivalent input voltage due to the half-bridge structure.

Table 3. Circuit Definition Calculations

NORMALIZED GAIN	RESONANT FREQUENCY	QUALITY FACTOR	NORMALIZED FREQUENCY	INDUCTOR RATIO
Equation 11.	Equation 12.	Equation 13.	Equation 14.	Equation 15.

Following the definitions in Table 3, the converter gain at different switching frequencies can be written as:

Equation 16.

Because of the FHA, this gain equation is an approximation. When the switching frequency moves away from the resonant frequency, the error becomes larger. However, this equation can be used as a design tool. The final results need to be verified by the time-based simulation or hardware test.

From Equation 16, when the switching frequency is equal to the resonant frequency, f_n = 1 and converter voltage gain is equal to 1. Converter gain at different loads and inductor ratio conditions are shown in Figure 16 through Figure 19.

Figure 16. M vs f_N

Figure 18. M vs f_N

Figure 17. M vs f_N

Figure 19. M vs f_N

Based on its theory of operation, the LLC resonant converter is controlled through pulse frequency modulation (PFM). The output voltage is regulated by adjusting the switching frequency according to the input and output conditions. Optimal efficiency is achieved at the nominal input voltage by setting the switching frequency close to the resonant frequency. When the input voltage drops low, the switching frequency is decreased to boost the gain and maintain regulation.

The UCC25600 resonant half-bridge controller uses variable switching frequency control to adjust the resonant tank impedance and regulate output voltage. This 8-pin package device integrates the critical functions for optimizing the system performance while greatly simplifying the design and layout.

8.1.2 Adjustable Dead Time

Resonant half-bridge converter relies on the resonant tank current at MOSFETs turn-off to achieve soft switching and reduce switching loss. Higher turn-off current provides more energy to discharge the junction capacitor, while it generates more turn-off loss. Smaller turn-off current reduces turn-off loss, but it requires longer time to discharge MOSFETs junction capacitors and achieve soft switching. By choosing an appropriate dead time, turn-off current is minimized while still maintaining zero-voltage switching, and best system performance is realized.

In UCC25600, dead time can be adjusted through a single resistor from the DT pin to ground. With internal 2.25-V voltage reference, the current flow through the resistor sets the dead time.

Equation 17.

To prevent shoot through when the DT pin accidentally connects to ground, a minimum 120-ns dead time is inserted into the 2 gate driver outputs. Any dead-time setting less than 120 ns will be limited to 120 ns.

8.1.3 Oscillator

With variable switching frequency control, UCC25600 relies on the internal oscillator to vary the switching frequency. The oscillator is controlled by the current flowing out of the RT pin. Except during soft start, the relationship between the gate signal frequency and the current flowing out of the RT pin can be represented as:

Equation 18.

Because the switching frequency is proportional to the current, by limiting the maximum and minimum current flowing out of the RT pin, the minimum and maximum switching frequency of the converter could be easily limited. As shown in Figure 20, putting a resistor from the RT pin to ground limits the minimum current and putting a resistor in series with the opto-coupler limits the maximum current.

Figure 20. Maximum and Minimum Frequency Setting for UCC25600

The frequency limiting resistor can be calculated based on following equations.

Equation 19.

Equation 20.

Equation 21.

Equation 22.

8.2.1 Design Requirements

8.2.2 Detailed Design Procedure

1. Resonant inductor(Lr), resonant capacitor(Cr), and (Lm) of half-bridge LLC
   1. Turns ratio of Main transformer:
   Equation 23. n = Np/Ns = 16.5
   2. Maximum resonant gain required:
   Equation 24. M_max = 110% × n × (2 × Vout)/(Vin_min) = 110% × 16.5 × (2 × 12 V)/375 V = 1.17
   3. Choose Ln and Q. The Ln range is typically selected from 3 to 9. Choose Q based on the curves below, where the peak gain must be higher than or equal to the maximum resonant gain required. Based on the below curves, Q selects 0.45.
   Equation 25. Ln = Lm/Lr = 5
   Equation 26.
   Figure 22. Peak Gain vs Q
   4. Calculate equivalent primary resistance:
   Equation 27. Req = (8 × n² × Vout²)/(π² × Pout) = (8 × 4.6² × 12²)/(π² × 300) = 108.6Ω
   5. Select Cr:
   Equation 28. Cr = 24nF
   6. Calculate Lr:
   Equation 29.
   7. Combine the above two equations:
   Equation 30. Lr = 55µH
   8. Calculate Lm:
   Equation 31. Lm = Ln × Lr = 275 µH
2. Calculate Rdt. In the UCC25600, dead time can be adjusted through a single resistor from DT pin to ground. With an internal 2.25-V voltage reference, the current flow through the resistor sets the dead time.
Equation 32. td = 20ns + Rdt × 24ns/kΩ
where
• td = 300 ns
• Rdt = 11.7 kΩ
3. Calculate C_SS. Refer to Soft Start for more details.
Equation 33. tss = 25 ms
Equation 34. tss = 2.8 V/5 µA × Css
Equation 35. Css = 44.6 nF
4. A 47nF capacitor is selected. Calculate RT1 and RT2. Refer to Oscillator for more details. RT1 and RT2 are used to limit maximum switching frequency and minimum switching frequency. RT1 and RT2 can be calculated based on following equations:
Equation 36. Ifmax = 6 ns/(1/2fmax - 150 ns)
Equation 37. Ifmin = 6 ns/(1/2fmin - 150 ns)
Equation 38. Ifmax = 2.5 V(1/RT1 + 1/RT2)
Equation 39. Ifmin = 2.5 V/RT2
5. Combine the four equations above:
Equation 40. RT1 = 511Ω
Equation 41. RT2 = 2.37 kΩ
6. Calculate Rs, Cs, Rp, and Cp. Refer to Overcurrent Protection for more details.
Equation 42. Rs = 300 kΩ
Equation 43. Cs = 22 pF
Equation 44. Rp = 4.99 kΩ
Equation 45. Cp = 1 µF

8.2.3 Application Curves

Figure 23. Typical Output Voltage Turn On (TP15)

Figure 25. Typical Soft-Start Waveform

Figure 24. Full System Loop Compensation (TP19 and TP21)

Figure 26. Typical Resonant Tank Current and Resonant Capacitor Voltage