Resonant LLC resonant converters have attracted much attention in recent years due to the soft-switching characteristics over a wide load/line range, high peak efficiency, high power density, and low EMI footprint. As a result, resonant LLC converters are widely considered for dc-dc converters when there is variation in voltage on the input side and output side. However, the optimal design of a resonant LLC converter is a non-trivial task as the converter is highly nonlinear and the design process involves many iterations for wide load/line range design.

The Power Supply Design Suite in PSIM makes this task considerably easier and faster. Pre-built design templates are provided for full-bridge and half-bridge resonant LLC converters. These templates also incorporate two user-friendly design tools below for optimal and robust design.

**Steady State Solver Tool:**The Steady State Solver Tool is based on time-domain analytical closed-form solutions for fast steady-state analysis. This tool provides instant resonant waveform and output calculations of peak and RMS values for device selection and loss calculation.

**Design Curve Tool:**The Design Curve Tool is also based on time-domain analytical closed-form solutions. Using this tool, one can compare the variation of the dc gains, RMS values, peak values, and average values with respect to the relative frequency at different values of inductance ratio (K_ind) and quality factors (Q_rated). For the required dc gains, the tool generates an Excel file automatically which contains calculated values of the frequency ranges, component values of the resonant tank, and RMS/peak/average values of LLC converter components for a combination of different Q_rated and K_ind values.

Since the design tools are instantaneous in generating design curves, output calculations, and output waveforms, it only takes the user a few minutes to obtain an optimized resonant converter design.

This application note describes how to design an optimized resonant LLC power converter for a 20-kW DC-DC converter with the **Full-bridge Resonant LLC** template.

The resonant LLC converter circuit for a 20-kW DC-DC converter has the following specifications:

Vin_rated = 700V; Vin_min = 650V; Vin_max =750V

Vo_rated = 500V; Vo_min = 400V; Vo_max = 550V

Po_rated = 20kW

f_res = 200 kHz

Several major steps are needed in order to design an LLC resonant converter using the Power Supply Design Suite:

- Define input and output requirements as well as the operating conditions in the Input Parameter panel
- Perform parameter optimization and design comparison using the Design Curve Tool
- Analyze and verify zero voltage switching (ZVS) and zero current switching (ZCS) operations, steady-state waveforms, output calculations, boundary conditions, and extreme case conditions of the converter using the Steady State Solver Tool
- Update the parameter file, and run time-domain simulation to validate the design

The following describes the details of each step.

Based on the 20kW DC/DC converter specification above, a resonant full-bridge resonant LLC circuit is selected with a full-bridge secondary diode rectifier.

In PSIM, go to **Design Suites** >> **Power Supply Design Suite**, and select **Full-bridge Resonant LLC**. After files are unpacked, a template circuit will be displayed as shown below.

At the left of the schematic is the Parameter Panel. It allows users to input the design specifications, and launch the Steady State Solver Tool and the Design Curve Tool.

Enter the input and output requirements, and define the initial design values of f_res, Q_rated (0.5 typically), and K_ind (5 typically). For this example, enter the values as below:

**Input Specifications:**

- Vin (operating input voltage) – 700
- Vin_rated (rated input voltage) – 700
- Vin_min (minimum input voltage) – 650
- Vin_max (maximum input voltage) – 750

**Output Requirement:**

- Vo (operating output voltage) – 500
- Vo_rated (rated output voltage) – 500
- Vo_min (minimum output voltage) – 400
- Vo_max (maximum output voltage) – 550
- Po_rated (rated output power) – 20000
- K_load (load factor) – 1

**Operating Conditions:**

- f_res (resonant frequency) – 200k
- Q_rated (rated quality factor) – 0.5
- K_ind (parallel-to-series inductance ratio Lm/Ls) – 5
- K_rel_freq (relative frequency factor) – 0.75

Then Click on **Update Parameter File** in the left panel and review all the parameters in the parameter file, the Steady State Solver tool, and the Design Curve Tool to verify the accuracy of input and output specifications. The parameter file (as shown in figure 1) on the left of the schematic also calculates parameter values of transformer turns ratio, resonant components values, load resistance value, filter capacitance value, etc.

The transformer turns ratio is calculated so that the maximum and minimum dc gain requirement for the resonant LLC tank can be determined.

Select the secondary to primary transformer turns ratio (asp) as shown below:

Note: Calculating asp this way ensures a well-balanced operation of the resonant LLC converter for both below and above resonant frequency regions and for low circulating current. It also makes sure that both buck and boost regions of the resonant tank are covered with unity gain at the resonant frequency.

For practical consideration, asp=2/3 is considered so that secondary to primary side turns ratio can be taken in the proportion of 2:3.

The required minimum and maximum values of dc gain are calculated as shown below:

G_dc_min = Vo_min/(Vi_max*a_sp) = 0.78

G_dc_max =Vo_max/(Vi_min*a_sp) = 1.24

Considering the overloading factor and another practical parasitic, the dc gain range from 0.75 to 1.25 is selected.

The Design Curve Tool provides the function to sweep Q_rated and K_ind to identify the optimum design. For this example, enter the value of Q_rated in the range of 0.3 to 0.8 and the value of K_ind in the range of 3 to 7.

Two sets of design curves and an Excel file with output parameters will be generated automatically using the tool. One has the option to modify input specifications with the range of Q_rated and K_ind in the left interface of the tool. One panel displays curves at different values of K_ind with a fixed Q_rated, and the other displays curves with different values of Q_rated with a fixed K_ind.

Click on **Calculate G_dc** to display the dc gain curves (as shown in Figure 2) with respect to the relative frequency factor (K_rel_freq) to find the range of relative frequency for the required dc gain. At the same time, the Excel file that shows the results of different Q_rated and K_ind is generated automatically as shown in Fig. 3.

*Figure 2: Design Curves with Q_rated = 0.3, K_ind = 3 to 7 with a step size of 1 in the top panel and
K_ind = 4, Q_rated = 0.2 to 0.9 with step size of 0.2 in the bottom panel. *

In Figure 2, the dc gain curves are generated with variation in relative frequency from the start of ZVS of primary switches (lagging mode below resonant) up to above resonant. The above resonant relative frequency is restricted here at 2 for practical design reasons.

*Figure 3: Generated Excel file with Q_rated = 0.3, K_ind = 3 to 7 and K_ind=4, Q_rated = 0.2 to 0.8.*

In Fig. 3, the detailed output calculations are generated at the minimum and maximum switching frequencies at each set of Q_rated and K_ind. The upper highlighted portion shows the variation in relative frequency factor (K_rel_freq) from maximum to minimum for each entered K_ind (from 3 to 7) at Q_rated = 0.3. The bottom highlighted portion shows the variation in K_rel_freq for each entered Q_rated (from 0.2 to 0.8) at K_ind = 4.

Note: The key idea in the optimization process of the resonant converter design is to find the optimum value of Q_rated and K_ind that will provide the narrow range of variation in operating frequency. A narrow range of the frequency is important for magnetics design, controller selection, and component sizing.

Some observations from the Excel file about the required frequency range are:

- At K_ind = 4 and Q_rated = 0.3, the required relative frequency range is from 0.76 to 1.63 for the required dc gain
- At K_ind = 4 and Q_rated = 0.6, the required relative frequency range is from 0.75 to 1.38 for the required dc gain
- At K_ind = 4 and Q_rated = 0.8, the required relative frequency range is from 0.75 to 1.31 for the required dc gain

Similar observations can be made for other K_ind (3 to 7) and Q_rated (0.3 to 0.8) values.

From a design point of view, a low value of Q_rated provides a design with a smaller size of magnetics and lower voltage stress on the capacitor. But on the other hand, by increasing the value of Q_rated, a lower switching frequency will be required to obtain the minimum dc gain. Also, a higher K_ind can ensure a lower transformer circulating current with lower power device conduction losses.

To have the best trade-off in the design, Q_rated is selected from 0.6 to 0.8 and K_ind is selected from 4 to 6, so that a narrow frequency range can be obtained for G_dc variation (from 0.75 to 1.25). These selections ensure a reasonably narrow range in frequency and enough circulating current to have the boost in below resonant operation. These selections also ensure a high enough quality factor to get minimum dc gain with less variation in frequency above the resonant frequency.

After comparing the calculated output values in the Excel file, select the final design values so that the overall design is well balanced to have the best trade-offs for efficiency, power density, cost, and voltage regulation.

*Figure 4: The generated Excel file for relative frequency (K_rel_freq_min and K_rel_freq_max) at Q_rated = 0.6, K_ind variation from 3 to 7.*

From the Excel file in Figure 4, one can find Q_rated = 0.75 and K_ind = 4 provide a narrower range of frequency variation, lower circulating current and lower turn-off current as compared to other conditions. Also, this combination ensures low voltage stress on resonant capacitance (Cs) and higher power density due to the reduced size of resonant capacitance and overall magnetics. Although a much higher value of Q_rated beyond 1 can be considered for its narrower range variation in frequency especially at light load, the rated quality factor directly affects the size of magnetics and capacitance. Hence a proper trade-off has to be made between required frequency range, components sizing, and amount of circulating current.

Enter the selected parameters Q_rated = 0.75 and K_ind = 4 in the parameter panel and click on **Update Parameter File** to obtain all designed parameters for resonant LLC power converter. The calculation of Ls, Cs, and Lm depends on the Q_rated, K_ind, and f_res. For the selected Q_rated and K_ind, the optimum values of Ls, Cs, and Lm can be obtained as below.

Ls = (Q_rated*Ro_rated_pri)/(2*pi*f_res) = 1.6202e-05 H

Cs = 1/(2*pi*f_res*Q_rated*Ro_rated_pri) = 3.9085e-08 F

Lm = K_ind*Ls = 6.4808e-05 H

It should be noted here that Ls is the total value of the series inductance needed for this design. In practical design, Ls should be the sum of the leakage inductance (L_lk) of the transformer and resonant series inductance (L_res).

Simulate the resonant LLC power circuit with the selected values of Ls, Cs, Lm, Q_rated, and K_ind. A lookup table of the relative frequency factor versus the voltage gain will be automatically generated by the Design Suite. By this way, the lookup table will output the switching frequency close to the required value to achieve the desired output voltage regulation at varying load and line conditions.

The required value of the switching or operating frequency can also be obtained from the Steady State Solver or Design Curve Tool to regulate the varying output voltage.

The simulation and the Steady State Solver results are shown at the rated condition.

Figure 5 shows the simulated results at the rated output voltage (500V) and rated input voltage (700V) at K_rel_freq = 0.9247 (185kHz) (below resonant mode). The Q_rated is 0.75 and K_ind = 4 with the required G_dc = 1.0527.

Figure 6 shows the same waveforms under the same operating conditions but from the Steady State Tool. The waveforms are identical, validating the Steady State Tool.

*Figure 5: Simulation results at the rated output voltage (500V) and rated input voltage (700V) at K_rel_freq = 0.9247 @185kHz (below resonant mode). *

*Figure 6: Waveforms from the Steady State Tool at the rated output voltage (500V) and rated input voltage (700V) at K_rel_freq = 0.9247 @185kHz (below resonant mode).*

*Figure 7: Simulation results at the minimum output voltage (400V) and rated input voltage (700V) at K_rel_freq = 1.196 @239.2kHz (above resonant mode).*

Figure 7 shows the simulated results at the minimum output voltage (300V) and rated input voltage (400V) at K_rel_freq = 1.196 (239.2kHz) (above resonant mode). The operating Q is 0.75 and K_ind = 4 with the required G_dc = 0.842.

The simulations can be done by including relevant parasitic, dead-time, MOSFET capacitance, etc. The calculated frequency from the tools will provide precise enough results to have proper load and line regulations for a non-ideal or lossy system.

One can find the detailed results under the variation of input and output conditions by using the Steady State Solver or Design Curve Tool.

Some of the results at the rated input voltage (700V) are shown below in Table 1:

*Table 1: Results at the different output voltage at rated input voltage. *

It should be noted here that ZVS for primary switches and ZCS for secondary diodes are maintained at all conditions. For operations below the resonant frequency with a dc gain of more than 1, the secondary diodes will operate in the discontinuous current mode, ensuring that there is no reverse recovery problem.

With the Power Supply Design Suite, the process of designing a resonant LLC converter for a wide range of input and output dc-dc applications, which is difficult, tedious, and time-consuming, is made considerably easier. The Steady State Tool and the Design Curve Tool provide the necessary information for quick design iteration and optimization, and to ensure that the converter operates in soft switching throughout the entire input/output voltage range. The final design is easily validated in time-domain simulation in PSIM.