8 Steps to Designing an LLC Resonant Converter

LLC resonant converters have become a cornerstone in power electronics. They are widely adopted across various markets because they can achieve high efficiency while minimizing electromagnetic interference (EMI) through soft-switching techniques. LLC topology offers several configurations optimized for specific applications. In particular, there are two prominent configurations for the primary side and two different methods for the secondary side.

 

Image used courtesy of Adobe Stock

 

Half-Bridge LLC Resonant Converter Design With a Center-Tapped Transformer

This section explores the detailed design process for a half-bridge LLC resonant converter using a center-tapped transformer (see Figure 1). Efficient power conversion can be achieved by combining the advantages of LLC topology with the flexibility of a center-tapped transformer.

 

 

Figure 2. Step-by-Step Flowchart for LLC Resonant Converter Design. Image used courtesy of MPS

 

Design Consideration

Two key design considerations can significantly impact the efficiency and performance of the LLC resonant converter:

Optimizing the resonant inductance ratio (L_N): A higher L_N typically improves efficiency under heavy-load conditions. It is recommended to maintain L_N within the 4 to 10 range to balance efficiency and component stress.

Selecting an appropriate quality factor (Q_E): To prevent excessive voltage stress on the resonant capacitor and minimize high inrush currents during start-up, Q_E must be maintained within the 0.34 to 0.49 range. This range ensures a good tradeoff between minimizing stress and maintaining overall converter performance.

 

Step 1: Determine the Converter Specifications

Table 1 shows the specifications of an example LLC resonant converter.

 

Table 1. Specifications of Example LLC Resonant Converter

Parameters	Values	Units
Input voltage (VIN)	400	VDC
Output voltage (VOUT)	48	VDC
Output power (POUT)	600	W
Resonant frequency (fR)	100	kHz
Minimum switching frequency (fSW_MIN)	50	kHz
MOSFET output capacitance	80	pF

Step 2: Transformer Turns Ratio

When calculating the transformer turns ratio (n), the gain (G) must be equal to 1 to work at the resonant frequency (f_R). n can be calculated with Equation (1):

\[n=\frac{N1}{N2}=\frac{V_{IN}}{2\times V_{OUT}}\times G\Rightarrow n=\frac{400}{2\times48}\times1\Rightarrow n=4.17\,\,\,\,\,(1)\]

Where n = 4.17 can be rounded to a whole number so n_LLC = 4.

 

Step 3: Determine the Maximum Magnetizing Inductance

To calculate the maximum magnetizing inductance (L_{M_MAX}), the following parameters must be determined: maximum dead time (t_{DEAD_MAX}), minimum switching period (t_{SW_MIN}), and output capacitance of the primary-side MOSFET (C_OSS).

The HR1002A, an enhanced LLC controller, is selected for this design due to its proven reliability under varying operational conditions. Based on the HR1002A datasheet, the controller’s t_{DEAD_MAX} is 2µs. The output capacitance of the selected MOSFET (C_OSS) is 80pF.

t_{SW_MIN} can be calculated with Equation (2):

\[t_{SW\_MIN}=\frac{1}{f_{START\_UP}}\Rightarrow\\\Rightarrow t_{SW\_MIN}=\frac{1}{3\times f_{SW}}\Rightarrow\\\Rightarrow t_{SW\_MIN}=\frac{1}{3\times100kHz}\Rightarrow\\\Rightarrow t_{SW\_MIN}=3.33\mu s\,\,\,\,\,(2)\]

L_{M_MAX} can be calculated with Equation (3):

\[L_{M\_MAX}=t_{MIN}\times\frac{t_{DEAD\_MAX}}{16\times C_{OSS}}\Rightarrow L_{M\_MAX}=3.3\mu s\times\frac{2\mu s}{16\times 80pF}\Rightarrow L_{M\_MAX}=5.2mH\,\,\,\,\,(3)\]

 

Step 4: L_N and Q_E Selection

As discussed regarding design considerations, Q_E is recommended to be within the range shown in Equation (4):

\(\frac{1}{3}\text{<}Q_{E}\text{<}\frac{1}{2}\Rightarrow\,0.33\text{<}Q_{E}\text{<}0.5\,\,\,\,\,(4)\)

In addition, Q_E is related to the resonant capacitor voltage stress and inrush current during start-up. Therefore, Q_E is selected to be 0.35, which is near the minimum. 

Similar to Q_E, the L_N ratio is recommended to be within the range shown in Equation (5):

\[4\leq L_{N}\leq 10\,\,\,\,\,(5)\]

To stabilize efficiency across all the load ranges, it is recommended to use an L_N ratio between 4 and 6. To prioritize efficiency at the maximum output power (P_OUT), it is recommended to use an L_N ratio between 6 and 10. In the example LLC resonant converter, L_N is selected to be 9.

 

Step 5: Resonant Tank Selection

To select the resonant tank, the following parameters must be determined: load resistance (R_L), equivalent load resistance (R_E), resonant capacitor (C_R), resonant inductor (L_R), and magnetizing inductance (L_M).

R_L can be calculated with Equation (6):

\[R_{L}=\frac{V^{\,\,\,\,\,\,\,\,\,\,\,2}_{OUT}}{P_{OUT}}\Rightarrow R_{L}=\frac{48^{2}}{600}\Rightarrow R_{L}=3.84\Omega\,\,\,\,\,(6)\]

R_E can then be calculated with Equation (7):

\[R_{E}=\frac{8\times n_{LLC}^{\,\,\,\,\,\,\,\,\,\,\,2}}{\pi^{2}}\times R_{L}\Rightarrow R_{E}=\frac{8\times4^{2}}{\pi^{2}}\times3.84\Rightarrow R_{E}=49.8\Omega\,\,\,\,\,(7)\]

C_R can be calculated with Equation (8):

\[C_{R}=\frac{1}{2\times\pi\times f_{R}\times R_{E}\times Q_{E}}\Rightarrow C_{R}=\frac{1}{2\times\pi\times100kHz\times49.8\times0.35}\Rightarrow C_{R}=91.31nF\,\,\,\,\,(8)\]

It is recommended that C_R be rounded to the nearest standard capacitance or that capacitors be placed in parallel to obtain the closest value. In this case, two 47nF capacitors are used in parallel for a total capacitance of 94nF.

L_R can be calculated with Equation (9):

\[L_{R}=\frac{1}{(2\times\pi\times f_{R})^{2}\times C_{R}}\Rightarrow L_{R}=\frac{1}{(2\times\pi\times100kHz)^{2}\times94nF}\Rightarrow L_{R}=26.95\mu H\,\,\,\,\,(9)\]

Where L_R = 26.95µH can be rounded to 27µH.

L_N can be calculated with Equation (10):

\[L_{N}=\frac{L_{M}}{L_{R}}\Rightarrow L_{M}=L_{N}\times L_{R}\Rightarrow L_{M}=9\times27\mu H\Rightarrow L_{M}=243\mu H\,\,\,\,\,(10)\]

L_M can be checked with Equation (11):

\[L_{M}\leq L_{M\_MAX}\Rightarrow243\mu H\leq5.2mH\,\,\,\,\,(11)\]

 

Step 6: Recalculation with the Final Values of L_R, C_R, and L_M

The resonant frequency (f_R) can be recalculated with the final values of L_R, C_R, and L_M using Equation (12):

\[L_{R}=\frac{1}{(2\times\pi\times f_{R})^{2}\times C_{R}}\Rightarrow\\\Rightarrow 2\times\pi\times f_{R}=\frac{1}{\sqrt{L_{R}\times C_{R}}}\Rightarrow\\\Rightarrow f_{R}=\frac{1}{2\times\pi\times\sqrt{L_{R}\times C_{R}}}\Rightarrow\\\Rightarrow f_{R}=\frac{1}{2\times\pi\times\sqrt{27\mu H\times94nF}}\Rightarrow\\\Rightarrow f_{R}=99.9kHz\,\,\,\,\,(12)\]

Q_E can be recalculated with the final values of L_R, C_R, and L_M using Equation (13):

\[C_{R}=\frac{1}{2\times\pi\times f_{R}\times R_{E}\times Q_{E}}\Rightarrow\\\Rightarrow Q_{E}=\frac{1}{2\times\pi\times f_{R}\times R_{E}\times C_{R}}\Rightarrow\\\Rightarrow Q_{E}=\frac{1}{2\times\pi\times99.9kHz\times49.8\times94nF}\Rightarrow\\\Rightarrow Q_{E}=0.34\,\,\,\,\,(13)\]

Where Q_E must be within the recommended range: 0.33 < QE < 0.5 0.33 < 0.34 < 0.5.

If Q_E is outside the specified range, adjust C_R and then repeat the calculations for Equation (8) through Equation (13).

 

Step 7: Checking the Results

To check the results, f_N, G, and V_IN are used to obtain the tank resonant voltage transfer function. Then, V_OUT is validated to ensure the converter’s proper operation. The resonant tank and gain can be verified using plots.

 

Tank Resonant Voltage Transfer Function

To ensure that the converter works in f_R, the following is assumed:

\[f_{N}=\frac{f_{SW}}{f_{R}}=1\Rightarrow f_{SW}=f_{R}=99.9kHz\]

The parameters are then replaced in the tank resonant voltage transfer function, G(f_N), which can be calculated with Equation (14):

\[G(fN)=\frac{1}{\sqrt{\Big[1+\frac{1}{L_{N}}-\frac{1}{f_{N}^{\,2}\times L_{N}}\Big]^{2}+Q_{E}^{\,\,\,\,2}\times\Big(\frac{1}{f_{N}}-f_{N}\Big)^{2}}}\Rightarrow\\\Rightarrow G(1)=\frac{1}{\sqrt{\Big[1+\frac{1}{9}-\frac{1}{1^{2}\times 9}\Big]^{2}+0.34^{2}\times\Big(\frac{1}{1}-1\Big)^{2}}}\Rightarrow\\\Rightarrow G(1)=1\,\,\,\,\,(14)\]

 

Output Voltage

The output voltage (V_OUT) can be calculated with Equation (15):

\[V_{OUT}=\frac{V_{IN}}{2\times n_{LLC}}\times G\Rightarrow V_{OUT}=\frac{400}{2\times4}\times1\Rightarrow V_{OUT}=50V\,\,\,\,\,(15)\]

With a unity gain, V_OUT is 50V instead of 48V.

There are two different methods to adjust V_OUT. The first method is to reduce the gain below 1, which can be calculated with Equation (16):

\[V_{OUT}=\frac{V_{IN}}{2\times n_{LLC}}\times G\Rightarrow G=\frac{V_{OUT}\times2\times n_{LLC}}{V_{IN}}\Rightarrow G=\frac{48\times2\times4}{400}\Rightarrow G=0.96\,\,\,\,\,(16)\]

The converter works at the normalized switching frequency (f_N), which has a ratio of about 1.2. f_N can be found solving equation (14) or plotting the resonant tank at the 0.96 gain (see Figure 4).

f_SW can be calculated with Equation (17):

\[f_{N}=\frac{f_{SW}}{f_{R}}\Rightarrow f_{SW}=f_{N}\times f_{R}\Rightarrow f_{SW}=1.2\times99.9kHz\Rightarrow f_{SW}=119.88kHz\,\,\,\,\,(17)\]

It is common to work within the f_R range instead of at the exact f_R due to components’ tolerances.

The second method to adjust V_OUT is by modifying the input voltage (V_IN), which can be calculated with Equation (18):

\[V_{OUT}=\frac{V_{IN}}{2\times n_{LLC}}\times G(f_{N})\Rightarrow\\\Rightarrow V_{IN}=\frac{V_{OUT}\times2\times n_{LLC}}{G(f_{N})}\Rightarrow\\\Rightarrow V_{IN}=\frac{48\times2\times4}{1}\Rightarrow\\\Rightarrow V_{IN}=384V\,\,\,\,\,(18)\]

By adjusting V_IN to 384V, the converter operates at f_R.

 

Verifying the Resonant Tank and Gain with Plots

The most effective way to validate the calculations is by plotting the tank resonant voltage transfer function using Equation (14) as well as plotting the gain using Equation (16). Consider the following two scenarios for the resonant tank gain.

In the first scenario, V_IN = 400V, L_R = 27µH, C_R = 94nF, and L_M = 243µH. Figure 3 shows the resonant tank gain at V_IN = 400V with 0.96 gain.

 

Figure 3. Resonant Tank Gain at V_IN = 400V, Gain = 0.96, and f_N = 1. Image used courtesy of MPS

 

At f_R, the gain is higher than necessary. To lower the gain to 0.96, the normalized frequency (f_N) must be determined.

Figure 4 shows the resonant tank gain after adding the calculated gain. The 1.2 ratio of f_N coincides with the 0.96 gain, which is indicated by the grey and black dashed lines.

 

Figure 4. Resonant Tank Gain at V_IN = 400V, Gain = 0.96, and f_N = 1.2. Image used courtesy of MPS

 

In the second scenario, V_IN is reduced to 384V, while the other conditions remain the same (L_R= 27µH, C_R = 94nF, and L_M = 243µH). Figure 5 shows the resonant tank gain at V_IN = 384V, where the converter operates at f_R with a unity gain.

 

Figure 5. Resonant Tank Gain at V_IN = 384V. Image used courtesy of MPS

 

The second scenario is applied for step 8 and the final design, which are described below.

 

Step 8: Calculating the Current and Voltage Stress of the LLC Converter

The current and voltage stress of the LLC converter includes the tank resonant stress, the primary-side semiconductor devices’ stress, and the secondary-side semiconductor devices’ stress.

 

Tank Resonant Stress

The tank resonant stress is determined by the magnetizing peak inductance current (I_{LM_PEAK}), resonant inductor RMS current (I_{LR_RMS}), resonant peak inductor current (I_{LR_PEAK}), and resonant capacitor voltage (V_CR).

I_{LM_PEAK} can be estimated with Equation (19):

\[I_{LM\_{PEAK}}=\frac{n_{LLC}\times V_{OUT}}{4\times L_{M}\times f_{R}}\Rightarrow I_{LM\_PEAK}=\frac{4\times48}{4\times243\mu H\times99.9kHz}\Rightarrow I_{LM\_PEAK}=1.98A\,\,\,\,\,(19)\]

I_{LR_RMS} can be calculated with Equation (20):

\[I_{LR\_RMS}=\frac{V_{OUT}\times\sqrt{4\times\pi^{2}+n_{LLC}^{\,\,\,\,\,\,\,\,\,\,\,4}\times R_{L}^{\,\,\,2}\times\Big(\frac{1}{L_{M}\times f_{R}}\Big)^{2}}}{4\times\sqrt{2}\times n_{LLC}\times R_{L}}\Rightarrow\\\Rightarrow I_{LR\_RMS}=\frac{48\times\sqrt{4\times\pi^{2}+4^{4}\times 3.84^{2}\times\Big(\frac{1}{243\mu H\times 99.9kHz}\Big)^{2}}}{4\times\sqrt{2}\times 4\times 3.84}\Rightarrow I_{LR\_RMS}=3.74A\,\,\,\,\,(20)\]

I_{LR_PEAK} can be calculated with Equation (21):

\[I_{LR\_PEAK}=\sqrt{2}\times I_{LR\_{RMS}}\Rightarrow I_{LR\_{PEAK}}=\sqrt{2}\times3.74\Rightarrow I_{LR\_PEAK}=5.29A\,\,\,\,\,(21)\]

V_CR can be calculated with Equation (22):

\[V_{CR}=\frac{I_{LR\_RMS}}{2\times\pi\times f_{R}\times C_{R}}\Rightarrow V_{CR}=\frac{3.74}{2\times\pi\times99.9kHz\times94nF}\Rightarrow V_{CR}=63.39V\,\,\,\,\,(22)\]

 

Stress of Primary-Side Semiconductor Devices

The stress of primary-side semiconductor devices is determined by the voltage stress of the primary side (V_Q1), peak current of the primary side (I_{Q1_PEAK}), and the RMS current of the primary side (I_{Q1_RMS}).

V_Q1 can be calculated with Equation (23):

\[V_{Q1}=V_{Q2}=V_{IN}=384V\,\,\,\,\,(23)\]

I_{Q1_PEAK} can be calculated with Equation (24):

\[I_{Q1\_PEAK}=I_{Q2\_PEAK}=I_{LR\_PEAK}=5.29A\,\,\,\,\,(24)\]

I_{Q1_RMS} can be calculated with Equation (25):

\[I_{Q1\_{RMS}}=I_{Q2\_{RMS}}=\frac{V_{OUT}\times\sqrt{4\times\pi^{2}+n_{LLC}^{\,\,\,\,\,\,\,\,\,\,4}\times R_{L}^{\,\,\,2}\times\Big(\frac{1}{L_{M}\times f_{R}}\Big)^{2}}}{8\times n_{LLC}\times R_{L}}\Rightarrow\\\Rightarrow I_{Q1\_{RMS}}=I_{Q2\_{RMS}}=\frac{48\times\sqrt{4\times\pi^{2}+4^{4}\times 3.84^{2}\times\Big(\frac{1}{243\mu H\times 99.9kHz}\Big)^{2}}}{8\times 4\times 3.84}\Rightarrow\\\Rightarrow I_{Q1\_RMS} = I_{Q2\_RMS} = 2.65A\,\,\,\,\,(25)\]

A high L_N means L_M is high as well, which reduces the RMS current in semiconductor devices.

 

Stress of Secondary-Side Semiconductor Devices

The stress of secondary-side semiconductor devices is determined by the voltage stress of the secondary side (V_Q3), peak current of the secondary side (I_{Q3_PEAK}), and the RMS current of the secondary side (I_{Q3_RMS}).

V_Q3 can be calculated with Equation (26):

\[V_{Q3}=V_{Q4}=2\times V_{OUT}\Rightarrow V_{Q3}=V_{Q4}=2\times48\Rightarrow V_{Q3}=V_{Q4}=96V\,\,\,\,\,(26)\]

I_{Q3_PEAK} can be calculated with Equation (27):

\[I_{Q3\_PEAK}=I_{Q4\_PEAK}=\sqrt{12}\times\frac{V_{OUT}\times\sqrt{12\times\pi^{4}+\frac{5\times\pi^{2}-48}{L_{M}^{\,\,\,\,2}\times f_{R}^{\,\,\,2}}\times n_{LLC}^{\,\,\,\,\,\,\,\,\,\,\,4}\times R_{L}^{\,\,\,2}}}{24\times\pi\times R_{L}}\Rightarrow\\\Rightarrow I_{Q3\_PEAK}=I_{Q4\_PEAK}=\sqrt{12}\times\frac{48\times\sqrt{12\times\pi^{4}+\frac{5\times\pi^{2}-48}{(243\mu H)^{2}\times (99.9kHz)^{2}}\times 4^{4}\times 3.84^{2}}}{24\times\pi\times 3.84}\Rightarrow\\\Rightarrow I_{Q3\_PEAK}=I_{Q4\_PEAK}=19.71A\,\,\,\,\,(27)\]

I_{Q3_RMS} can be calculated with Equation (28):

\[I_{Q3\_RMS}=I_{Q4\_RMS}=\sqrt{3}\times\frac{V_{OUT}\times\sqrt{12\times\pi^{4}+\frac{5\times\pi^{2}-48}{L_{M}^{\,\,\,\,2}\times f_{R}^{\,\,\,2}}\times n_{LLC}^{\,\,\,\,\,\,\,\,\,\,\,4}\times R_{L}^{\,\,\,2}}}{24\times\pi\times R_{L}}\Rightarrow\\\Rightarrow  I_{Q3\_RMS}=I_{Q4\_RMS}=\sqrt{3}\times\frac{48\times\sqrt{12\times\pi^{4}+\frac{5\times\pi^{2}-48}{(243\mu H)^{2}\times (99.9kHz)^{2}}\times 4^{4}\times 3.84^{2}}}{24\times\pi\times 38.4}\Rightarrow\\\Rightarrow I_{Q3\_RMS}=I_{Q4\_RMS}=9.85A\,\,\,\,\,(28)\]

 

Final Design

By calculating the current and voltage stresses on the resonant tank and semiconductor devices, the LLC converter design using the HR1002A can be completed. Table 2 shows the design results.

 

Table 2. Design Results

Parameters	Values	Units
Input voltage	384	V
Magnetizing inductance	243	µH
Transformer turns ratio	4	-
Resonant inductance	27	µH
Resonant capacitance	94	nF
Peak current (Q1, Q2, and LR)	5.29	A
RMS current: Q1, Q2, and LR)	2.65	A
Resonant capacitor voltage	63.39	V
Peak current (Q3 and Q4)	19.71	A
RMS current (Q3 and Q4)	9.85	A

The HR1002A is an enhanced LLC controller that provides robust adaptative dead-time adjustment (ADTA) as well as several protections, including shoot-through and capacitive mode protection (CMP) to avoid hard switching. There are also two over-current protection (OCP) levels, where one level provides a configurable delay for enhanced surge performance. Brown-in and brownout thresholds set the minimum V_IN at which the converter can start working.

Due to the capabilities of the HR1002A, the power converter stage also requires only a few external components to function effectively.

Figure 6 shows the schematic of the half-bridge LLC with a center-tapped transformer using the HR1002A.

 

 

Figure 6. Half-Bridge LLC with a Center-Tapped Transformer Using the HR1002A. Image used courtesy of MPS

 

LLC Topology in Real-World Applications

Selecting the LLC topology for the primary and secondary sides is critical for optimizing performance across various applications. The half-bridge LLC with a center-tapped transformer is ideal for power levels up to 1 kW.

By adhering to the design principles discussed in this article, including optimizing the resonant inductance ratio and quality factor, engineers can ensure that converters operate within the desired parameters while reducing the risk of component failure. Moreover, the HR1002A controller further enhances LLC converter designs with its advanced protection features, ensuring reliability and durability in real-world applications.

For more solution options, explore MPS's selection of integrated, high-reliability LLC controllers.