Wireless Power Transfer (WPT) systems have attracted much attention for contactless energy conversion in many applications such as electric vehicles, consumer electronics, biomedical engineering, wireless power technology, etc. A resonant converter-based wireless power transfer system includes all the benefits of resonant converters, such as soft-switching characteristics over a wide load/line range, high peak efficiency, high power density, low EMI footprint, and additional benefits like contactless power transmission.

However, the optimal design of a resonant-based WPT converter system is a non-trivial and tedious task as the converter is highly nonlinear, has a higher-order resonant tank, and the design process involves many iterations.

The Power Supply Design Suite in PSIM provides pre-built resonant converter-based templates for analyzing and optimizing resonant tanks with accuracy. The resonant converter templates can be easily modified into resonant WPT converter templates. These templates also incorporate two user-friendly design tools for optimal and robust design.

This application note describes how to design a series-series compensated resonant WPT converter system for a 6.6-kW EV on-board charger using the **Full-bridge Resonant CLLLC** template.

The resonant WPT converter is typically used as the isolated dc-dc stage of an EV On-Board Charger (OBC). The resonant converter for a 6.6-kW OBC has the following specifications:

Vin_rated = 400V; Vin_min = 390V; Vin_max =410V

Vo_rated = 420V; Vo_min = 300V; Vo_max = 450V

Po_rated = 6.6kW

f_res = 200 kHz

Several steps are needed to design a resonant WPT system using the Power Supply Design Suite:

- Define input and output requirements as well as the operating conditions in the Input Parameter panel.
- Perform design iterations and design comparisons using the Design Curve Tool.
- Analyze and verify zero voltage switching (ZVS) and zero current switchings (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 a time-domain simulation to validate the design.

The following describes the details of each step.

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

*Figure 1: The unpacked resonant CLLLC template from the Design Suite*

In Figures 1, the Parameter Panel on the left of the schematic window allows users to input the design specifications, launch the Steady State Solver Tool and the Design Curve Tool. The parameter file on the left of the circuit stores the calculated parameter values of the CLLLC circuit.

In a resonant converter, the resonant elements are calculated based on rated quality factor (Q_rated), magnetic ratio (K_ind), and resonant frequency (f_res) in the CLLLC template.

In a wireless power transfer system, the transformer turns ratio a_sp is typically 1. With that:

Cs1 = Cs2

Ls1 = Ls2

In the circuit, Lm is the magnetizing inductance, and Ls1 and Ls2 are the series inductances. The series inductances Ls1 and Ls2 can be the leakage inductances of the transformer. However, if the calculated values are higher than the leakage inductances, external inductors would be needed.

The transformer can be replaced by a coupled inductor, with the self and mutual inductances defined as follows:

L11 = Ls1 + Lm

L22 = Ls2 + Lm

L12 = L21 = Lm

The circuit can be modified as seen below.

*Figure 2: The modified resonant CLLLC template for wireless power transfer*

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) 400
- Vin_rated (rated input voltage) 400
- Vin_min (minimum input voltage) 390
- Vin_max (maximum input voltage) 410

**Output Requirement:**

- Vo (operating output voltage) 420
- Vo_rated (rated output voltage) 420
- Vo_min (minimum output voltage) 300
- Vo_max (maximum output voltage) 450
- Po_rated (rated output power) 6600
- 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 “**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.

For resonant converter system, the resonant elements are calculated as follow based on selected Q_rated, K_ind, and f_res:

a_sp = 1

Ls1 = (Q_rated*Ro_rated_pri)/(2*pi*f_res)

Cs1 = 1/(2*pi*f_res*Q_rated*Ro_rated_pri)

Lm = K_ind*Ls

Ls2 = Ls1

Cs2 = Cs1

It should be noted that the resonant CLLLC template has a 5th order symmetrical resonant tank which has five resonant elements: Cs1, Ls1, Ls2, Cs2, and Lm. With a_sp = 1, the inductance Ls2 and capacitance Cs2 are the same as inductance Ls1 and capacitance Cs1.

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

G_dc_min = Vo_min/(Vi_max*1) = 0.73

G_dc_max =Vo_max/(Vi_min*1) = 1.15

We will find the optimized values of resonant components for the dc gain range of 0.7 to 1.2 to compensate for small parasitic in the real prototype/circuit.

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 0.2 to 0.5 and the value of K_ind in the range of 4 to 10. Make sure to set a_sp = 1.

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 below.

*Figure 3: Design Curves with Q_rated = 0.4, K_ind = 4 to 10 in the top panel, and K_ind=4, Q_rated = 0.2 to 0.4 in the bottom panel.*

In Figure 3, 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.

Using Figure 3, it can be directly concluded that the K_ind=4 (or the lowest magnetic ratio) will provide the narrowest variation in frequency in both below and as well as above resonant operation to meet the gain requirement. The lowest value of Q_rated will need the lowest variation in frequency in the below resonant region. But it can also be concluded that the highest value of Q_rated will ensure the lowest variation in frequency in the above resonant region. There is clearly a trade-off here in the selection of a value of Q_rated.

In Figure 4, the detailed output calculations are generated at the minimum and maximum switching frequencies at each set of Q_rated and K_ind.

*Figure 4: An example of generated Resonant_Parameter_Optimization excel file with Q_rated = 0.4, K_ind = 4 to 10 and K_ind=4, Q_rated = 0.2 to 0.4.*

The upper highlighted portion shows the variation in relative frequency factor (K_rel_freq) from maximum to minimum for each entered K_ind (from 4 to 10) at Q_rated = 0.4. The bottom highlighted portion shows the variation in K_rel_freq for each entered Q_rated (from 0.2 to 0.4) 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 = 0.4, the required relative frequency range is from 0.78 to 1.21 for the required dc gain.
- At K_ind = 6 and Q_rated = 0.4, the required relative frequency range is from 0.71 to 1.23 for the required dc gain.

Similar observations can be made for other K_ind (4 to 10) and Q_rated (0.2 to 0.4) 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 below 0.5, and K_ind is selected from 4 to 10 so that a narrow frequency range can be obtained for G_dc variation (from 0.7 to 1.3). 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 5 shows the results of outputs at different values of Q_rated and K_ind.

*Figure 5: Generated Excel file for relative frequency (K_rel_freq_min and K_rel_freq_max) at Q_rated = 0.4, K_ind variation from 4 to 10.*

From the Excel file in Figure 5, one can find Q_rated = 0.4, and K_ind = 6 provides a narrower range of frequency variation, lower circulating current, lower turn-off current, and a balanced design as compared to other conditions. For this on-board charger application, a lower value of Q_rated (less than 0.5) will also ensure low voltage stress on resonant capacitance (Cs) and higher power density by having a reduced size of resonant capacitance and overall magnetics. Hence, Q_rated = 0.4 and K_ind = 6 are selected as the final design.

Enter the selected parameters Q_rated = 0.4 and K_ind = 6 in the parameter panel and click on **Update Parameter File**. This will update the parameter file “parameters-main.txt.” Double click to open the parameter, and set a_sp = 1 manually (see Line 49 in the image below). Then select **Edit** >> **Show Values** to show the values of all the parameters, as shown below.

*Figure 6: Modify the parameter file and calculate values*

This step is necessary as, by default, the transformer ratio a_sp is calculated based on the input and output voltages, and it may not be 1. Also, this change is needed every time the button **Update Parameter File** is clicked, as it will overwrite the entire file.

From the parameter file, based on selected Q_rated and K_ind, the designed values of Ls, Cs, and Lm are obtained as below.

**Resonant parameters values are:**

Ls1 = Ls2 = (Q_rated*Ro_rated_pri)/(2*pi*f_res) = 8.50e-06 H

Cs1 = Cs2 = 1/(2*pi*f_res*Q_rated*Ro_rated_pri) = 7.44e-08 F

Lm = K_ind*Ls1 = 5.10e-05 H

**The coupled inductor values are:**

L11 = Ls1+Lm = 5.95e-05 H

L22 = Ls2+Lm = 5.95e-05 H

L12 = Lm = 5.10e-05 H

Simulate the resonant power circuit with the selected values. The required value of the switching or operating frequency can be obtained from the design tools to regulate the varying output voltage.

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.

Figure 7 shows the simulated results at the rated output voltage (420V) and rated input voltage (400V) at K_rel_freq = 0.89 (178 kHz) (below resonant mode). The Q_rated is 0.4 and K_ind = 6 with the required G_dc = 1.12.

*Figure 7: Simulation results at the rated output voltage (420V) and rated input voltage (400V) at K_rel_freq = 0.89 @178kHz (below resonant mode)*

Figure 8 shows the same waveforms under the same operating conditions but from the Steady State Tool. The waveforms are identical, validating the Steady State Solver.

*Figure 8: Waveforms from the Steady State Tool at the rated output voltage (420V) and rated input voltage (400V) at K_rel_freq = 0.89 @178kHz (below resonant mode).*

Figure 9 shows the simulated results at the minimum output voltage (300V) and rated input voltage (400V) at K_rel_freq = 1.26 (252kHz) (above resonant mode).

*Figure 9: Simulation results at the minimum output voltage (300V) and rated input voltage (400V) at K_rel_freq = 1.26 @252kHz (above resonant mode).*

As shown above, the Q_rated is 0.4, and K_ind is 6 with the required G_dc = 0.7673 at the rated output requirement. The operating Q is 0.56 as the output voltage is decreased from rated 420V to 300V to verify the design at the worst-case condition.

**Note:** There are two operation modes in on-board charger application: constant current charging (CC) and constant voltage charging (CV). The above design selections are for CV mode. Note that load resistance (Ro), load factor (K_load), and operating Q will be changed in CC mode. For example, in the CC mode, where the output voltage is at 300V, the operating Q will increase from 0.4 to 0.56. Similarly, the K_load will increase from a rated value of 1 to 1.4. It is important for the user to double-check the selected design parameters still work for the CC mode.

One can find the detailed results under the CC mode operation by using the Steady State Solver or Design Curve Tool.

Some of the results under CC mode with rated input voltage (400V) are shown below in Table 1:

*Table 1: Results at the varying output voltage (CC mode) at their calculated operating frequency.*

It should be noted here that ZVS for primary switches and ZCS for secondary diodes are maintained at all conditions.

With the Power Supply Design Suite, the process of designing a resonant wireless power transfer system for the on-board charger EV application, 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.