A Holistic Design Optimization Method for LLC Converters in Light Electric Vehicle Chargers

The passive components of <inline-formula> <tex-math notation="LaTeX">$LLC$ </tex-math></inline-formula> resonance converters are traditionally designed based on a resonance frequency and switching frequency range considering the required voltage conversion rate while ensuring zero-voltage switching (ZVS) of the primary-side power devices. Afterward, the subelements such as the transformer, power stage, and heat–sink are locally designed. However, this may only lead to locally optimized designs. In this article, a systematic design framework is proposed that attempts to determine the resonance frequency by considering the nonlinear battery load profile, power loss, volume, and cost of all main components. To achieve smaller-sized transformers, a series-connected primary and parallel-connected secondary windings with a multicore configuration is also considered. The proposed algorithm aids designers to optimally size the <inline-formula> <tex-math notation="LaTeX">$LLC$ </tex-math></inline-formula> and provides a step-by-step design methodology. An <inline-formula> <tex-math notation="LaTeX">$LLC$ </tex-math></inline-formula> stage of a light electric vehicle (LEV) battery charger converting 370–430 V to an output voltage range of 36–54 V rated at 3700 W with a peak efficiency of 98.2% has been designed validating the proposed design procedure.


I. INTRODUCTION
T HE L LC converter is a commonly used dc/dc res- onance converter topology in converting high voltage to isolated low voltage in a variety of applications.It has been demonstrated extensively that the design with an L LC converter can achieve both high efficiency and high power density [1], [2], [3].L LC converters can switch under zero-voltage switching (ZVS) for zero to rated load with a low turn-off current for the primary switches while achieving zero-current switching (ZCS) for the synchronous rectifiers (SRs) below resonance frequency.In addition to low power losses, soft turning-on allows for minimizing the generated electromagnetic noise [3], [4].In comparison to soft-switching PWM-controlled converters, L LC resonance converters can work at a higher switching frequency with higher efficiency particularly at light load, resulting in a higher power density [5], [6], [7].However, the selection and design of components remain a difficult task, particularly for varying loads such as batteries in light electric vehicles (LEVs).These vehicles are defined by the industry as electric vehicles with a power range from 1 to 10 kW and voltage classes between 24 and 72 V [8].Within these voltage classes, the 48-V category is commonly utilized, thus, this study has selected a 48-V output for the design in focus.
The common approach to designing an L LC converter is to determine the switching frequency range and resonance frequency and then select the magnetics, power switches, and heat-sinks, accordingly [9].The challenge with this approach is that the switching frequency is chosen based on the designer's experience or availability of components without conducting a systematic design framework [10].The downside of this design procedure is clear; the resonant elements such as resonance inductance (L r ), magnetizing inductance (L m ), and resonance capacitor (C r ) values, and corresponding core material and size for magnetics are not optimally selected.This approach hinders the power density as the total power losses and power density are determined based on the initially selected switching frequency range and resonance frequency [11].
The optimization of L LC converters is more difficult than conventional PWM-controlled converters due to their variety of operating modes and nonlinear dynamics [12].Many designs and optimization methodologies have been proposed for this type of converter in the past decades.Optimal design methods are developed based on the operation mode analysis in [12] and [13], but these approaches require utilizing sophisticated calculation tools.A simple and highly accurate design procedure is presented in [14], but the wide output voltage range and load profile have not been discussed.Based on the characteristics of the battery charging profiles, the time-weighted average efficiency index is proposed in [15], which represents the average weight of conversion efficiency during the battery charging period.However, the presented design methodology only considers the power losses without taking cost and volume into account.The wide adjustable output voltage range for lithium-ion battery charger systems has been analyzed in [16], [17], and [18] considering the charging profiles and corresponding worst-case scenarios for the primary side ZVS operation.On the other hand, all these research efforts are only toward finding the optimum resonance tank design under limited design criteria.To obtain optimal solutions across multiple objectives with varying design frequencies, the designers still require a multiobjective optimization method considering the design frequency, power losses, system cost, and volume.A comprehensive optimization design procedure considering magnetic design, power switches, and associated heat-sinks has not been proposed for the L LC resonance converter operating under a wide load range.
In this article, a systematic design framework for the L LC converter is proposed to find the optimal resonance frequency and minimum and maximum switching frequency limits that satisfy the required voltage gains at corresponding quality factors by minimizing the system-level fitness function.The high-level block diagram summarizing the proposed optimization tools is shown in Fig. 1.For each resonance frequency, satisfying L r , L m , and C r values are calculated.For each calculated combination, a transformer and an inductor are designed based on the analytical models for every possible core in the database.Next, the transformer and the inductor are selected among the designed candidates, which minimizes the defined local fitness function.A key strength of this approach lies in its capacity to apply diverse fitness functions to local-and system-level designs.In this approach, a multicore transformer configuration with primary windings in series and secondary windings in parallel is also considered instead of a single-core transformer as in the traditional L LC resonance converter.On the power-stage side, the primary and secondary power switch losses for the devices in the database and the required heat-sink sizes considering the thermal resistances of the packages are calculated.After obtaining the design space, a system-level fitness function consisting of power loss, system volume, and cost is applied to find the most optimal resonance frequency together with the corresponding locally optimized L r -L m -C r combinations and all other nontrivial components.
Different from the previous studies, the algorithm provides.
1) The magnetic design and switch selection has been carried out by considering total energy optimization based on the user charging profile as opposed to the worst-case scenarios or nominal point designs.All losses have been computed for these four operating points and weighted based on the different operating conditions, contributing to 50%, 20%, 20%, and 10% of the overall consideration, respectively [19], [20].2) Inclusion of thermal resistances of power switches and corresponding heat-sink volumes.3) Determination of optimal effective relative permeability for gapped magnetic cores in the database that is found by sweeping the operating flux density.4) Primary-series secondary-parallel connected multicore transformer structure.5) New derivations of current equations in relation to switching frequency.6) A high-level system fitness function consisting of power losses, system volume, and cost.

II. PROPOSED OPTIMIZATION ALGORITHM
The resonance tank design, which depends on the resonance frequency, determines the soft switching state.A smaller L n (L m /L r ) value provides a higher gain for a constant quality factor (Q) value and moves the operation point away from the capacitive region providing ZVS turn-on for the primary switches.As L n decreases, the magnetization current increases causing an increase in the circulating current-related conduction losses.A smaller Q value makes the gain higher, whereas a higher Q may not meet the design requirements, and may transit the operation point to the capacitive region.Therefore, design optimization is required for L LC converters, particularly in wide input and output voltage applications with dynamic load profiles.

A. Effect of Battery Load on Design Optimization
The design requirements for an L LC resonance converterbased lithium-ion battery charger are significantly different Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.than the regular passive load applications because of the nonlinear I -V characteristics of the battery load [18].The charge process for a lithium-ion battery usually contains constantcurrent (CC) and constant-voltage (CV) charging stages, which are represented by four key points as shown in Fig. 2. At the beginning point, the input current drawn from the high-voltage dc bus is the lowest in the CC region; however, the switching frequency is highest due to the required low-voltage conversation ratio.The turning point marks the transition from the CC to CV charging mode and represents the region in which maximum power is transferred.The charging current in the CV stage is much smaller than that in the CC stage; hence, the light-load efficiency is more important for this stage.Because of these reasons, the designs optimized for a certain operating point may not be able to operate at other operation points.For instance, the circulating conduction losses may overheat the power switches, or the magnetic core may be overheated due to core losses at high switching frequencies observed at the beginning point.Similarly, a design made based on the beginning point may fail at the turning point due to reasons such as increased conduction loss on the secondary-side power FETs and transformer.Moreover, designs made for a single operation point may not be efficient at the other operating points.
In the presented design framework, all four key operation points are considered in the optimization process.First, for a given resonance frequency, the switching range that covers the voltage conversation ratio of wide input and output voltage ranges is found.The power stage and magnetics are designed and evaluated at other operating points as well.The designs that do not meet the design criteria such as thermal limits and saturation flux density are eliminated.Furthermore, the designs are evaluated at all four operation points with different weights assigned to the fitness function for each operation point as where w OP,i denotes the weights assigned to each operation point, and f (V bat OP,i , I bat OP,i ) is the fitness function of each operation point in the local optimization loop.As a result, the proposed algorithm offers to optimize the design for a given operation point as well as across multiple operation points.In this study, the weight distributions have been defined as 50%, 20%, 20%, and 10%, respectively.Significantly, our algorithm is inherently adaptable, allowing for the alteration of these weight distributions to accommodate specific user needs or distinct operating conditions.

B. Determination of Switching Frequency Range
The parametric analyzes are conducted by sweeping L n , Q, and resonance frequency ( f 0 ), which inherently determine the switching frequency range.Using the first harmonic approximation (FHA) method, L r , L m , and C r values are expressed as (2) where R e is the ac equivalent load resistance.The voltage gain (M) of the converter can be expressed in terms of frequency rate (F), L n , and Q with the relationship given in the following equation: Here, F denotes f s / f 0 .By rearranging ( 5) and solving for F, both the minimum and maximum switching frequency that would satisfy the minimum and maximum voltage conversion ratio can be calculated as given in the following equation: Some L n and Q pairs may require a large switching frequency range to meet the required M of the application.To avoid inefficient results, the maximum frequency is limited to 1.8 times the resonance frequency.

C. Transformer and Resonance Inductor Design
The magnetic model developed in this study designs locally optimized transformer and inductor according to the given L m and L r values, respectively, and provides these locally optimized magnetic designs to the system-level optimization tool.Since high-power LEV battery chargers generate high output currents, that is, 68.5 A at 54-V battery voltage for a charger rated at 3700 W, it is a good practice to parallel transformers to decrease the current density on the secondary windings.On the other hand, the current density on the primary windings is not as high due to being fed from high bus voltage.This allows connecting the primary windings of transformers in series to lower the number of turns.Due to the difficulty in controlling the leakage inductance and the possibility of saturation of the magnetic material, a separate Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
resonance inductor is designed instead of integrating it into the transformer core.
The transformer and inductor are designed for each L n , Q, and f 0 combination using the core database.This database comprises EE-type cores associated with four distinct materials N87, 3C94, 3C95, and 3F36.Furthermore, these cores present in a spectrum of 16 different volumes, varying from 1490 mm 3 (20/10/06) to 102 000 mm 3 (65/32/27), amounting to a total of 64 different core variants.The current density is calculated for the cores that are provided in the database as given in (7), where A p is defined as the product of the core window area and the cross-sectional area, and k a and k w are the coefficients.ρ w is the resistivity of copper, and k u is the window utilization factor.γ is the total losses except for the dc copper loss.The typical values of k a , k w , and k u are 40, 10, and 0.6, respectively [22] The cross-sectional areas of the primary and secondary (A w ) windings are calculated in ( 8) and ( 9), respectively.The cross-sectional areas are used to calculate the conductor dimensions The AWG value closest to the calculated conductor dimensions is selected as the conductor diameter (r pri , r sec ), and new current density values are updated for the selected cross section at standard AWGs.As a design constraint, the current density limit is set as 3.5 A/mm 2 .Since the design is optimized at multiple operation points according to the battery charging profile as detailed in Section II-A, I Lr rms requires to be expressed in relationship to f s .I Lr rms is the sum of the referred secondary current of the transformer referred to the primary side, and the magnetizing current (I Lm ).
The resultant I Lr rms expression that is valid for both below and above resonance operation is found as where Similarly, (12) expresses the secondary-side rms current that is used to calculate the current density in the windings and Cu losses on the secondary side The operating flux density is the paramount variable for gapped magnetic design, as various cores result in different loss coefficients for frequency and flux density.Therefore, it is taken as the main design variable in this study.The optimization algorithm sweeps the operating flux density and calculates the optimal relative permeability (µ opt ), which allows utilizing the core optimally based on its power dissipation capability and saturation flux density (B sat ) limits where Since the airgap (g) directly affects the operating flux density and the number of turns (N ), the required N for the given L m are calculated using the inductance-per-square (A L ) turn corresponding to the calculated optimal airgap as given in the following equation: The accurate estimation of leakage inductance in transformers is critical for L LC resonance converters because a well-matched resonance frequency is required [23].The leakage inductance referred to as the primary can be found from the energy stored in the magnetic field as in (17), where a is the winding length, b is the winding build, and c is the insulation thickness By using the calculated number of winding and conductor diameters, the dc resistance can be calculated by (18), where MLT is the mean-length-turn of the winding The skin effect, which causes an increase in the resistivity of the copper as the effective conductive area is reduced at higher frequencies, is determined by (19).The skin depth is used in finding the ac resistance of round windings as given in (20), where σ is the conductivity of the conductor material, and r is the radius of the winding.For foil windings, the ac resistance can be calculated as described in [24] δ After finding the ac resistances and current values, the copper and core losses are calculated by ( 21) and (22), where V e is the volume of the core.The Steinmetz equation is used for core loss calculation, and C m , α, and β coefficients are derived by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
using the P(W/mm 3 ) -B(mT) graphs for different frequency values given by the manufacturer data To estimate the temperature rise of the magnetic components, the thermal resistances of the cores are calculated by the empirical formula given in (23) for natural convection cooling, and temperature rise is checked by using ( 24) [24].The maximum temperature rise is restricted to 90 • C as a design constraint The optimization algorithm sweeps the operating flux density to find the optimal operating flux density across a large design space by minimizing a fitness function, which includes power loss, cost, and volume of the transformer and inductor.The cost includes core, winding, and labor costs given in ( 25)-( 27), where σ core,x , σ wdg,x , and σ lab,x are the specific costs per weight considering different magnetic core and the winding types.fc core,x , fc wdg,x , and fc lab indicate the fixed costs for the magnetic cores including the coil formers, connectors, and labor, where N stack represents the stacking factor.The power loss includes core loss, temperature-dependent copper loss, and ac winding loss due to the skin effect.More information on the magnetic design for gapped cores can be found in [25] core = N stack • fc core,x + σ core,x • W core (25) wdg = fc wdg,x + σ wdg,x • W wdg (26

D. Power Switch and Heat-Sink Selections
The first criterion in choosing a power device for the primary and secondary sides is to satisfy the ZVS operation.For the given design variables of L m and f 0 , the energy stored in the magnetizing inductance must be sufficient to soft-switch the primary side FETs.Besides, in the dead-time period, the energy from the magnetic field, associated with I Lm , needs to charge and discharge the equivalent switch node capacitance (C eq ).The minimum energy and dead time required to ensure ZVS operation are given in the following equation: where C eq is the equivalent capacitance referred to the switch node, which includes the total parasitic output capacitance of the primary side power devices, the total parasitic output capacitance of the secondary side power devices reflected to the primary side, the parasitic capacitance of the switch node traces as well as the transformer and inductor winding capacitances.For simplicity, C eq has been taken equal to 4 × C oss pri in literature [6].Since the ZVS operation of the primary power switches is guaranteed by choosing appropriate power devices in accordance with (28), there are no power losses during turn on.However, there are still conduction and turn-off losses occurring in the primary power switches.Since the duty cycle of the diagonal power switches are identical to that of the remaining diagonal power switches with 180 • phase shift, the total power dissipation of the full-bridge leg can be found by Even though the turn-off power losses are not as high as the capacitive losses of a hard-switched converter, they can be considerably high when the switching frequency is low and magnetizing current is high.The total turn-off power losses are expressed as where Here, R g is the internal gate resistance, R gext is the external resistance, C iss is the effective input capacitance, V plt is the gate plateau voltage, and V th is the threshold voltage.The other frequency-dependent power loss component is the gate drive loss, which is expressed as Another loss component, which may become significant in high-frequency designs is the dead-time losses.Depending on the switching period, it is either inserted as a constant time or a percentage of the soft-switching time and can be expressed as Here, V sd is the body diode voltage drop, and I sd is the average source to drain current during total body-diode conduction time (t bdc ) both during turn on and turn off.The total conduction losses on the secondary side synchronous switches of the center-tapped configuration are expressed as In the case of using SiC diodes, the total conduction losses per center-tap configuration are expressed as Note that I o , and therefore, I sec rms decrease proportionally with a parallel number of transformers and power devices per each secondary side output stage.The secondary-side synchronous devices are ZCS turned on and off at the below resonance operation.In the above resonance operation, the secondary-side power devices are turned on under current, where di/dt is limited by the loop and leakage inductances.
To calculate the heat-sink size required for each L n , Q, and f 0 combination, and therefore to choose the best power device and package, it is necessary to estimate the thermal resistance from the junction of the power device to the heat-sink.For this purpose, a MOSFET/SiC diode database from different manufacturers has been created along with package information.It is important to note that this extensive database encompasses 18 different switches for the primary side and another 16 switches for the secondary side.For total thermal resistance calculation, finite-element analysis tools can be used; however, this requires heavy computation.For simplification, the theory on iso-flux rectangles and strips on compound flux channels as explained in [26] has been utilized for each layer.The die-attached pad (DAP) thicknesses are dependent on the construction of the die and the package, and the whole thermal pad area is used for cooling and filled with vias that are 8 mil in diameter.This is because the power loop is not as critical in soft-switching converters as in hardswitching converters.It is considered that the top and bottom Cu layer is 70-µm thick, and total PCB thickness is 1.6 mm and vias are plated with 25 µm Cu, and filled with conducting Epoxy.
For each power device in the database, the required heat-sink is calculated based on the product of power losses and thermal resistances.A correlation between the heat-sink surface area and corresponding thermal resistance is obtained.Then, the heat-sink in the database that has the closest surface area to this value is selected from the database, which comprises 72 different heat-sinks of varying sizes.
The costs of heat-sinks generally depend on the base material, volume, and weight as well as the manufacturing and engineering costs.Heat-sink costs can be calculated in (37), where σ sink,x is the specific costs per volume depending on the heat-sink type and fc sink,x is fixed costs which can result from additional engineering work and processing steps which are independent of heat-sink volume [27] sink = fc sink + σ sink,x W sink .

E. Optimization Flowchart
After finding the volume, cost, and power losses of the local best primary and secondary power devices as well as the transformer and the inductor, the values are stored for the corresponding L n and Q combination.In this way, a design space is created with locally optimized designs.The final selection of the design parameters is achieved by assigning weights to the volume, size, and cost of the locally optimized designs and finding a global solution that minimizes the fitness function.The flowchart of the proposed framework is shown in Fig. 3.

III. RESULTS AND DISCUSSIONS
A 3700-W L LC converter with an input-output voltage range of 430-370 and 54-48 V is designed using the proposed optimization framework under a 97% efficiency constraint.The algorithm sweeps the resonance frequency between 250 and 500 kHz at the outer loop, while the minimum and maximum frequencies are internally swept through L n and Q sweeps.Both the weights of the local-and system-level fitness functions are chosen as 60%, 20%, and 20% for volume, power loss, and cost, respectively.Fig. 4(a) shows the design space considering magnetic designs achieved using every feasible core in the database for each resonance frequency and L n -Q combinations.As it can be seen in Fig. 4, an increase in f 0 decreases the total volume and cost of the magnetic component; however, the power losses also increase.By applying a local fitness function to the magnetic model, the design space is further reduced.
The resultant design spaces in the case of using SR and SiC diodes on the secondary side are shown in Fig. 4(b) and (c), respectively.These points show the total volume, cost, and efficiency of the converter for the local best designs at each swept resonance frequency.For high power design specifications, the use of SR on the secondary side brings an advantage in efficiency and heat-sink volume, even though it increases the cost.The details of the design space with SR is provided in Fig. 5.
By applying the same fitness function applied locally to the whole design space, the optimum design parameters are found as 37.52 µH, 1.3 µH, 9.38 µH, and 19.73 nF for L m , L k , L r , and C r , respectively.The algorithm suggests using 40 m /650 V and 7.2 m /150 V MOSFETs on the primary and secondary sides, respectively.The optimal f 0 , f s range, and efficiency values for this optimized system are found as 370 kHz, 255.6-610 kHz, and 97.83%, respectively.For higher efficiency and smaller heat-sink size, two MOSFETs are paralleled; therefore, there are a total of eight devices on the secondary side.The core material is 3F36.The design parameters of the transformer and the inductor are provided in Table I.
For detailed in-depth analysis, the volume, loss, and cost for the primary and secondary FETs, the transformer and the inductor are provided with the radar chart given

IV. EXPERIMENTAL RESULTS
A 3700 W/48 V L LC prototype has been designed to verify the theoretical calculations used in the optimization tool.The photograph of the designed converter is shown in Fig. 7. Using the proposed optimization algorithm, the L m , L k , and L r values were found as 37.52 µH, 1.3 µH, and 7.78 µH, respectively.However, there is typically an error margin of 5%-10% in the manufacturing of wounded magnetics.The designed L m , L k , and L r values have been measured as 35.245, 1.4, and 8.2 µH, respectively.Here, the loop inductance on the PCB enclosing the impedance network from the half-bridge is calculated approximately as 0.5 µH [28].Therefore, the resonance frequency has been experimentally obtained around 350 kHz.Fig. 8 shows the operation of the L LC converter under different loads up to 3890 W. Here, V ds is the drain-source voltage of primary device Q 2 , and i Lr is the current through resonance inductor L r .As seen in Fig. 8, the primary-side devices operate under ZVS in both full-load and light-load conditions over the entire switching frequency range.The oscillation that starts after i Lr = i Lm is due to the resonance between the leakage inductance and secondary rectifier's junction capacitance in the below resonance region.
The gain curve obtained by the FHA analysis, simulation, and experimental data at the nominal operation point are shown in Fig. 9(a).As seen from Fig. 9(a), the gain obtained from the simulations is very similar to that obtained by the experiments.Since the effects of harmonics other than the fundamental harmonics increase in the below resonance region, the gain obtained in this region from FHA is lower than that in simulation and experiment.Moreover, the lumped interwinding and intrawinding parasitic capacitances of the transformer impact the voltage gain curve slightly.
The expected efficiency at the turning operation point, where the transferred power is maximum, had been provided by the proposed tool as 98%.The designed converter exhibits a peak efficiency of 98.2% at around 60% load and 98% efficiency at 80% load as shown in Fig. 9   To demonstrate the benefits of the suggested method, the recommended optimization technique has been implemented using volume-weighted design parameters for two benchmark designs presented in [29] and [30] with 3-kW output power and an output voltage range of 48-54 V. Efficiency, boxed volume, and cost are compared for each design, and the results   are displayed in Fig. 11 as stacked bar charts.As the algorithm aims to minimize design volume, it achieves a slightly lower full load efficiency (98.1%) compared to [30] (98.4%), but significantly higher than [29] (95.3%).Additionally, it suggests a much smaller boxed volume of 343 cm 3 , in contrast to the volumes of [29] and [30], which are 740 and 452 cm 3 , respectively.
The improvement in volume can also be observed separately for each design in the figure, specifically in terms of the magnetic components' volume, which comprises the total volume of the high-frequency transformer and the resonant inductor.Moreover, the proposed algorithm yields highly satisfactory results in terms of cost.The design in [30] is the most expensive due to the utilization of 16 switches in the secondary part and four magnetic components, including two parallel transformers and two series inductors.As a result, the cost of [30] serves as the base value for comparison and is considered as 1 p.u.In contrast, [29] has the most cost-effective magnetic design, as the transformer's leakage inductance is used as a resonant inductor.However, due to the use of eight MOSFETs with very small R dson values on the secondary side, the total cost of the [29] design rises dramatically to 0.83 p.u. Finally, the proposed design's cost is determined to be 0.7 p.u., making it the most affordable option with two parallel transformers, a resonant inductor, and eight MOSFETs on the secondary side.

V. CONCLUSION
In this study, a systematic design approach has been presented for the L LC converter that determines the resonance frequency, minimum, and maximum switching frequency limits that satisfy the quality factors at corresponding voltage gains of an LEV battery charger by minimizing the system-level fitness function for optimum design.During the design and optimization process L r , L m , and C r values have been calculated for each resonance frequency.For each L-L-C combination, a transformer and an inductor considering distributed core structure have been designed based on the developed analytical models for every possible core in the database.Among the designed candidates, the magnetic designs that minimize the local fitness function are recorded.For the operation conditions of each combination, the primary and secondary power device losses have been analytically calculated, and the required heat-sink volumes are estimated by using thermal models of bottom-side cooled devices cooled by mounting heat-sinks on a four-layer 1.6-mm-thick PCB.
After obtaining a design space, a system-level fitness function including volume, efficiency, and cost has been applied to find the optimal design.The proposed framework is essential to size the L LC converter optimally based on the given weights between cost, size, and efficiency considering the load profile of an LEV battery charger.A 3700 W/48 V L LC prototype has been designed based on the outcome of the proposed framework, where minimum peak efficiency was constrained to 97%.The designed prototype achieves a peak efficiency of 98.2% at 60% load.

Fig. 1 .
Fig. 1.High-level block diagram of the optimization of the L LC converter.

Fig. 2 .
Fig. 2. Typical charging characteristics of a Li-ion battery cell and key operation points [21].

Fig. 3 .
Fig. 3. Detailed flowchart of the system-level design procedure for the L LC converter.

Fig. 4 .
Fig. 4. Three-dimensional design space.(a) Magnetic model.(b) SR on the secondary side.(c) Use of diodes on the secondary side.

Fig. 5 .
Fig. 5. Two-dimensional design space with SR on the secondary side.(a) Efficiency cost.(b) Volume cost.(c) Volume efficiency.

Fig. 6 .
Fig. 6.Radar chart for the optimal design point.(a) Total volume.(b) Total cost.(c) Total power losses.(d) Power losses on primary FETs.(e) Power losses on secondary FETs.(f) System-level results.
(b).Fig.10provides the thermal test results of the proposed L LC converter under natural convection cooling switched at 340-kHz transmitting Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.