Fundamental Harmonic Approximation Research Articles

Dynamic Modeling and Control of Self-Oscillating Parallel Resonant Converters Based on a Variable Structure Systems Approach

This paper describes a novel modeling approach for self-oscillating resonant power converters operating under a control method based on the variable structure of the system (VSS). Using a fundamental harmonic approximation, the link between control and switching frequency in steady state is found to be accurately described by an affine function that depends on the load. Besides, this link has been extended in order to characterize the control-to-switching frequency dynamics, resulting in a novel small-signal continuous-time model. The resulting control-to-switching frequency transfer function can be appended to the well-known models for frequency modulation, in order to obtain a complete control-to-output system. The new model exposes that the dynamics of the converter under the VSS-based control approach presents advantages with respect to the conventional methods as frequency modulation: 1) reduced dc gain variation for uncertain loads and 2) improved phase margin at high frequencies. The dynamic modeling is complemented with the design of a controller for regulating the output voltage of a parallel resonant converter, whose performance and robustness are compared with the standard frequency modulation. Numerical simulations and experimental results confirm and verify the analytical derivations.

Time-Domain Analysis of a Phase-Shift-Modulated Series Resonant Converter with an Adaptive Passive Auxiliary Circuit

This paper presents a comprehensive time-domain analysis of series resonant converters operating with phase-shift-modulated full-bridge above resonance. Closed-form formulas for all quantities are derived using two methods: the commonly used fundamental harmonic approximation as well as a precise time-domain analysis considering the effect of all the harmonics. Detailed analytical method describes steady-state behavior of the converter in three mutually exclusive and collectively exhaustive modes of operation based on continuity of the resonant inductor current: a discontinuous mode and two continuous modes. The difference between two continuous modes is in the existence of natural zero-voltage switching in the leading leg of the full bridge. Quantitative predictions of the key quantities from two methods are compared and the accuracy of the first harmonic approximation is examined. The time-domain approach provides useful insights for design considerations with no need to know the load value. It precisely determines closed-form equations for the boundary conditions of the three operation modes. An adaptive passive auxiliary circuit is suggested to guarantee zero-voltage switching for the entire operating conditions. Experimental results from a 100 W prototype confirm the predicted time-domain behavior and achievement of soft switching using the proposed auxiliary circuit.

Design Guidelines for a Capacitive Wireless Power Transfer System with Input/Output Matching Transformers

A capacitive wireless power transfer (C-WPT) system uses an electric field to transmit power through a physical isolation barrier which forms a pair of ac link capacitors between the metal plates. However, the physical dimension and low dielectric constant of the interface medium severely limit the effective link capacitance to a level comparable to the main switch output capacitance of the transmitting circuit, which thus narrows the soft-switching range in the light load condition. Moreover, by fundamental limit analysis, it can be proved that such a low link capacitance increases operating frequency and capacitor voltage stress in the full load condition. In order to handle these problems, this paper investigates optimal design of double matching transformer networks for C-WPT. Using mathematical analysis with fundamental harmonic approximation, a design guideline is presented to avoid unnecessarily high frequency operation, to suppress the voltage stress on the link capacitors, and to achieve wide ZVS range even with low link capacitance. Simulation and hardware implementation are performed on a 5-W prototype system equipped with a 256-pF link capacitance and a 200-pF switch output capacitance. Results show that the proposed scheme ensures zero-voltage-switching from full load to 10% load, and the switching frequency and the link capacitor voltage stress are kept below 250 kHz and 452 V, respectively, in the full load condition.

Optimum Design of LLC Resonant Converter using Inductance Ratio (Lm/Lr)

The main benefits of LLC resonant dc/dc converter over conventional series and parallel resonant converters are its light load regulation, less circulating currents, larger bandwidth for zero voltage switching, and less tuning of switching frequency for controlled output. An unique analytical tool, called fundamental harmonic approximation with peak gain adjustment is used for designing the converter. In this paper, an optimum design of the converter is proposed by considering three different design criterions with different values of inductance ratio (Lm/Lr) to achieve good efficiency at high input voltage. The optimum design includes the analysis in operating range, switching frequency range, primary side losses of a switch and stability. The analysis is carried out with simulation using the software tools like MATLAB and PSIM. The performance of the optimized design is demonstrated for a design specification of 12 V, 5 A output operating with an input voltage range of 300–400 V using FSFR 2100 IC of Texas instruments.

Energy Compression of Dielectric Barrier Discharge With Third Harmonic Circulating Current in Current-Fed Parallel-Series Resonant Converter

An advanced technique of energy compression with the third harmonic circulating current generation is presented in this paper to improve the surface treatment performance in the dielectric barrier discharge (DBD) systems. First, the relationship between the energy compression degree and contact angle is explored, which shows that the polymer surface wettability can be improved by the high energy compression degree in DBD. And then, an additional inductor is inserted into the resonant tank in the current-fed parallel-series resonant converter to generate the third harmonic current component, which can reduce the discharge-time-ratio and compress the energy transferred to the DBD loads. Furthermore, the method of rectifier-compensated fundamental plus third harmonic approximation (RCFTHA) is introduced to describe the current-fed parallel-series resonant converter by superposing two equivalent linear circuits operating at the fundamental and third harmonic frequencies, respectively. Consequently, the discharge-time-ratio optimization with the parallel-series resonant tank design is realized. Finally, the experimental results from a 350-W prototype substantiate the effectiveness of the energy compression with the third harmonic circulating current and the accuracy of RCFTHA.

Resonant Tank Design Considerations and Implementation of a LLC Resonant Converter with a Wide Battery Voltage Range

This paper illustrates resonant tank design considerations and the implementation of a LLC resonant converter with a wide battery voltage range based on the fundamental harmonic approximation (FHA) analysis. Unlike the conventional design at zero load, the parameter K (the ratio of the transformer magnetizing inductor Lm to the resonant inductor Lr) of the LLC converter in this paper is designed with two charging points, (Vo_min, Io_max1) and (Vo_max, Io_max2), according to the battery charging strategy. A 2.9kW prototype with an output voltage range of 36V to 72V dc is built to verify the design. It achieves a peak efficiency of 96%.

Compact and Efficient Bipolar Coupler for Wireless Power Chargers: Design and Analysis

Compactness and efficiency are the two basic considerations of the wireless battery chargers for electric vehicles (EVs) and plug-in hybrid EVs. The double-sided LCC compensation topology for wireless power transfer (WPT) has been proved to be one of the efficient solutions lately. However, with the increase of the numbers of compensation components, the volume of the system may become larger, which makes it less attractive. To improve the compactness, a bipolar coupler structure with a compensation-integrated feature is proposed. The inductors of the LCC compensation networks are designed as planar-type and attached to the power-transferring main coils. Extra space and magnetic cores for the compensated inductors outside of the coupler are saved. The cost is that extra couplings between the compensated coils (inductors) and the main coils are induced. To validate the feasibility, the proposed coupler is modeled and investigated by 3-D finite-element analysis tool first. The positioning of the compensated coils, the range of the extra couplings, and the tolerance to misalignment are studied. This is followed by the circuit modeling and characteristic analysis of the proposed WPT topology based on the fundamental harmonic approximation. At last, a 600 mm × 600 mm with a nominal 150-mm-gap wireless charger prototype, operated at a resonant frequency of 95 kHz and a rated power of 5.6 kW has been built and tested. A peak efficiency of 95.36% from a dc power source to the battery load is achieved at rated operation condition.

Operation Modes of a Secondary-Side Phase-Shifted Resonant Converter

In this work, a unidirectional full-bridge resonant converter with secondary-side phase-shifted control is addressed. With the variation of voltage gain and power level, this converter may enter into different operational modes, including three continuous current modes and one discontinuous current mode. The details in each operation mode are discussed one by one. The boundary conditions between these modes have been identified. Additionally, the steady-state analysis of all continuous current modes is performed uniformly by using the fundamental harmonics approximation approach. Experimental results based on a lab prototype converter are also included to verify the operation modes predicted by the theoretical analysis.

Integrated ${LCC} $ Compensation Topology for Wireless Charger in Electric and Plug-in Electric Vehicles

This paper presents an integrated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCC$</tex-math></inline-formula> compensation topology for electric vehicle/plug-in hybrid electric vehicle wireless chargers. The effect of the coupling between the additional coil and the main coil on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LCC$</tex-math></inline-formula> compensation topology is studied. The proposed topology will reduce the size of the additional coil and make the system more compact with extremely high efficiency. The basic characteristics of the proposed topology are analyzed based on fundamental harmonic approximation. Furthermore, based on the steady-state model, three categories of operation modes are presented and analyzed. In order to realize zero-voltage switching, the series capacitor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{2} $</tex-math></inline-formula> on the secondary side is tuned. A numerical method is used to analyze the impact of different values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta C_{2}$</tex-math></inline-formula> on the turnoff current, and the best value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{2}$</tex-math></inline-formula> is chosen to build a prototype to verify the analysis.

Precise Characteristics Analysis of Series/Series-Parallel Compensated Contactless Resonant Converter

The series/series-parallel (S/SP) compensated contactless resonant converter has a desirable feature of being insensitive to variation of parameters including the transformer's coupling coefficient. However, the error resulting from the use of fundamental harmonic approximation is significant, thus complicating the design procedure and affecting the effectiveness of the control. In this paper, a precise characteristics analysis of the S/SP converter is presented. A generalized equivalent circuit of the S/SP resonant tank is derived, and the cause of the waveform distortion is revealed. Then, more accurate expressions for the key variables of the resonant tank and the output voltage gain are given. Finally, a 1.5 kW contactless resonant converter with S/SP compensation is constructed. Experimental results are in good agreement with the calculated results.

The FHA Analysis of Dual-Bridge LLC Type Resonant Converter

The dual bridge resonant converter is designed in this paper. In this converter the LLC type resonance configuration is proposed .This types is compared with the other configurations and its benefits are narrated in this paper. The steady-state analysis of the LLC configuration is done using fundamental harmonics approximation method and the values for the components of resonance configuration is found and used for simulation. The simulation results shows that the converter is able to achieve the zero voltage switching for the wide load range and attains a good efficiency. DOI: http://dx.doi.org/10.11591/ijpeds.v4i4.6513

A Generalized Approach for the Steady-State Analysis of Dual-Bridge Resonant Converters

In this paper, a dual-bridge DC/DC resonant converter with a generalized series and parallel resonant tank is analyzed. A general approach based on Fundamental Harmonic Approximation is used to find the universal steady-state solutions. The analysis results for particular resonant tank configurations are exemplified with several typical resonant tank configurations respectively. The corresponded soft-switching conditions are discussed too. To illustrate the usefulness of the generalized approach, a dual-bridge (LC)(L)-type resonant converter working in below resonance mode is designed based on the analysis results. Finally, simulation and experimental plots of the design example are included to evaluate the validity and the accuracy of the proposed analysis approach.

A LLC-Type Dual-Bridge Resonant Converter: Analysis, Design, Simulation, and Experimental Results

In this paper, a high-frequency isolated dual-bridge LLC -type resonant converter is proposed. The steady-state analysis of the proposed converter is performed using a modified fundamental harmonics approximation approach, by which the component stress can be obtained quickly without complicated calculation. Necessary and sufficient conditions for zero-voltage switching of all switches are derived too. To illustrate the usefulness of the FHA analysis for a fast design, a design example of a 100 kHz, 200 V input, 40-48 V output 300 W converter is given. Computer simulation and experiment results are included for the purpose of validation. It is shown that this converter is able to maintain zero-voltage switching operation for a wide load range while keeping high efficiency.

Design Methodology of LLC Resonant Converters for Electric Vehicle Battery Chargers

In this paper, an inductor–inductor–capacitor (LLC) resonant dc–dc converter design procedure for an onboard lithium-ion battery charger of a plug-in hybrid electric vehicle (PHEV) is presented. Unlike traditional resistive load applications, the characteristic of a battery load is nonlinear and highly related to the charging profiles. Based on the features of an LLC converter and the characteristics of the charging profiles, the design considerations are studied thoroughly. The worst-case conditions for primary-side zero-voltage switching (ZVS) operation are analytically identified based on fundamental harmonic approximation when a constant maximum power (CMP) charging profile is implemented. Then, the worst-case operating point is used as the design targeted point to ensure soft-switching operation globally. To avoid the inaccuracy of fundamental harmonic approximation approach in the below-resonance region, the design constraints are derived based on a specific operation mode analysis. Finally, a step-by-step design methodology is proposed and validated through experiments on a prototype converting 400 V from the input to an output voltage range of 250–450 V at 3.3 kW with a peak efficiency of 98.2%.

A Modified High-Efficiency LLC Converter With Two Transformers for Wide Input-Voltage Range Applications

This paper proposed a modified LLC converter with two transformers in series, which has four operation configurations, covering the range of four times the minimum input voltage. To optimize the proposed LLC converter in an attempt to achieve good efficiency, a numerical method is developed based on the LLC converter's steady-state equations. In order to minimize the magnetizing current and thus minimize the conduction and core losses, an optimal objective is proposed to find the maximum magnetizing inductance. An optimization procedure and a design example are given. A 250-W 210-V output prototype with input voltage ranging from 25 to 100 V is built to verify the developed numerical model and optimal design method. The dc gain obtained from experimental data agrees pretty well with that from the developed numerical model. Two conventional LLC converters are designed using fundamental harmonic approximation and the proposed optimal design, respectively, to make comparison with the proposed LLC converter and validate the proposed optimal design. Experimental results show that the proposed converter with proposed optimal design can achieve the peak efficiency up to 98%, while maintaining a very wide input voltage range.

Operation Mode Analysis and Peak Gain Approximation of the LLC Resonant Converter

With the advantage of achieving zero voltage switching for a wide input voltage range, the LLC resonant topology has become increasingly popular for use in high power density and high-efficiency power converter applications. However, when the LLC converter is applied to wide input voltage range applications, the widely used fundamental harmonic approximation is incapable of guiding the design due to its inaccuracy. Thus an accurate LLC converter model is desired. In this paper, a generalized mode analysis is presented that provides highly accurate prediction on resonant current and voltage behavior and dc gain characteristic. Also, because operation modes are affected by load, frequency, and gain conditions, the boundaries and distribution of modes are discussed and illustrated. Based on the mode analysis, an approximation method is developed to estimate the peak gain point, which is useful in LLC design. This approximation demonstrates high accuracy within the simulation results. An experimental prototype is built to verify the analysis.

Approximate Analysis of Resonant LLC DC-DC Converter

This paper presents an approximate analysis of LLC resonant converter with capacitive filter operating above and below resonance. An equivalent ac resistance model of the rectifier valid for discontinuous as well as continuous conduction modes is proposed. The dc voltage conversion ratio is then obtained using the fundamental harmonic approximation analysis method. Based on the analysis, LLC converter design plots and guidelines are suggested. The theory is verified by simulation and experiment.

Verification of Operation Modes of Designed LLC Resonant Converter

This paper describes the design of the LLC resonant converter, which is done by means of fundamental harmonic approximation (FHA). Output power of proposed converter is 1kW with output voltage 48 V at switching frequency of 500 kHz. Performance of converter at different operational conditions was verified through simulation analysis by utilization of OrCAD PSpice software. The simulation results of multiple parametrical experiments were obtained and consequently evaluated into graphical interpretation of efficiency of proposed converter.

Generation of higher harmonics of nonlinear shear surface acoustic waves.

An infinite set of coupled equations for envelopes of harmonics is obtained, and the successive approximations procedure for it is demonstrated. For the stationary wave, the amplitude of the third harmonic having a maximum at a certain depth and the correction for the first harmonic due to back action of the third harmonic are found. It is ascertained that the fundamental harmonic approximation is legitimate under the monochromatic excitation.