Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method

Yingzong Jiao; Minghui Wang; Binbin Li; Zexiang Zhu; Hefeng Zhai

doi:10.1109/EI268505.2025.11425086

Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method

Yingzong Jiao^*
, Minghui Wang
, Binbin Li^*
, Zexiang Zhu
, Hefeng Zhai

^*Corresponding author for this work

School of Electrical Engineering and Automation, Harbin Institute of Technology
Electric Power Research Institute of CSG

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper addresses the output impedance modeling of LLC resonant converters operating in Discontinuous Conduction Mode (DCM). An extended describing function method, based on continuous time-domain waveform Fourier analysis, is proposed. The steady-state operation of the LLC resonant converter is first analyzed in detail via piecewise linear analysis and boundary condition determination, yielding the steady-state output current expression. Subsequently, a small-signal voltage perturbation is applied to the output side. By employing piecewise linear analysis, boundary condition analysis, and Fourier series expansion, the small-signal expression of the output current is derived. Linearization of this small-signal output current component ultimately yields the output admittance expression, thereby completing the output impedance model. Simulations verified the superior accuracy of the proposed model across the 1-20 kHz range compared to the traditional extended describing function method, validating the effectiveness and accuracy of the approach.

Original language	English
Title of host publication	2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3197-3203
Number of pages	7
ISBN (Electronic)	9798331548599
DOIs	https://doi.org/10.1109/EI268505.2025.11425086
State	Published - 2025
Externally published	Yes
Event	2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025 - Jilin, China Duration: 5 Dec 2025 → 8 Dec 2025

Publication series

Name	2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025

Conference

Conference	2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025
Country/Territory	China
City	Jilin
Period	5/12/25 → 8/12/25

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 7 Affordable and Clean Energy

Keywords

discontinuous conduction
impedance modeling
LLC resonant converter

Access to Document

10.1109/EI268505.2025.11425086

Cite this

Jiao, Y., Wang, M., Li, B., Zhu, Z., & Zhai, H. (2025). Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method. In 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025 (pp. 3197-3203). (2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/EI268505.2025.11425086

Jiao, Yingzong ; Wang, Minghui ; Li, Binbin et al. / Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method. 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025. Institute of Electrical and Electronics Engineers Inc., 2025. pp. 3197-3203 (2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025).

@inproceedings{b055306cd294464fabc55d6b428f246e,

title = "Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method",

abstract = "This paper addresses the output impedance modeling of LLC resonant converters operating in Discontinuous Conduction Mode (DCM). An extended describing function method, based on continuous time-domain waveform Fourier analysis, is proposed. The steady-state operation of the LLC resonant converter is first analyzed in detail via piecewise linear analysis and boundary condition determination, yielding the steady-state output current expression. Subsequently, a small-signal voltage perturbation is applied to the output side. By employing piecewise linear analysis, boundary condition analysis, and Fourier series expansion, the small-signal expression of the output current is derived. Linearization of this small-signal output current component ultimately yields the output admittance expression, thereby completing the output impedance model. Simulations verified the superior accuracy of the proposed model across the 1-20 kHz range compared to the traditional extended describing function method, validating the effectiveness and accuracy of the approach.",

keywords = "discontinuous conduction, impedance modeling, LLC resonant converter",

author = "Yingzong Jiao and Minghui Wang and Binbin Li and Zexiang Zhu and Hefeng Zhai",

note = "Publisher Copyright: {\textcopyright} 2025 IEEE.; 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025 ; Conference date: 05-12-2025 Through 08-12-2025",

year = "2025",

doi = "10.1109/EI268505.2025.11425086",

language = "英语",

series = "2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3197--3203",

booktitle = "2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025",

address = "美国",

}

Jiao, Y, Wang, M, Li, B, Zhu, Z & Zhai, H 2025, Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method. in 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025. 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025, Institute of Electrical and Electronics Engineers Inc., pp. 3197-3203, 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025, Jilin, China, 5/12/25. https://doi.org/10.1109/EI268505.2025.11425086

Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method. / Jiao, Yingzong; Wang, Minghui; Li, Binbin et al.
2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025. Institute of Electrical and Electronics Engineers Inc., 2025. p. 3197-3203 (2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method

AU - Jiao, Yingzong

AU - Wang, Minghui

AU - Li, Binbin

AU - Zhu, Zexiang

AU - Zhai, Hefeng

PY - 2025

Y1 - 2025

N2 - This paper addresses the output impedance modeling of LLC resonant converters operating in Discontinuous Conduction Mode (DCM). An extended describing function method, based on continuous time-domain waveform Fourier analysis, is proposed. The steady-state operation of the LLC resonant converter is first analyzed in detail via piecewise linear analysis and boundary condition determination, yielding the steady-state output current expression. Subsequently, a small-signal voltage perturbation is applied to the output side. By employing piecewise linear analysis, boundary condition analysis, and Fourier series expansion, the small-signal expression of the output current is derived. Linearization of this small-signal output current component ultimately yields the output admittance expression, thereby completing the output impedance model. Simulations verified the superior accuracy of the proposed model across the 1-20 kHz range compared to the traditional extended describing function method, validating the effectiveness and accuracy of the approach.

AB - This paper addresses the output impedance modeling of LLC resonant converters operating in Discontinuous Conduction Mode (DCM). An extended describing function method, based on continuous time-domain waveform Fourier analysis, is proposed. The steady-state operation of the LLC resonant converter is first analyzed in detail via piecewise linear analysis and boundary condition determination, yielding the steady-state output current expression. Subsequently, a small-signal voltage perturbation is applied to the output side. By employing piecewise linear analysis, boundary condition analysis, and Fourier series expansion, the small-signal expression of the output current is derived. Linearization of this small-signal output current component ultimately yields the output admittance expression, thereby completing the output impedance model. Simulations verified the superior accuracy of the proposed model across the 1-20 kHz range compared to the traditional extended describing function method, validating the effectiveness and accuracy of the approach.

KW - discontinuous conduction

KW - impedance modeling

KW - LLC resonant converter

UR - https://www.scopus.com/pages/publications/105035801095

U2 - 10.1109/EI268505.2025.11425086

DO - 10.1109/EI268505.2025.11425086

M3 - 会议稿件

AN - SCOPUS:105035801095

T3 - 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025

SP - 3197

EP - 3203

BT - 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025

Y2 - 5 December 2025 through 8 December 2025

ER -

Jiao Y, Wang M, Li B, Zhu Z, Zhai H. Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method. In 2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025. Institute of Electrical and Electronics Engineers Inc. 2025. p. 3197-3203. (2025 IEEE 9th Conference on Energy Internet and Energy System Integration, EI2 2025). doi: 10.1109/EI268505.2025.11425086

Output Impedance Modeling of LLC Resonant Converter Based on Fourier Analysis of Continuous-Time Domain Waveforms Using the Extended Describing Function Method

Abstract

Publication series

Conference

UN SDGs

Keywords

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