Exact Closed-Form Feedforward Inversion for Dual-Bridge Series Resonant DC-DC Converter via State-Plane Analysis

Jul 16, 2026

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This paper derives exact closed-form feedforward inversion maps for a dual-bridge series resonant DC/DC converter (DB SRC) using state-plane trajectory analysis. The converter is driven by four modulation variables: primary duty cycle d, secondary shorting time s, phase shift β, and switching frequency ω. Compared with first harmonic approximation (FHA), the exact state-plane method yields a frequency-dependent inversion model that becomes algebraically identical to FHA at resonance. Above-resonance operation removes the 5–72% commutation-angle errors inherent to FHA feedforward, producing closed-form real-time implementable control maps.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

Introduction

Converter topology and modulation

Circuit description

Switching waveforms and control variables

Exact state-plane analysis and relationship to FHA

Exact Closed-Form Feedforward Inversion for Dual-Bridge Series Resonant DC/DC Converter via State-Plane Analysis Alex Borisevich, [akpc806b@gmail.com](akpc806b@gmail.com) arXiv :2607 .02948v2 [ ee ss . SY] 9 Jul 2026 Abstract—This paper derives exact closed-form feedforward inversion maps for the dual-bridge series resonant converter (DB SRC) using state-plane trajectory analysis. The converter employs four modulation variables: primary duty cycle d, secondary shorting time s, phase shift β, and switching frequency ω . While the established first harmonic approximation (FHA) provides frequency-independent inversion, the exact state-plane approach yields frequency-dependent inversion model that is proven algebraically identical to FHA at resonance frequency. For practical above-resonance operation, the exact inversions eliminate the 5–72% commutation angle errors inherent in the FHA-based feedforward. The resulting controller architecture mirrors the parallel nonlinear compensation structure of the FHA-based design, with feedforward maps now operating on resonant-time quantities that naturally couple commutation and frequency control. All results are expressed in closed form suitable for real-time implementation. Index Terms—Series resonant converter, state-plane analysis, dual active bridge, first harmonic approximation, DC-DC converter, soft switching. I. INTRODUCTION The dual-bridge (DB) series resonant converter (SRC) offers significant advantages for high-power isolated DC/DC applications including electric vehicle chargers, battery energy storage, and DC power distribution [1]–[3] . The topology features controlled full-bridge circuits on both primary and secondary sides connected through a series LC resonant tank and a transformer, enabling bidirectional power flow, voltage boost capability, and near-sinusoidal transformer current. The modulation scheme employs four independent control variables: primary bridge duty cycle d, secondary bridge shorting time s, phase shift β between bridges, and switching frequency ω [4] . This provides sufficient degrees of freedom to simultaneously regulate output power and optimize efficiency through soft-switching operation. Existing analytical models for the DB SRC are predominantly based on the first harmonic approximation (FHA), which assumes purely sinusoidal tank current [5] . While computationally simple and adequate for many operating conditions, the FHA inherently neglects higher harmonics and cannot provide exact values of commutation currents needed for ZVS analysis. State-plane trajectory analysis, pioneered by Oruganti and Lee [6], [7], provides an exact geometric method for analyzing resonant converters. The key insight is that in normalized coordinates, the LC tank trajectory under constant applied voltage is a circular arc, and the steady-state is found by stitching arcs Fig. 1. Dual-bridge series resonant DC/DC converter circuit. together with periodicity constraints. This approach has been successfully applied to SRC converters with passive rectifiers [8]–[10] and to LLC resonant converters [11] . However, the state-plane method has not been systematically applied to the DB SRC with all four modulation degrees of freedom (d, s, β , ω), where both bridges are actively controlled. The secondary-side modulation introduces additional switching intervals and complicates the trajectory structure compared to passive rectifier topologies. In this paper, we develop the complete exact state-plane analysis for the DB SRC under generalized modulation and establish its precise relationship to the FHA model from [5] . The main contributions are: 1) Closed-form expressions for the exact steady-state trajectory, output transconductance, and commutation angles under arbitrary (d, s,β,ω) modulation. 2) A rigorous proof that the FHA is recovered as the fundamental-frequency term of the exact solution, with explicit error bounds. 3) Quantitative characteri

FAQs

What problem does the paper address for the dual-bridge series resonant DC/DC converter?

It addresses the accuracy limits of FHA-based feedforward inversion by deriving exact closed-form inversion maps that correctly capture commutation behavior needed for ZVS analysis.

Which control variables define the modulation of the DB SRC in this work?

The modulation uses four independent variables: primary duty cycle d, secondary shorting time s, phase shift β, and switching angular frequency ω.

How does the exact state-plane inversion compare with FHA-based feedforward?

The exact model is frequency-dependent and is proven algebraically identical to FHA at resonance frequency, while above-resonance it eliminates the 5–72% commutation-angle errors caused by FHA assumptions.

Jul 16, 2026

Upload by Aurora