[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84672-en":3,"doc-seo-84672-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84672,4810365810221,"Aurora","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Exact Closed-Form Feedforward Inversion for Dual-Bridge Series Resonant DC-DC Converter via State-Plane Analysis","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.","Exact Closed-Form Feedforward Inversion for Dual-Bridge Series Resonant DC/DC Converter via  \nState-Plane Analysis  \nAlex Borisevich, [akpc806b@gmail.com](akpc806b@gmail.com)  \narXiv :2607 .02948v2 [ ee ss . SY] 9 Jul 2026  \nAbstract—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.  \nIndex Terms—Series resonant converter, state-plane analysis, dual active bridge, first harmonic approximation, DC-DC converter, soft switching.  \nI. INTRODUCTION  \nThe 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.  \nThe 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.  \nExisting 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.  \nState-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  \nFig. 1. Dual-bridge series resonant DC/DC converter circuit.  \ntogether with periodicity constraints. This approach has been successfully applied to SRC converters with passive rectifiers [8]–[10] and to LLC resonant converters [11] .  \nHowever, 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.  \nIn 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:  \n1) Closed-form expressions for the exact steady-state trajectory, output transconductance, and commutation angles under arbitrary (d, s,β,ω) modulation.  \n2) A rigorous proof that the FHA is recovered as the fundamental-frequency term of the exact solution, with explicit error bounds.  \n3) Quantitative characteri","cbCaijsU978wDCa9","https://ap.wps.com/l/cbCaijsU978wDCa9","pdf",1030533,5,1,22,"English","en",105,"# Introduction\n## Converter topology and modulation\n### Circuit description\n### Switching waveforms and control variables\n## Exact state-plane analysis and relationship to FHA","[{\"question\":\"What problem does the paper address for the dual-bridge series resonant DC/DC converter?\",\"answer\":\"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.\"},{\"question\":\"Which control variables define the modulation of the DB SRC in this work?\",\"answer\":\"The modulation uses four independent variables: primary duty cycle d, secondary shorting time s, phase shift β, and switching angular frequency ω.\"},{\"question\":\"How does the exact state-plane inversion compare with FHA-based feedforward?\",\"answer\":\"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.\"}]",1784197586,55,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"exact-closed-form-feedforward-inversion-for-dual-bridge-series-resonant-dc-dc-converter-via-state-plane-analysis","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/exact-closed-form-feedforward-inversion-for-dual-bridge-series-resonant-dc-dc-converter-via-state-plane-analysis/84672/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-29","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the paper address for the dual-bridge series resonant DC/DC converter?","Question",{"text":76,"@type":77},"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.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which control variables define the modulation of the DB SRC in this work?",{"text":81,"@type":77},"The modulation uses four independent variables: primary duty cycle d, secondary shorting time s, phase shift β, and switching angular frequency ω.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the exact state-plane inversion compare with FHA-based feedforward?",{"text":85,"@type":77},"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 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