{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/137822"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/137822","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"PCB Integrated Matrix Transformer for a High-Power Single Phase CLLC Resonant Converter with the Novel Application of Circular Orthogonal Parallel Airgaps","abstract":"This work presents the design, analysis, and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase 11kW 250kHz bi-directional DC/DC CLLC resonant converter (1PCLLC) for use in electric vehicle on-board chargers (OBC's). By utilizing a variable DC-link, system efficiency is maximized and regulated according to battery load requirements. A gain range of 0.72 – 1.35 is calculated, netting a transformer configuration with a leakage inductance ratio, L_n, (L_n=L_m/L_r) range of 3-5. Further converter loss calculations condense the L_n range to 4 and 5. A PCB-based matrix transformer structure with built-in controllable leakage inductance is utilized. With the distance of the airgaps dictating magnetizing inductance (L_m ), winding arrangements and reluctance variations are parameterized to achieve L_n. The reluctance model is revisited by integrating leakage flux \"core walls\" into the reluctance model, significantly improving the accuracy of calculated L_n values. Two transformer configurations are evaluated: a 3UI-core-based matrix design and a 2UI-core-based matrix design, both consisting of 1UI elemental structures with non-perfectly interleaved windings. The 2UI-core-based configuration demonstrates a greater and more even flux distribution across the core plate which results in overall lower transformer losses, netting it the optimal design choice for 11kW power applications. To further improve transformer power density, circular orthogonal (C.O) airgap and circular orthogonal parallel (C.O.P) airgap core structures are introduced. Introductory designs aim to mitigate high – frequency AC winding losses caused by fringing field from the airgaps by distributing the airgap evenly above the long edge of the PCB copper traces; compared to traditional parallel (T.P) airgap core structures, where the airgap is positioned on the matrix core leg, leading to current crowding along the inner short edge of the PCB copper traces. C.O airgap core structure exhibited a dangerously low leakage inductance value, which resulted in a revaluation of how the flux is realistically distributed throughout the transformer. Parallel airgaps from the T.P airgap core structure are added to the C.O airgap core structure netting the C.O.P airgap core structure. An 11kW 250kHz SiC-based single phase full-bridge CLLC prototype converter is used to experimentally validate the proposed transformer designs. With T.P airgap core structure, the converter achieves 97.9% peak efficiency and meets transformer specifications for the required gain parameters within an acceptable frequency range. With C.O.P airgap core structure, the converter achieves 98.3% peak efficiency while also meeting the required gain parameters within an acceptable frequency range, verifying the prototype design of C.O.P airgap core structure for novel applications in matrix transformers.","abstract_html":"This work presents the design, analysis, and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase 11kW 250kHz bi-directional DC/DC CLLC resonant converter (1PCLLC) for use in electric vehicle on-board chargers (OBC's). By utilizing a variable DC-link, system efficiency is maximized and regulated according to battery load requirements. A gain range of 0.72 – 1.35 is calculated, netting a transformer configuration with a leakage inductance ratio, L_n, (L_n=L_m/L_r) range of 3-5. Further converter loss calculations condense the L_n range to 4 and 5. A PCB-based matrix transformer structure with built-in controllable leakage inductance is utilized. With the distance of the airgaps dictating magnetizing inductance (L_m ), winding arrangements and reluctance variations are parameterized to achieve L_n. The reluctance model is revisited by integrating leakage flux "core walls" into the reluctance model, significantly improving the accuracy of calculated L_n values. Two transformer configurations are evaluated: a 3UI-core-based matrix design and a 2UI-core-based matrix design, both consisting of 1UI elemental structures with non-perfectly interleaved windings. The 2UI-core-based configuration demonstrates a greater and more even flux distribution across the core plate which results in overall lower transformer losses, netting it the optimal design choice for 11kW power applications. To further improve transformer power density, circular orthogonal (C.O) airgap and circular orthogonal parallel (C.O.P) airgap core structures are introduced. Introductory designs aim to mitigate high – frequency AC winding losses caused by fringing field from the airgaps by distributing the airgap evenly above the long edge of the PCB copper traces; compared to traditional parallel (T.P) airgap core structures, where the airgap is positioned on the matrix core leg, leading to current crowding along the inner short edge of the PCB copper traces. C.O airgap core structure exhibited a dangerously low leakage inductance value, which resulted in a revaluation of how the flux is realistically distributed throughout the transformer. Parallel airgaps from the T.P airgap core structure are added to the C.O airgap core structure netting the C.O.P airgap core structure. An 11kW 250kHz SiC-based single phase full-bridge CLLC prototype converter is used to experimentally validate the proposed transformer designs. With T.P airgap core structure, the converter achieves 97.9% peak efficiency and meets transformer specifications for the required gain parameters within an acceptable frequency range. With C.O.P airgap core structure, the converter achieves 98.3% peak efficiency while also meeting the required gain parameters within an acceptable frequency range, verifying the prototype design of C.O.P airgap core structure for novel applications in matrix transformers.","abstract_has_math":false,"creators":["Buchman, Anthony Ludwig"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Electrical Engineering","degree_department":"Electrical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Li, Qiang"],"committee_members":["Dimarino, Christina Marie","Lu, Guo Quan"],"year":2025,"date_issued":"2025-09-23","date_published":"2025-09-23","updated_at":"2026-07-22T22:19:24Z","subjects":["High Frequency Resonant Converter","CLLC","DC/DC Converter","PCB Integrated Magnetics","On-board Charger","Matrix Transformer","Fringing Flux Reduction","Segmented Airgap","Traditional Parallel (T.P) Airgaps","Circular Orthogonal (C.O) Airgaps","Circular Ortho"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:44635"],"render_values":[{"text":"vt_gsexam:44635","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/137822","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Li, Qiang"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Dimarino, Christina Marie","Lu, Guo Quan"]},{"key":"dc:contributor.department","label":"Department","values":["Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["Buchman, Anthony Ludwig"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-09-24T08:00:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2025-09-24T08:00:16Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-09-23"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["High Frequency Resonant Converter","CLLC","DC/DC Converter","PCB Integrated Magnetics","On-board Charger","Matrix Transformer","Fringing Flux Reduction","Segmented Airgap","Traditional Parallel (T.P) Airgaps","Circular Orthogonal (C.O) Airgaps","Circular Ortho"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:44635"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/137822"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work presents the design, analysis, and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase 11kW 250kHz bi-directional DC/DC CLLC resonant converter (1PCLLC) for use in electric vehicle on-board chargers (OBC's). By utilizing a variable DC-link, system efficiency is maximized and regulated according to battery load requirements. A gain range of 0.72 – 1.35 is calculated, netting a transformer configuration with a leakage inductance ratio, L_n, (L_n=L_m/L_r) range of 3-5. Further converter loss calculations condense the L_n range to 4 and 5. A PCB-based matrix transformer structure with built-in controllable leakage inductance is utilized. With the distance of the airgaps dictating magnetizing inductance (L_m ), winding arrangements and reluctance variations are parameterized to achieve L_n. The reluctance model is revisited by integrating leakage flux \"core walls\" into the reluctance model, significantly improving the accuracy of calculated L_n values. Two transformer configurations are evaluated: a 3UI-core-based matrix design and a 2UI-core-based matrix design, both consisting of 1UI elemental structures with non-perfectly interleaved windings. The 2UI-core-based configuration demonstrates a greater and more even flux distribution across the core plate which results in overall lower transformer losses, netting it the optimal design choice for 11kW power applications. To further improve transformer power density, circular orthogonal (C.O) airgap and circular orthogonal parallel (C.O.P) airgap core structures are introduced. Introductory designs aim to mitigate high – frequency AC winding losses caused by fringing field from the airgaps by distributing the airgap evenly above the long edge of the PCB copper traces; compared to traditional parallel (T.P) airgap core structures, where the airgap is positioned on the matrix core leg, leading to current crowding along the inner short edge of the PCB copper traces. C.O airgap core structure exhibited a dangerously low leakage inductance value, which resulted in a revaluation of how the flux is realistically distributed throughout the transformer. Parallel airgaps from the T.P airgap core structure are added to the C.O airgap core structure netting the C.O.P airgap core structure. An 11kW 250kHz SiC-based single phase full-bridge CLLC prototype converter is used to experimentally validate the proposed transformer designs. With T.P airgap core structure, the converter achieves 97.9% peak efficiency and meets transformer specifications for the required gain parameters within an acceptable frequency range. With C.O.P airgap core structure, the converter achieves 98.3% peak efficiency while also meeting the required gain parameters within an acceptable frequency range, verifying the prototype design of C.O.P airgap core structure for novel applications in matrix transformers."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Driven by major investments in battery technology, renewable energy, and zero-emission systems, electric vehicles have revolutionized the transportation sector worldwide. As a result, the DC/DC stage of the on-board-charger (OBC), which enables high-efficiency fast charging and galvanic isolation in electric vehicles, has seen substantial research and development. This work proposes the design and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase CLLC resonant converter (1PCLLC). The reluctance model is used to derive magnetic matrix parameters, with further integration of the leakage flux \"core walls\" increasing the accuracy of calculated leakage inductance. A comparison between 3UI and 2UI core structures shows that the 2UI configuration exhibits a lower overall loss across the same total footprint for 11kW power. To increase the power density of the transformer, the introductory design and novel application of circular orthogonal parallel (C.O.P) airgaps in the core structure is proposed. With traditional parallel (T.P) airgap core structure, the converter achieves a peak efficiency of 97.9%. With C.O.P airgap core structure, the converter achieves a peak efficiency of 98.3%, verifying the prototype design of the C.O.P core structure for novel use in matrix transformers. Both transformer structures achieve the necessary gains in a reasonable frequency range."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["PCB Integrated Matrix Transformer for a High-Power Single Phase CLLC Resonant Converter with the Novel Application of Circular Orthogonal Parallel Airgaps"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Li, Qiang"],"dc:contributor.committeemember":["Dimarino, Christina Marie","Lu, Guo Quan"],"dc:contributor.department":["Electrical Engineering"],"dc:creator":["Buchman, Anthony Ludwig"],"dc:date.accessioned":["2025-09-24T08:00:16Z"],"dc:date.available":["2025-09-24T08:00:16Z"],"dc:date.issued":["2025-09-23"],"dc:description.abstract":["This work presents the design, analysis, and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase 11kW 250kHz bi-directional DC/DC CLLC resonant converter (1PCLLC) for use in electric vehicle on-board chargers (OBC's). By utilizing a variable DC-link, system efficiency is maximized and regulated according to battery load requirements. A gain range of 0.72 – 1.35 is calculated, netting a transformer configuration with a leakage inductance ratio, L_n, (L_n=L_m/L_r) range of 3-5. Further converter loss calculations condense the L_n range to 4 and 5. A PCB-based matrix transformer structure with built-in controllable leakage inductance is utilized. With the distance of the airgaps dictating magnetizing inductance (L_m ), winding arrangements and reluctance variations are parameterized to achieve L_n. The reluctance model is revisited by integrating leakage flux \"core walls\" into the reluctance model, significantly improving the accuracy of calculated L_n values. Two transformer configurations are evaluated: a 3UI-core-based matrix design and a 2UI-core-based matrix design, both consisting of 1UI elemental structures with non-perfectly interleaved windings. The 2UI-core-based configuration demonstrates a greater and more even flux distribution across the core plate which results in overall lower transformer losses, netting it the optimal design choice for 11kW power applications. To further improve transformer power density, circular orthogonal (C.O) airgap and circular orthogonal parallel (C.O.P) airgap core structures are introduced. Introductory designs aim to mitigate high – frequency AC winding losses caused by fringing field from the airgaps by distributing the airgap evenly above the long edge of the PCB copper traces; compared to traditional parallel (T.P) airgap core structures, where the airgap is positioned on the matrix core leg, leading to current crowding along the inner short edge of the PCB copper traces. C.O airgap core structure exhibited a dangerously low leakage inductance value, which resulted in a revaluation of how the flux is realistically distributed throughout the transformer. Parallel airgaps from the T.P airgap core structure are added to the C.O airgap core structure netting the C.O.P airgap core structure. An 11kW 250kHz SiC-based single phase full-bridge CLLC prototype converter is used to experimentally validate the proposed transformer designs. With T.P airgap core structure, the converter achieves 97.9% peak efficiency and meets transformer specifications for the required gain parameters within an acceptable frequency range. With C.O.P airgap core structure, the converter achieves 98.3% peak efficiency while also meeting the required gain parameters within an acceptable frequency range, verifying the prototype design of C.O.P airgap core structure for novel applications in matrix transformers."],"dc:description.abstractgeneral":["Driven by major investments in battery technology, renewable energy, and zero-emission systems, electric vehicles have revolutionized the transportation sector worldwide. As a result, the DC/DC stage of the on-board-charger (OBC), which enables high-efficiency fast charging and galvanic isolation in electric vehicles, has seen substantial research and development. This work proposes the design and optimization of a PCB-based matrix transformer with integrated controllable leakage inductance for a single-phase CLLC resonant converter (1PCLLC). The reluctance model is used to derive magnetic matrix parameters, with further integration of the leakage flux \"core walls\" increasing the accuracy of calculated leakage inductance. A comparison between 3UI and 2UI core structures shows that the 2UI configuration exhibits a lower overall loss across the same total footprint for 11kW power. To increase the power density of the transformer, the introductory design and novel application of circular orthogonal parallel (C.O.P) airgaps in the core structure is proposed. With traditional parallel (T.P) airgap core structure, the converter achieves a peak efficiency of 97.9%. With C.O.P airgap core structure, the converter achieves a peak efficiency of 98.3%, verifying the prototype design of the C.O.P core structure for novel use in matrix transformers. Both transformer structures achieve the necessary gains in a reasonable frequency range."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:44635"],"dc:identifier.uri":["https://hdl.handle.net/10919/137822"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["High Frequency Resonant Converter","CLLC","DC/DC Converter","PCB Integrated Magnetics","On-board Charger","Matrix Transformer","Fringing Flux Reduction","Segmented Airgap","Traditional Parallel (T.P) Airgaps","Circular Orthogonal (C.O) Airgaps","Circular Ortho"],"dc:title":["PCB Integrated Matrix Transformer for a High-Power Single Phase CLLC Resonant Converter with the Novel Application of Circular Orthogonal Parallel Airgaps"],"dc:type":["Thesis"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:19:24Z"}