Three-Dimensional Frequency-Dependent Thermal Model for Planar Transformers in <i>LLC</i> Resonant Converters
Bibliographic record
Abstract
In this paper, a thorough thermal analysis is carried out in order to find an analytical three-dimensional (3-D) frequency-dependent thermal model of planar transformers (PTs) used in high-frequency power converters. Because of the tendency of having higher power density as well as miniaturization of power converters, the components have to work near their thermal limit margins. This issue is more critical for planar magnetics in LLC converters due to their variable high-frequency operation, making thermal modeling and heat transfer analysis tools necessary. The proposed 3-D frequency thermal model is obtained based on the lumped parameters network (LPN) according to different thermal resistances of the PT including convection, conduction, and radiation heat exchanges. It should be noted that not only the 3-D geometry effect of the core is applied to the proposed model, but thermal surface resistances are also considered to model the high-frequency operation effect. Moreover, the lumped capacitance thermal model is used to analyze the transient thermal variation of the transformer. The LLC resonant converter with two PTs, including EE58/11/38 and ER51/10/38 planar cores, is considered to show the compatibility of the proposed 3-D-frequency LPN model. In addition, the temperature distribution of different parts of the transformers is evaluated using finite element method modeling and compared with the proposed 3-D frequency-dependent LPN model. Experimental results confirm the improved accuracy of the proposed LPN model and show the proposed model predicts the temperature distribution in PTs with an error of less than 3%. Considering the improved accuracy and low computational time of the method, the proposed 3-D frequency-dependent model is a powerful and fast design tool to evaluate the temperature distribution for different designs, and so can be used to effectively optimize the transformer from thermal point of view.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".