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The ZVS and ZCS capability of the switching devices with high operating frequency of the CLLC converters encourages its application in various EV platforms to improve efficiency. In the literature, various authors proposed many methods to control the CLLC converters efficiently, but up to now, no simple and accurate small\u2010signal equivalent circuit modelling is available. As dynamic networks are load\u2010dependent, closed\u2010loop voltage and current controllers provide more stable operations in these converters. In this paper, a detailed mathematical modelling of the CLLC converters with time domain analysis has been presented. The proposed mathematical model accurately predicts the small\u2010signal behaviors seen in pulse\u2010frequency\u2010modulated (PFM) CLLC resonant converters whether the switching frequency is below, near to, or above the resonant frequency. Stable closed\u2010loop controllers for both current and voltage loops in battery charging applications are designed and detailed. A prototype hardware is been built and the experimental results with the load variations with the designed controllers are tested and the results are been discussed in the paper.<\/jats:p>","DOI":"10.1002\/cta.4431","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T18:03:33Z","timestamp":1736791413000},"page":"5969-5976","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Small\u2010Signal Modelling of Bidirectional CLLC Converters for Onboard Charging Application in Electric Vehicles"],"prefix":"10.1002","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5971-6578","authenticated-orcid":false,"given":"Nidumolu","family":"Vijaya\u00a0Anand","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering Prasad V Potluri Siddhartha Institute of Technology  Vijayawada India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yalla","family":"Naveen","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering Indian Institute of Technology (BHU)  Varanasi UP India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,1,13]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/63.712309"},{"key":"e_1_2_6_3_1","doi-asserted-by":"crossref","unstructured":"K. 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