# Closed-form design optimization for LLC converters with wide output voltage range based on FHA

## TL;DR

This paper introduces a new, efficient method for designing LLC converters that work well across a wide range of voltages.

## Contribution

A closed-form analytical design strategy is proposed, enabling optimal LLC converter design without numerical solvers.

## Key findings

- The proposed method achieves full output voltage range under worst-case conditions.
- The converter maintains soft switching across the entire operating range.
- Peak efficiency is achieved near full load with reduced computational cost.

## Abstract

This paper presents a novel design optimization strategy for LLC resonant converters that enhances full-load efficiency while operating across wide input and output voltage ranges. Achieving regulation over a wide output voltage range imposes more stringent design constraints on the converter, demanding higher inductance ratio and wider switching frequency range compared to constant output voltage applications. While numerical optimization techniques are effective for determining the optimal parameters of the converter; however, this effectiveness comes at a substantial computational cost. This work establishes a set of closed-form analytical equations that not only constitute a complete, step-by-step procedure for optimal design without reliance on numerical solvers, but also provide a framework for analyzing design trade-offs. The proposed methodology distinguishes itself from conventional approaches by offering a systematic and non-iterative procedure that is computationally efficient for determining an optimal design. The proposed procedure is validated through the simulation of a 495 W LLC converter specified for a wide operational range with a 320–370 V input and a 35–165 V output. The converter achieved the full output voltage range at the worst-case conditions and attained peak efficiency near the full load, while maintaining soft switching across the entire operating range.