A design methodology for transformers including integrated and center-tapped structures for LLC resonant converters is proposed. In the LLC resonant converter, the resonant inductor in the primary side can be merged in the transformer as a leakage inductance. And, the absence of the secondary filter inductor creates low voltage stress on the secondary rectifiers and is cost-effective. A center-tapped structure of the transformer secondary side is widely used in commercial applications because of its higher efficiency and lower cost than full-bridge structures in the rectifying stages. However, this transformer structure has problems of resonance imbalance and transformer inefficiency caused by leakage inductance imbalance in the secondary side and the position of the air-gap in the transformer, respectively. In this paper, gain curves and soft-switching conditions are derived by first harmonic approximation (FHA) and operating circuit simulation. In addition, the effects of the transformer including integrated and center-tapped structures are analyzed by new FHA models and simulations to obtain an optimal design. Finally, the effects of the air-gap position are analyzed by an electromagnetic field simulator. The proposed analysis and design are verified by experimental results with a 385W LLC resonant converter.