In dynamic wireless power transfer systems, the large-air-gap magnetic field in couplers is characterized by a divergent and complex magnetic path and strong multi-variable coupling, thus resulting in a lack of concise and accurate theoretical design guidance. In response to these challenges, the research takes three-phase meander-type configuration as an example. By combining magnetic vector potential calculations with fast Fourier transform, a closed-form analytical solution for the traveling-wave magnetic field is derived based on an equivalent surface current model, thereby clarifying the multi-variable coupling relationships. On this basis, a rapid and accurate fully analytical design methodology is established, reducing the design cycle from several hours to minutes while maintaining the calculation error within 2%, significantly improving design efficiency. Under the proposed analytical design framework, a systematic design process and guidelines are developed, and a design example of a 2 kW system is implemented. Experimental results show excellent agreement with the design targets, validating the precision and efficiency of the proposed methodology.