This paper presents analytic solutions for an optimal modulation scheme featuring low switching losses for a bidirec- tional single-phase dual active bridge (DAB) DC-DC converter used for charging high-voltage batteries of electric vehicles. The proposed modulation scheme facilitates zero-voltage switching (ZVS) for either the primary- or secondary-side full bridge of the DAB converter throughout the whole operating range while maintaining low conduction losses. The expressions are derived based on the current required for an ideal ZVS transition and enable for a direct computation of the respective optimal modulation parameters.