As a basic unit of solid-state transformer (SST), the single-phase system composed of H-bridge and dual-active-bridge (DAB) is becoming an exciting topic for its high-efficiency, flexible power flow. However, the inherent second-harmonic power brings dc-link voltage ripple and phase shift oscillation, especially for the back-to-back systems with bilateral harmonics. In this paper, the behavior of DAB's high-frequency link under second harmonic is modeled and described, revealing the inevitable dc-bias and current-stress increase. A modulation-based dc-bias eliminating strategy is presented, which uses two sawtooth carriers to generate a transitional period without any calculations. To reduce magnetic material's waste, a second-harmonic correction to transformer design is proposed. Moreover, the optimal inductance for single-phase shift (SPS) with minimal current stress and full-range ZVS is obtained. These strategies enhance the ripple immunity of DAB, enabling the reduction of dc-link capacitance. Comprehensive simulations and experiments are performed to validate the accuracy and effectiveness of these optimizations.