The Smart Transformer, a Solid-State transformer with control functionalities, is a promising smart grid technology. One of the main challenge of this system lies in making available a Medium-Voltage dc link, which can be tackled with modular solution. Thus, several isolated dc-dc converter can be used as a basic modules. In this paper, a Quad-Active-Bridge (QAB) dc-dc converter is used as modules for the entire dc-dc conversion stage of a ST. Besides the feature of high power density and soft-switching operation (also found in others converters), this converter offers an additional power path, named 'MV crosslink' through the HF transformer in the Medium-Voltage (MV) side, increasing the power controllability among the MV cell without involving the LV side. To ensure soft-switching for all operation range of the QAB converter, the triangular current mode modulation strategy, previously study for the dual-active-bridge converter, is extended to the QAB converter in this work. In addition, it is considered to use in the MV side the H-Bridge cell and the multilevel neutral-point-clamped cell, to reduce the required voltage rating of the semiconductors. The theoretical analysis is performed for both converters. The theoretical analysis is verified by simulation and experimental results.