Steadily increasing requirements for grid connected converters, their growing unit power and output voltage call for flexible high-power medium-voltage grid emulators. Four-quadrant Cascaded H-Bridge (CHB) topology features high output voltage resolution and high effective switching frequency which enable high-dynamic high-fidelity grid emulation. This paper conducts a direct performance comparison between synchronization based either on primary or secondary transformer side voltage measurements, and shows that despite non-idealities (turn ratios, phase-shift angles and different stray inductances) in a typical phase-shifting multiwinding transformer, bidirectional CHB cells can be effectively synchronized to their respective supply voltages using transformer primary side voltage measurements and nameplate values in a high dynamics application. Consequently, cell input filters can be omitted, making the grid emulator more compact, cheaper, faster and exhibiting more robust grid synchronization and operation. Theoretical developments and designs are verified by means of high fidelity time domain simulations that include magnetic coupling of the windings through the core and through the air.