The low-voltage dc-dc converter (LDC) in electrical vehicles (EVs) is to convert high dc voltage (270V~430V) from traction battery to low dc voltage (12.5V~15.5V) for the vehicle auxiliary systems. Galvanic isolation is required in the LDC due to safety considerations. Three challenges exist in the LDC design: (1) wide regulation range; (2) high output current; (3) thermal management. The single stage solutions, such as phase-shift full-bridge converter and LLC resonant converter, have been widely studied in the past. A matrix transformer is widely adopted in single-stage LDC design to deal with the large current. At last, the low-profile design allows large footprint area for high power density and ease of cooling design. However, the trade-off between wide regulation range and efficiency exists in single-stage LDC design. Recently, a two-stage solution is proposed to achieve high efficiency and wide regulation range at the same time. The fixed turn ratio LLC stage serves as a dc transformer (DCX) to meet the galvanic isolation requirements and PWM dc-dc stage regulates the output voltages. In this thesis, a variable ratio matrix transformer-based LLC converter is proposed for two-stage LDC efficiency improvement. The transformer secondary copper losses are reduced by taking advantage of the adaptive number of element transformers. In addition, the PWM dc-dc stage achieves better efficiency with variable intermediate bus voltage. The operation principle and design considerations are studied in this thesis. The proposed 1600W two-stage LDC prototype achieves 96.82% full load efficiency under 400V input condition which is 1.2% efficiency higher than the fixed ratio LLC based two-stage design. Last but not least, the prototype shows a comparable efficiency to the fixed ratio LLC based two-stage design even under the low input voltage (270V) condition. / M.S. / The electrical vehicle market is growing rapidly in recent years. However, the driving range is one of the bottlenecks which imperils market growth in the future. Thus, efficient power modules in electric vehicles are desired to extend the driving range. Low voltage dc-dc converter is one of the power modules in electric vehicles which is rated at several kilowatts and converts traction battery voltage for the vehicle auxiliary system, such as air conditioner, headlights, power steering and etc. In this thesis, a variable ratio matrix transformer-based LLC converter is proposed for the two-stage low-voltage dc-dc converter efficiency improvement. Consequently, the driving range of electric vehicles is further extended.