The matrix converter (MC) presents a promising topology that needs to overcome certain barriers (complexity of the modulation and control techniques, protection systems, etc.) in order to gain a foothold in the industry. Traditionally, the MC has been controlled by means of a DSP, together with a field-programmable gate array (FPGA). The sole aim of the latter is to perform the safe commutation of the converter. This involves a waste of resources, as the excellent features of the FPGA are infrautilized by the control system. This paper deals with the implementation of the double-sided space vector modulation (DS SVM), commutation, reference-frame changes, and protection of the MC through a series of hardware blocks (cores) integrally implemented in an FPGA. The designed cores are technology-independent descriptions, which means that the developed design can be used in the FPGAs of any manufacturer. Moreover, the proposed design, which has been validated experimentally, has obviated the need to use a DSP. Likewise, given that all the processing capabilities have been integrated in a single chip, it can be said that an FPGA-based system on a programmable chip (SoPC) has been designed. Due to the computational capacity of the developed cores, processing time is reduced to the order of nanoseconds. This allows a response in real time and very high modulation frequencies can be attained. Moreover, these cores operate independently, and simultaneously, therefore obviating the need for sequential control and its resulting latencies and leading to an increase in the safety of the MC.