The need for high-speed digitizers and transceivers is a fundamental phenomenon in electronics nowadays. However, most of the state-of-the-art devices in that cathegory are not reconfigurable as they were designed to implement common algorithms on the digitized data. The aim of this thesis is to implement such high-speed digitizing based on reconfigurable devices.
The author of this thesis has designed the schematics of a custom Printed Circuit Board (PCB) for the FlexRIO product family of National Instrument (NI), called FlexRIO Adapter Module (FAM). The design includes writing firmware in VHDL and with the graphical programming of LabVIEW FPGA software for the FlexRIO FPGA Module to interface it with the FAM, as well as interfacing the whole through the PXI host interface to the NI software called LabVIEW. The newly introduced FAM, when manufactured, will be the currently fastest broadband transceiver as well as digitizer for the NI FlexRIO. It unifies various functions already seen on previous NI-designed FAM cards on one board, and also introduce new features for maximized flexibility. It can be used in various applications, including Data Acquisition Systems (DAQ), RF transceiving and ultra-high speed control.
Providing theoretical background for modelling the design’s various parts, the author used both well-known mathematical tools and his own mathematical constructs. He introduced a new representation of Boolean algebra, the Boolean Module Theory (BM). In the Boolean module, the Boolean functions can be studied as a linear algebra over Boolean matrices, in a unique way not defined before. One application of the Boolean module is that, combining it with a Hilbert space-like module of time dependency, they can model the notion of any sequential logic. Another application is the proper mathematical formalism of what is known today as Boolean Differential Calculus (BDC). It has been shown that the Boolean module is the module of differential forms over the n-dimensional Boolean cube. Thus, the Boolean Differential Forms can be studied in the context of the Boolean Module. The author shows that other applications are possible also.