The purpose of this thesis is to construct the homology groups of a complex over an R-module. The thesis begins with hyperplanes in Euclidean n-space. Simplexes and complexes are defined, and orientations are given to each simplex of a complex. The chains of a complex are defined, and each chain is assigned a boundary. The function which assigns to each chain a boundary defines the set of r-dimensional cycles and the set of r—dimensional bounding cycles. The quotient of those two submodules is the r-dimensional homology group.

The research presented in this thesis leverages silicon-germanium (SiGe) heterojunction bipolar transistor (HBT) technology to develop microwave front-end electronics for active phased-array antennas. The highly integrated electronics will reduce costs and improve the feasibility of snow measurements from airborne and space-borne platforms. Chapter 1 presents the motivation of this research, focusing on the technological needs of snow measurement missions. The fundamentals and benefits of SiGe HBTs and phased-array antennas for these missions are discussed as well. Chapter 2 discusses SiGe power amplifier design considerations for radar systems. Basic power amplifier design concepts, power limitations in SiGe HBTs, and techniques for increasing the output power of SiGe HBT PAs are reviewed. Chapter 3 presents the design and characterization of a robust medium power X-band SiGe power amplifier for integration into a SiGe transmit/receive module. The PA design process applies the concepts presented in Chapter 2. A detailed investigation into measurement-to-simulation discrepancies is outlined as well. Chapter 4 discusses the development and characterization of a single-chip X-band SiGe T/R module for integration into a very thin, lightweight active phased array antenna panel. The system-on-package antenna combines the high performance and integration potential of SiGe technologies with advanced substrates and packaging techniques to develop a high performance scalable antenna panel using relatively low-cost materials and silicon-based electronics. The antenna panel presented in this chapter will enable airborne SCLP measurements and advance the technology towards an eventual space-based SCLP measurement instrument that will satisfy a critical Earth science need. Finally, Chapter 5 provides concluding remarks and discusses future research directions.

The master thesis expresses the opinion on application of the Free Flight concept in European Airspace. In the beginning, the reason and the circumstances for concept application are characterized from both theoretical and practical approach. Afterwards, the key technology elements are defined as well as the ideal approach for developing them. Especially system ASAS was a subject of the deep investigation. Then the system ADS-B is introduced with all related issue from a performance point of view. Finally, the main factors affecting the capacity of the ASAS system in specific area of Airspace are investigated.