ABSTRACT.The theory and applications is mainly researched in this thesis, which contains theory research and engineering design. In theory research, the various methods of designing matching networks are discussed. The engineering design contains two parts, one is the development of matching networks for multicouplers in VHF and UHF, and the other is the design of microwave FET amplifiers. The former belongs to the design of matching networks for the passive load, and the latter active load. The main contributions of the author's work are as follows:(I)The elements?values and structure of Chebyshev and Butterworth matching networks being not optimum are pointed out, and the method of dealing these questions is presented.(2)The ra,idon, initial estiniates method is put forward and combined with Powell algorithm, which is applied to optimize high-degree nonlinear objective functions with a very good result. In the meantime, it offers an effective method to optimize complicated matching networks.(3)Some new kinds of objective function are given, and the measure to increase yield of design-cenlering value design method is adopted for designing broad-band matching networks with a distinctly high yield.(4)Two matching networks for four-channel multicouplers (VHF and Ill-IF) are designed. The difficulties and measures of designing them are discussed. The rules of choosing the structures of matching networks are given. The constructions of objective functions for optimization are given in detail. And practical measures for increasing design yield are presented. So it is almost not necessary for the designed devices to be adjusted with meeting the requirements.(5)The method of designing broad-band microwave FET amplifiers, the design of whose input, output and interstage matching networks belong to the design of ones for active loads, is researched. A program, which can greatly reduce the difficulty of designing microwave FET amplifiers, is provided. (chapter seven is a brief introduction of the method)(6)A new kind of structure of bias circuit for microwave active devices is presented, which has a wider band relative to existing ones and greatly increases the infection of bias circuit to the performances of devices.