Passive network synthesis
Passive network synthesis mainly studies the problem of achieving a given network description function through a limited number of passive components such as resistors, inductors, capacitors and transformers. A few years ago, the advent of a mechanical component called "inertial capacitance" made the research of passive network synthesis theory once again of important practical significance. In recent years, some scholars have launched researches in this field and achieved a series of new results.
As an important part of circuit and system theory, the research results of passive network synthesis have played an important role in promoting the development of systems and control fields.
In 1931, Brune first defined in the literature the real rational function F(s)' that satisfies Re[FO)]y when Re[y]M. Such functions are called positive real functions. The literature proves that for any passive network, its impedance or admittance function must be a positive real function. Moreover, a general method that can realize any positive real function through a finite number of resistors, capacitors, inductors and transformers is constructed, that is, the Brune synthesis method. The proposal of this method lays the foundation for the further development of passive network synthesis theory. In 1939, using the idea of resistance extraction and the realization of the two-port reactance network, the Dariington synthesis method was constructed. This method can realize any positive real function as a cascade connection of a resistor and a two-port reactance network with a transformer. It is difficult to realize the transformer in the actual circuit system, so it is necessary to try to avoid the use of such components. However, the problem of transformerless realization of passive one-port network was not solved until nearly 20 years after Brune's synthesis method was proposed. In 1949, the Bott-Duffin synthesis method was proposed in the literature, which proved that any positive real function can be realized by only a finite number of resistors, capacitors and inductances. However, this method will produce a large number of redundant components. Wen S makes appropriate improvements to the Bott-Duffin synthesis method, but it still cannot fundamentally reduce the redundancy of the components. Although other synthesis methods (see literature [14-18]) have been proposed later, the simplest implementation problem of passive network synthesis has never been solved. For a multi-port passive network, it can be constructed with a limited number of resistors, capacitors, inductors and transformers. However, the problem of its implementation without transformers has not yet been resolved. After the 1970s, the development and widespread use of integrated circuits made the research of passive network synthesis gradually lose people's interest.