A General Method to Construct Arbitrary Passive S-parameter Network Using the Synchronously Tuned Coupling Resonators

In this paper, we discuss a general method to construct arbitrary passive reciprocal Scattering parameter (S-parameter) network, which may represent a functional device or a network composed by a series of devices, using the topology of synchronously tuned coupling resonators (STCR). To achieve this aim, firstly, we generalize the common STCR circuit from two-port case to arbitrary multi-port case. Then, with the help of matrix decomposition technology, the relationship between the S-parameter and the coupling coefficient matrix is constructed. On the basis of this formula, we further demonstrated that the arbitrary lossless reciprocal S-parameter matrix can be constructed by less than N+2 resonators, who resonance at the frequency of given frequency. In addition, cooperating with the method to extend a lossy network to a lossless network, this method will help us to achieve a general method to construct the narrow band arbitrary passive reciprocal S-parameter network using a fixed automated design procedure.