The partial realization problem for complex Hamburger series and complex lossless multiport networks

A Broadband Single-Stage Equivalent Circuit for Modeling LTCC Bandpass Filters

“…where (37) Note that in (35)- (37), , , and are real constants, and denote the real residue and the real pole, respectively, and and for are pairs of complex and conjugate residues and poles, respectively. All these constants, residues, and poles in (35)- (37) are determined based on a well-known vector-fitting procedure [25]- [28].…”

“…All these constants, residues, and poles in (35)- (37) are determined based on a well-known vector-fitting procedure [25]- [28]. Under low-loss condition, standing for the transfer function of a complex pole pair can be approximated as (38) On the other hand, and according to the equivalent circuits shown in Fig.…”

“…It is finally noted that the automatic generation of mathematically equivalent circuits for microwave passive components has been reported in the open literature [31]- [34] and even developed as commercial tools [35], [36]. In their typical procedure for modeling a two-port reciprocal component, rational approximation is applied to the three network parameters, i.e., , , and or , , and for establishing the equivalent circuits based on Cauer or Foster network synthesis techniques [37], [38]. When compared to the proposed modified T-equivalent circuits, the equivalent circuits established in their ways generally need more circuit elements to achieve a similarly large bandwidth.…”