All Passive Realization of Lossy Coupling Matrices Using Resistive Decomposition Technique

A complex coupling matrix has been extensively used in lossy filters and negative group delay devices. For the realization, conventional technique decomposes the complex coupling matrix into lossy resonators and complex inverters. Since the complex inverter does not follow the passivity in some cases, the resultant realization may be globally passive but locally active. This paper proposes a new decomposition technique to ensure the passivity everywhere. It decomposes the complex coupling matrix into a resistive connection matrix and a conventional real coupling matrix, which are both passively realizable. This technique provides a passive realization of the complex coupling matrix. Furthermore, a loss equalization technique is also proposed, to further achieve a uniform quality factor (Q) distribution among all the lossy resonators. Several illustrative examples and an experimental validation are finally provided.