In traditional adaptive frequency sampling (AFS) techniques, it is inevitable to invert an N x N matrix in order to solve for the coefficients of targeted rational interpolation functions, where N is the number of samples. The ill-conditioned matrix of a large N restricts traditional AFS techniques to an electromagnetic simulation accelerator for a circuit with few poles or narrow bandwidth responses. In this paper, the general Stoer-Bulirsch (S-B) algorithm is employed in developing a new AFS scheme (S-B AFS). Since the S-B algorithm is a recursive tabular method and requires no matrix inversion, it can process a large number of,sampling data for obtaining a rational interpolation function without suffering from singularity problems. This attribute virtually leads the proposed AFS approach to an ultra broad-band interpolation with a single rational function. The new proposed approach greatly improves the efficiency of the traditional AFS techniques and simplifies the AFS process. In order to enable the S-B algorithm to be used in the proposed S-B AFS approach, three legitimate grid paths for constructing two pairs of complementary rational models are being proposed in this paper for modeling a general microwave circuit. Four practical broad-band examples are given to demonstrate the effectiveness of the S-B AFS, including waveguide harmonic filters, a waveguide diplexer, and a broad-band microstrip diplexer.
