A Broad-Band Adaptive-Frequency-Sampling Approach for Microwave-Circuit EM Simulation Exploiting Stoer–Bulirsch Algorithm

In traditional adaptive frequency sampling (AFS) techniques, it is inevitable to invert an matrix in order to solve for the coefficients of targeted rational interpolation functions, where is the number of samples. The ill-conditioned matrix of a large 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.