An efficient second‐order model reduction enhanced by H‐LU for the finite element method full‐wave electromagnetic simulations

Abstract

In this work, a UWB BPF based on the uniform MMR using a pair of MMRs is proposed. All three resonant frequencies within the UWB BPF are reassigned and the spacing g between the two parallel-coupled MMRs is properly regulated, a UWB filter with high performances is obtained. Measured results show high performances with insertion loss lower than 2 dB (from 3.1 to 7.5 GHz lower than 0.5 dB) and return loss higher than 10 dB (from 3.2 to 8.9 GHz higher than 15 dB) as well as group delay variation less than 0.18 ns within the UWB passband (3.1-10.6 GHz).

Method of moments wide‐band simulations of the microstrip circuits with second‐order Arnoldi reduced model

“…It is found that (6) is linear with respect to the frequency s . As a result, the SOAR algorithm in [3, 4] can be applied to obtain the projection matrix Q of q orthogonal vectors. If we let , then (6) can be written as then a reduced model can be obtained after projections where , …”

“…However, when the matrix equation represents quadratic dependence with respect to frequency, the standard Arnoldi process cannot be employed directly. A second‐order Arnoldi (SOAR) [3] process is proposed for the quadratic systems resulting from the FEM [4]. For the microstrip circuits, the method of moments (MoMs) with the layered media Green's function, only need to discretise the surface of the conductor as unknowns.…”

“…In [6], the partial-element equivalent circuit formulation is combined with the standard Krylov space-based model reduction method, while it increases the size of the original equation during the reduced model construction, thus more computations are required. The advantage of the SOAR over standard Krylov space-based method is that no extra unknowns are introduced during the production of the orthogonal vectors [3,4]. In this Letter, the impedance matrix is first expanded with second-order Taylor series, then the SOAR can be applied to linearise the expanded equation, finally a multipoint reduced model is constructed to extract the S-parameters effectively within a wideband.…”

“…It is found that (6) is linear with respect to the frequencys. As a result, the SOAR algorithm in [3,4] can be applied to obtain the projection matrix Q of q orthogonal vectors. If we let x = Qx, then (6) can be written as…”