Application of the tree‐cotree splitting for improving matrix conditioning in the full‐wave finite‐element analysis of high‐speed circuits

Abstract

frequency, because the typical value of PAE cannot be reached over there. In the band of 13.8 -14.8 GHz, theoretical and experimental PAE has excellent coherence, and a maximum PAE of about 22% can be achieved. CONCLUSIONWe present a maximum 45-W (CW) result for a spatial combiner circuit based on four driver amplifiers and four HPAs, integrated with the power dividers/combiners and microstrip probe transitions. A power variation less than Ϯ1 dB was achieved, and the combining efficiency was more than 87%, while the maximum PAE was 22%, within the band from 13.8 to 14.8 GHz. So high gain and high efficiency were reached. The combining structure itself was compact and has a strong potential for higher powers. APPLICATION OF THE TREE-COTREE SPLITTING FOR IMPROVING MATRIX CONDITIONING IN THE FULL-WAVE FINITE-ELEMENT ANALYSIS OF HIGH-SPEED CIRCUITS

VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

“…Therefore, the E-H formulation is not truly multi-scale, but exhibits catastrophic breakdown when the dimensions of objects become much smaller than the local wavelength. Different formulations using tree-cotree, or loop-tree decomposition [12][13][14][15][16], have to be sought when the frequency is low or the wavelength is long. Due to the low-frequency catastrophe encountered by E-H formulation, the vector potential formulation has become popular for solving low frequency problems [17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Simulation of LWD tool response using the dual-primal finite element tearing and interconnecting method incorporated with tree-co-tree splitting

“…In order to account for the decoupling between the electric and magnetic fields at low frequencies, two sets of basis functions, namely rotational-like basis functions j N and pure-gradient basis functions j N ∇ , are used to expand the electric field. This separate representation significantly improves the condition number of the system matrix [4], [5].…”

The model reduction of multi-agent system depended on the spanning tree of directed graph

“…Remark 1: The decomposition of the spanning tree and co-spanning tree subgraph actually has been wildly applied to solve the magnetostatic problems, such as tree-cotree gauging [24], finite element analysis [25], in which the decomposition is referred as Tree-Cotree Splitting (TCS) technique. As known that the spanning tree structure plays a vital role in the analysis of networked multi-agent system, but scarcely any literatures could offer a detailed interpretation for that from the control profiles.…”