回路論的手法に基づく回路網表現による複雑なレイアウト配線のクロストーク解析に関する研究

摘要

The research presented here is aimed toward developing a novel approach to analyzecrosstalk between transmission lines of complex configuration on high-speed digital printedcircuit boards (PCBs). The trend of modern electronics goes toward small packages andhigh performance. Together with this trend, electromagnetic interference (EMI) within theproduct itself such as crosstalk, important aspect of designing product for electromagneticcompatibility (EMC), becomes crucial day by day. As a typical method, multi-conductortransmission line (MTL) equations is often used to analyze crosstalk between wires in acable or traces on a PCB. However, this method is insufficient to analyze crosstalk betweenlines of complex configuration like those on practical PCBs because the solution of thismethod is restricted to the models of parallel lines having same length. Therefore, thisresearch proposes a new approach to analyze crosstalk between lines in various complexconfigurations like those on practical high-speed digital PCBs.MTL equations obtain the mutual coupling, that is, crosstalk between lines by the mutualcapacitance and the mutual inductance on the cross-section of transmission lines. That iswhy this method is restricted to the models of parallel lines having same length even thoughcrosstalk is easily analyzed. Therefore, other approaches are needed to analyze crosstalkbetween non-parallel lines or lines of arbitrary arrangement. In this thesis, an approach isdeveloped by regarding each transmission line as a transmitting antenna and a receivingantenna like an antenna theory familiar with us. Currents flowing on a transmission linegenerate electromagnetic fields and these fields affect nearby transmission lines and inducedistributed voltage and current sources on the lines. Thus, each line affects each otheras playing a role of a transmitting antenna and a receiving antenna. This is thoughtas the mutual coupling mechanism in this thesis. The proposed approach estimates thecoupling by directly calculating the mutual electromagnetic coupling between transmissionlines using a field theory based on the coupling mechanism mentioned previously. The linevoltage and line current is obtained by incorporating the mutual coupling taking by abovemechanism with the transmission line theory which have a good efficiency in that it is veryconvenient to solve the problem of line-structure propagating transverse electromagnetic(TEM) mode like that on PCBs dealt with here. We call this approach “Circuit-conceptapproach”.In this thesis, several models are set theoretically to estimate crosstalk using the circuitconceptapproach and experiment is conducted to verify the proposed approach. Thepatterns often seen on practical PCBs are not only parallel lines but also non-parallel lines,bend, vias and so on. Thus, we chose the models of bent lines having vias at the endsof the lines and obtained ABCD network expression for those to analyze crosstalk in thefrequency domain. Crosstalk between two microstrip lines in arbitrary directions on twodifferent layers including vias at both ends of lines such as line-structure on embedded PCBsare also theoretically analyzed by the circuit-concept approach. As a preliminary step, themodels in a homogeneous medium are analyzed. And then the models in an inhomogeneousmedium like the substrate on PCBs are analyzed. To obtain crosstalk between microstriplines on a PCB, we need accurately to estimate electromagnetic field in the substrate. Thus,the quasi-dynamic model is proposed to estimate electromagnetic fields in inhomogeneousmedia using an image theory. The proposed approach can be applied for the analysis ofmulti-conductor lines of complex structures, such as on multilayer PCBs, MCM.