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UBC Theses and Dissertations

Numerical methods for frequency dependent line parameters with applications to microstrip lines and pipe-type cables Zhou, Dan H.

Abstract

Signal lines such as microstrip lines have recently assumed increased importance in VLSI circuit design and computer package design. Their behavior has become a key factor in system performance. As the circuit implementation size or area reduces almost to its physical limits, the circuit speed is so high that devices can react in less than nanoseconds. Under these conditions, the trans-mission line characteristics of microstrip lines become dominant compared to their simple function for signal linkage. Many numerical methods have been introduced to simulate these signal lines. To employ these models, the transmission line characteristics must be determined first. With signal transients containing the frequency of interest, traditional formulae are inappropriate to calculate line parameters because of skin and proximity effects. A common strategy is to apply the subdivision principle — to subdivide the line conductors into smaller parts so that the traditional formulae may be used. Based on this strategy, new numerical methods have been developed in this thesis to determine microstrip line parameters including skin and proximity effects. The developed techniques include a Linear Current Subconductor Technique (LCST), and an advanced method of subareas (ANS). These methods are derived from the traditional subconductor method and the traditional method of subareas, respectively. LCST combines the simplicity of the traditional subconductor method with the accuracy of finite element methods. AMS avoids the procedures of optimization and recursion of traditional subareas methods. To generate the LCST, the conductors of microstrip lines are firstly divided into subconductors by a 26 rule (6 is the skin depth at the considered frequency). For the subconductors system, an impedance matrix is then built using Ohm's law and the concept of Geometric Mean Distances (GMD). Secondly, the current distributions in the subconductors are solved from the telegrapher's equations. Thirdly, a linear current distribution is evaluated from the results of the previous step. After substituting linear currents back into the telegrapher's equations, correction factors are obtained for the subconductor's impedance matrix. Finally, the corrected impedance matrix is reduced to an equivalent line impedance matrix by a bundling procedure. Another important application of the proposed sub conductor technique is in the calculation of the parameters of underground cables in electric power systems. Due to the irregular arrangement of the conductors in the cable no analytical formulas are available for these calculations. As an example, the LCST technique is ap-plied to pipe-type cables and the results are compared to those of previously published work using a finite element technique. In the case of ANS, after a similar subdivision procedure, the Maxwell coefficients matrix of subareas is setup from Green's functions. A bundling procedure is then used to convert the Maxwell coefficients matrix of the subareas into the Maxwell coefficients matrix of the line conductors. The inverse of the resultant matrix is the line capacitance matrix. In simulations of microstrip lines and pipe-type cables, the proposed LCST and ANS techniques proved to be efficient and accurate. Compared to the traditional uniform current density technique, the LCST results in savings of up to 99% and 98% in memory requirement and CPU cost, respectively, while the ANS technique results in savings of up to 80% as compared to the conventional uniform charge distribution technique. In comparisons with a finite element method and a traditional subconductor method, the results from LCST presented an average difference of about 4.0%. The resulting average difference was of 6.31% for the ANS technique as compared with two finite element methods and a software package from A. Djordjevic et al, ("Analysis Of Arbitrarily Oriented Microstrip Transmission Lines...", IEEE Trans. on MTT, vol.MTT-33,no.10, Oct.1985). Yet to be researched is the extension of LCST and ANS into otherline structures with open boundaries. Other potential applications are in telecommunications and computer high speed networking, as well as supercomputer packaging.

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