Analytical Solution for Two Parallel Traces on PCB in the Time Domain with Application to Hairpin Delay Lines

Fengchao XIAO  Kimitoshi MURANO  Yoshio KAMI  

IEICE TRANSACTIONS on Communications   Vol.E92-B   No.6   pp.1953-1959
Publication Date: 2009/06/01
Online ISSN: 1745-1345
DOI: 10.1587/transcom.E92.B.1953
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Section on 3rd Pan-Pacific EMC Joint Meeting -- PPEMC'08--)
crosstalk,  serpentine,  meander,  delay,  mode decomposition,  telegrapher's equations,  signal integrity,  time-domain transmission,  

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In this paper the time-domain analysis of two parallel traces is investigated. First, the telegrapher's equations for transmission line are applied to the parallel traces on printed circuit board (PCB), and are solved by using the mode decomposition technique. The time-domain solutions are then obtained by using the inverse Laplace transform. Although the Fourier-transform technique is also applicable for this problem, the solution is given numerically. Contrarily, the inverse Laplace transform successfully leads to an analytical expression for the transmission characteristics. The analytical expression is represented by series, which clearly explains the coupling mechanism. The analytical expression for the fundamental section of a meander delay line is investigated in detail. The analytical solution is validated by measurements, and the characteristics of the distortions in the output waveforms of meander delay lines due to the crosstalk are also investigated.