Frequency-dependent RLGC extraction for a pair of coupled transmission lines using measured four-port S-parameters

We present a method that extracts a frequency dependent tabular RLGC HSPICE model from a four-port coupled-line measurement. Typically, these RLGC matrices per unit length have been computed using field solvers. This paper shows that the using a conventional modal decomposition can extend a two-line method for a single transmission line to a two-line method for symmetrical coupled lines. Focus of the study is on the use of a high-frequency Taylor series extrapolation technique for odd- and even-mode impedances to extract the frequency dependent RLGC matrices and HSPICE W element. The use of high frequency series expansions of the characteristic impedances and accurately extracted eigenvalues of the coupled line allows us to extract an accurate W element model beyond the fundamental frequency limitation where the length of transmission line becomes /z / 2. The method is applied to a coupled line printed on an organic package substrate. It is found that the extracted W element is accurate, convenient for length scaling, causal, and stable.