Addressing transient errors in passive macromodels of distributed transmission-line networks

Parameterized models for crosstalk analysis in high-speed interconnects

“…The RM S and RM S weighted errors of the corresponding parametric macromodels over the reference grid are equal to 1 · 10 −5 and 3 · 10 −5 . The magnitude of the parametric macromodels of Z pul, (12) is shown in Fig. 2.…”

“…Then, the univariate macromodels of the modal impedances have been computed for the previous set of spacing points. The magnitude and phase of Z n, (12) computed from the perunit-length impedance and admittance data and its respective macromodels are shown in Figs. 3-4 for modes n = {0, 1, 13}, S = 346 µm, for validation purpose.…”

Delay extraction-based passive macromodeling techniques for transmission line type interconnects characterized by tabulated multiport data

“…With the continually increasing operating frequencies and circuit densities, accurate and fast signal integrity analysis is becoming critically important for validation of highspeed VLSI designs [1][2][3][4][5][6][7][8][9]. In addition, advanced interconnect models are necessary to capture high frequency effects that have become more pronounced due to the increased integration of analog circuits with digital blocks, the demand for lower power consumption, and miniaturization of designs.…”

“…Several techniques can be found in the literature for macromodeling multiconductor transmission line (MTL) type interconnects characterized by per-unit-length (p.u.l) RLGC parameters. The prominent approaches include method of characteristics (MoC) [7], matrix rational approximations [6], and delay extraction based methods [9].…”

“…The multiconductor transmission line system described by (2) does not have a direct representation in the timedomain, which makes it difficult to interface with nonlinear transient simulators. In order to overcome this problem, the partial differential equations of (1) are approximated using matrix rational approximations (MRA) [12], which can be converted into a set of equivalent subcircuits for SPICE simulation [6].…”