S-parameter based macro model of distributed-lumped networks using exponentially decayed polynomial function

Abstract

A Scattering-Parameters {S-Parameters) based macromodel of distributed-lumped networks is presented. The networb can include capacitive cutsets, inductive loops, RLC meshes, and lossy transmission lines. An ef)cienl network reduction algorithm is &veloped to reduce [he original nelwork into a network containing one multipor[ component together with the sources and loads of interest. The S-Parameters of the circuit components are approximated by Taylor series to simpllfi the reduction process. Exponentially Decayed Polynomial Function (EDPF) approximation is used to derive the macromodel, the higher accuracy can be obtained by selecting titrte constant according to an error cri[erion. The ntacrontodel is always stable for a stabte sys[em and very jkxible that the accuracy of the model can be controlled by adjusting [he order of approximation. The experimental results indicate that our model can approach the accuracy of SPICE with one or two order less computing time.

Efficient simulation of lossy and dispersive transmission lines

“…positive poles for Pade approximation [14], but usually arises in fitting the attenuation data of frequency-dependent lines.…”

“…In order to simplify the following discussion, consider the well known trapezoidal rule for numerical integration. In other words, approximate the "excitation" as (14) where , , and is the remainder term. Substitution of (14) into (13) and performing the integration yields (15) where and Note that is the error due to the interpolation for .…”

RCLK-VJ network reduction with Hurwitz polynomial approximation

“…In the second category, the moment-matching technique has been used to approximate waveforms of a linear interconnect network using its lower order moments [6,7,8]. Since the advent of Asymptotic Waveform Evaluation(AWE) technique, many interconnect delay evaluation models [9,10,11] have been proposed.…”

Calculation of ramp response of lossy transmission lines using two-port network functions

“…The basic electrical parameters of a transmission line are resistance along the line, inductance along the line, conductance shunting the line, and capacitance shunting the line. (1) (2) By combining equations (1) and (2), we can come up with the following equation: (3) Equations (1), (2), (3) are the fundamental relationships governing wave propagation along a uniform transmission line. The shunt conductance is often negligible, hence we set g=0.…”