Kron‐Branin modeling of symmetric star tree interconnect

Abstract

SummaryAn analytical modeling method of symmetric tree interconnect is developed in this paper. The tree topology is composed of multibranch distributed interconnects of printed circuit board (PCB). The interconnects are constituted by elementary transmission line (TL) defined by its characteristic impedance and propagation constant. The star symmetric tree model is built with the Kron‐Branin (KB) formalism elaborated with the graph topology. Reduction method allowing to simplify the graph from single‐input multiple‐output (SIMO) to single‐input single‐output (SISO) circuit is used. The interconnect tree branch currents are determined from the reduced SISO structure. The symmetric tree S‐parameter and access and transfer impedance models are expressed in function of constituting elementary TL parameters with the KB formalism. The particular behaviors of short‐circuit and open‐ended star tree are investigated versus the tree number of output branches. The developed KB model effectiveness is validated with microstrip star tree designed and simulated with a 3D electromagnetic computational and electronic circuit designer commercial tool. Three different proofs of concept (POC) of star trees comprised of three‐output, four‐output, and five‐output branches are computed. The simulated reflection and transmission coefficients from DC to 5 GHz are in good agreement with the KB models. The proposed model is potentially useful for the PCB complex interconnect modeling and signal integrity analysis.