Kron‐Branin modeling of symmetric star tree interconnect

Abstract

Summary An 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.

Bandpass NGD TAN of Symmetric H-Tree With Resistorless Lumped-Network

“…The H-tree interconnects [20][21][22][23][24] enable to share certain signals as clock distribution with beneficial simplicity of synchronization. Moreover, further tree topologies [25][26][27][28][29] were also introduced for data distribution of different devices as multiphase clock multiplexer, DACs with arbitrary number of levels and clock tree routers. However, the modelling of tree structures against the delay constraints [27][28] remains an open challenge for the electronic circuit design engineers.…”

“…Therefore, further modelling methodology related to the tree topology responses prediction must be developed. One of the less deployed ways of the tree interconnect modelling was suggested recently in [29] by considering the tensorial analysis networks (TAN).…”

“…In difference to the existing works on the NGD circuit design which are limited to two-port topology [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], in the best of the authors' knowledge, a first study on NGD topology implemented with multi-port system is developed in the present paper. As a rigorous method, the analytical approach of the NGD H-tree topology will be developed via the unfamiliar TAN formalism based on the Kron's method [29][30][31][32][33][34][35][36].…”

“…This unfamiliar TAN formalism was exploited [31][32][33][34][35] to solve electromagnetic compatibility problem of electronic and electrical complex systems. More recently, the potential of TAN formalism became an opportunity to develop, with fast and accurate analytical modelling methods, star tree interconnect lines [29]. The TAN method was also exploited to develop Sparameter model of multi-port system as coaxial cable networks in very few calculation steps [36].…”