Regular Article

Kron–Branin modelling of ultra-short pulsed signal microelectrode

¹ Normandy University UNIROUEN, ESIGELEC, IRSEEM, Technopole du Madrillet, Avenue Galilée, BP 10024, 76801 Saint Etienne du Rouvray, France
² Normandy University UNIROUEN, GPM UMR 6634 CNRS, Technopole du Madrillet, Av. de l’Université, 76801 Saint Etienne du Rouvray, France

^* e-mail: Zhifei.Xu@esigelec.fr

Received: 17 November 2017
Received in final form: 23 January 2018
Accepted: 21 February 2018
Published online: 8 June 2018

Abstract

An uncommon circuit modelling of microelectrode for ultra-short signal propagation is developed. The proposed model is based on the Tensorial Analysis of Network (TAN) using the Kron–Branin (KB) formalism. The systemic graph topology equivalent to the considered structure problem is established by assuming as unknown variables the branch currents. The TAN mathematical solution is determined after the KB characteristic matrix identification. The TAN can integrate various structure physical parameters. As proof of concept, via hole ended microelectrodes implemented on Kapton substrate were designed, fabricated and tested. The 0.1-MHz-to-6-GHz S-parameter KB model, simulation and measurement are in good agreement. In addition, time-domain analyses with nanosecond duration pulse signals were carried out to predict the microelectrode signal integrity. The modelled microstrip electrode is usually integrated in the atom probe tomography. The proposed unfamiliar KB method is particularly beneficial with respect to the computation speed and adaptability to various structures.