3D Smith charts scattering parameters frequency-dependent orientation analysis and complex-scalar multi-parameter characterization applied to Peano reconfigurable vanadium dioxide inductors

Andrei A Muller,Adrian M Ionescu,Junrui Zhang,Montserrat Fernandez-Bolaños,Esther Sanabria-Codesal,Anna Krammer,Matteo Cavalieri,Emanuele Casu,Riyaz A Khadar,Andreas Schuler,Alin Moldoveanu,Victor Asavei

doi:10.1038/s41598-019-54600-5

Abstract

Recently, the field of Metal-Insulator-Transition (MIT) materials has emerged as an unconventional solution for novel energy efficient electronic functions, such as steep slope subthermionic switches, neuromorphic hardware, reconfigurable radiofrequency functions, new types of sensors, terahertz and optoelectronic devices. Employing radiofrequency (RF) electronic circuits with a MIT material like vanadium Dioxide, VO2, requires appropriate characterization tools and fabrication processes. In this work, we develop and use 3D Smith charts for devices and circuits having complex frequency dependences, like the ones resulting using MIT materials. The novel foundation of a 3D Smith chart involves here the geometrical fundamental notions of oriented curvature and variable homothety in order to clarify first theoretical inconsistencies in Foster and Non Foster circuits, where the driving point impedances exhibit mixed clockwise and counter-clockwise frequency dependent (oriented) paths on the Smith chart as frequency increases. We show here the unique visualization capability of a 3D Smith chart, which allows to quantify orientation over variable frequency. The new 3D Smith chart is applied as a joint complex-scalar 3D multi-parameter modelling and characterization environment for reconfigurable RF design exploiting Metal-Insulator-Transition (MIT) materials. We report fabricated inductors with record quality factors using VO2 phase transition to program multiple tuning states, operating in the range 4 GHz to 10 GHz.

Highlights

The field of Metal-Insulator-Transition (MIT) materials has emerged as an unconventional solution for novel energy efficient electronic functions, such as steep slope subthermionic switches, neuromorphic hardware, reconfigurable radiofrequency functions, new types of sensors, terahertz and optoelectronic devices
The Smith chart, invented in 19391, is a graphical tool widely used in various fields of electrical engineering and applied physics when dealing with frequency dependent reflection coefficients or impedances
Since the paths of the reflection coefficients of distinct circuits may coincide within a specific frequency on the Smith chart a frequency dependency visualization is missing in order to get an insight beyond the reflection coefficients paths, regarding their dynamics within it

Summary

Introduction

The field of Metal-Insulator-Transition (MIT) materials has emerged as an unconventional solution for novel energy efficient electronic functions, such as steep slope subthermionic switches, neuromorphic hardware, reconfigurable radiofrequency functions, new types of sensors, terahertz and optoelectronic devices. This counter-clockwise dynamics phenomenon recurrent existence in lossy circuits with non-Foster elements[19,21,22,23,24], led to some misleading conclusions: in[21,22,23,24] the authors assume that the existence of this phenomenon proves the presence of a non-Foster element, while in[25] it is stated that passive linear devices cannot exhibit driving point immittances with counter-clockwise frequency dependency on the Smith chart Because of their lack in zooming capacity, 2D Smith chart representations may oversee the changes of orientation occurring for the input impedances and reflection coefficients (while increasingly sweeping the frequency), in simple passive networks too. Their parametric curves equations describe more than a simple geometrical image (their path on the Smith chart), they contain the information about their motion on it (as for example: orientation and speed)

Methods

Findings

Conclusion