3 in 3) or scanning microwave microscopy 4, while being mostly present in microwave-terahertz frequency region in the design and characterization of antennas 5, transmission lines 6, 7, power amplifiers 8, filters 9 or acoustic resonators 10. The Smith chart is extensively employed in the design/measurement stage of a large variety of circuits, from metasurfaces 2 to coils 3 (Supplementary Fig.

The Smith chart, invented in 1939 1, is a graphical tool widely used in various fields of electrical engineering and applied physics when dealing with frequency dependent reflection coefficients or impedances. We report fabricated inductors with record quality factors using VO 2 phase transition to program multiple tuning states, operating in the range 4 GHz to 10 GHz.

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 show here the unique visualization capability of a 3D Smith chart, which allows to quantify orientation over variable frequency. 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. 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. Employing radiofrequency (RF) electronic circuits with a MIT material like vanadium Dioxide, VO 2, requires appropriate characterization tools and fabrication processes. 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.

How inductance moves on a smith chart