  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, teraherz and
optoelectronic devices. Designing radiofrequency (RF) electronic circuits with
a MIT material like vanadium dioxide, VO2, requires the understanding of its
physics and appropriate models and tools, with predictive capability over large
range of frequency (1-100GHz). Here, we develop 3D Smith charts for devices and
circuits having complex frequency dependences, like the ones resulting by the
use of 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 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 3D multi-parameter modelling and design environment
for the complex case of Metal-Insulator-Transition (MIT) materials where their
permittivity is dependent on the frequency. In this work, we apply 3D Smith
charts to on Vanadium Dioxide (VO2) reconfigurable Peano inductors. 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.
Finally, we fabricate new Peano curves filters used to extract the
frequency-dependent dielectric constant of VO2 within 1 GHz-50 GHz for the
accurate design of RF electronic applications with phase change materials
