( d) 3D Smith chart representation of the two port reflection coefficient and newly implemented frequency dependent 3D Smith chart representation for it. ( b) Extended Smith chart ( c), 3D Smith chart as in 2018 (without frequency dependency). Smith chart limitations and clockwise and counter-clockwise frequency dependency of Foster and non-Foster elements on a newly introduced frequency dependent 3D Smith chart. The next developments of the 3D Smith chart 13, 14 propose a Java tool with the 3D Smith chart which additionally displays the group delay and amplifier stability circles too. 1b,c) further conveying the theoretical support and advance for an intuitive spherical drawing for which the first insights have been presented in 12. 1a) onto the Riemann sphere in order to make it usable for all circuits (Fig. The 3D Smith chart proposed in 11 generalizes the Smith chart (which is limited within the unit circle to circuits with reflection coefficients ( Γ = Γ r + j Γ i ) magnitudes smaller than unity Fig. 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. Upon clicking, a point is "selected" and r and z will be populated with their correct values (and a change event is fired).Ĭlicking the element again un-selects/unlocks the point.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. R and z will both be null when the element is "unlocked", meaning the cursor will follow the mouse around the element. In the example above, the smith-chart element's z value will be, corresponding to the r-value of. R and z are automatically kept in sync (i.e., each is the correct value corresponding to the other on the Smith chart), and either can be set to change the selected point on the chart. z: The corresponding normalized load impedance again a complex number represented in the same way.Ĭorresponds to the (x, y) position selected on the smith chart r: The reflection coefficient a complex number of magnitude no greater than 1, represented as an array of components.The smith-chart element has two attributes: The custom element is now available and may be used in HTML directly as with: Import the library in your main entrypoint: import 'web-component-smith-chart' A web component for displaying or selecting points on a Smith Chart.
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