![]() The East hemisphere is the place of inductive circuits, whereas the West hemisphere hosts the capacitive circuits. As a result, the classical 2D Smith chart including the passive loads 2 is mapped stereographically into the North hemisphere, while the circuits with negative resistance (that are outside the classical planar Smith chart) are mapped into the South one. The reflection coefficient plane is mapped stereographically through the South Pole on the surface of a unit sphere. The mathematical theory of the 3D Smith chart 1 unifies active and passive microwave circuit design on the surface of a Riemann sphere. 1 Representation of the 2D (a) and 3D (b) Smith charts. The corresponding resistance, inductance, and capacitance values, as well as transmission lines and stubs, can be directly computed.Fig. One can simply enter the desired normalized impedance parameters and then choose a matching route. The S-parameters can also be represented on a 2D Smith chart.ĭesign mode enables users to obtain normalized matching circuit solutions. These parameters include impedance, stability circles, constant gain circles, group delay, quality factor, and unilateral power gain. ![]() With analysis mode, a touchstone file can be loaded to allow one to view a number of parameters on the 3D Smith chart. ![]() Users can take advantage of both analysis and design modes. Users can also modify colors, as well as the step between circles. These displays include constant normalized resistance (r), reactance (x), conductance (g), and susceptance (b) circles. Moreover, the program interface includes rendering options, which allow users to select the desired displays. Furthermore, the inductive region is designated in the east, while the capacitive region is represented in the west. The north hemisphere of the 3D Smith chart represents positive resistance. Specifically, the south hemisphere represents negative resistance, with the south pole denoting an infinite reflection coefficient. However, negative resistance is indeed portrayed in the 3D Smith chart. In addition, RF/microwave engineers already know that negative resistance (|reflection coefficient| > 1) cannot be shown within the confines of the traditional Smith chart. However, the 3D Smith chart shows a perfect match at the north pole. For example, as most already know, the center of the classical Smith chart denotes a perfect match. The 3D Smith chart differs from the traditional Smith chart in a number of ways. With this tool, users can observe impedance/admittance, as well as stability circles, group delay, quality factor, and unilateral power gain. It works for all passive and active circuits-even when negative resistance is present. The 3D Smith chart tool is an easy-to-install 3D representation of the classical Smith chart that is intended for high-frequency one- and two-port circuits. The result is a 3D Smith chart tool, which the team says is a new vision in microwave analysis and design (see figure). However, one team of engineers decided to take the classical Smith chart and put a much different spin on it. The Smith chart, which is unquestionably one of the most important and fundamental aspects of microwave engineering, has a long history that spans more than 70 years. One team decided to transform the traditional Smith chart into a three-dimensional tool.
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