The app has a user manual with examples explained in a simple way, so that the designer becomes familiar with it immediately. Although this can be solved by calculation, the visual image is always more advantageous. In this case, one of the most advantageous applications for the chart, having studied the stability circles of an amplifier, is the location of the stability regions graphically. In its version 1, the app, which can be found on the website 3D Smith Chart / A New Vision in Microwave Analysis and Design, shows some design options and configurations, although some applications should be undoubtedly added In future versions. New advantages are observed in this respect in that it is possible to represent the infinite values from the Möbius transform to a Riemann’s sphere and thus having a three-dimensional graphical tool where practically all passive and active impedances and parameters which can be difficult to draw in the traditional chart as stability circles. The object was to study its potential with respect the traditional chart in microwave engineering. In this entry I had the first contact with the three-dimensional Smith’s chart. Due to both reflection coefficients, S 11 y S 22 are into the stable regions, then the amplifier is stable. In this case, the stable region in the input stability circle is inside and in the otuput stabiliy circle is outside. 14 – Low noise amplifier and stability circles The entire complex surface is represented on a spherical surface by a stereographic projection of this plane.įig. The Riemann’s sphere is a mathematical solution for representing the complete complex plane, including infinity. But with oscillators still have the problem of complex infinity, which could be solved through a representation in a Riemann’s sphere. In a graphical computer environment, representing the circles is already performed by the software itself through the calculations, being able to limit the chart to the passive region and drawing only a part of the circle of stability. However, the extension is needed when the amplifier stability circles are analyzing, since in most of cases the centers of these circles are located outside the passive impedance chart. However,this chart shows two issues: 1) although it allows to represent all the impedances, there is a problem with the complex infinity, so it remains limited and 2) the chart has large dimensions that make it difficult to us in a graphic environment, even in a computer-aided environment. 2- Smith’s Chart expanded to active impedances Traditionally, Smith’s Chart has been represented in polar form as shown belowįig. These circles made it easier for him to represent any impedance in a polar space, with the maximum matching placed in the center of the chart and the outer circle representing the pure reactance. By means of the mathematical expressions that define the impedances in the transmission lines, he got to represent the impedance complex plane by circles with constant resistances and reactances. When Phillip Smith was working at Bell Labs, he have to match one antenna and he was looked for a way to solve the design graphically. In this post, I will try to show the handling of the three-dimensional Smith Chart and its application for a low-noise amplifier design. Advances in 3D rendering software make it easy to use for design. Last years, three-dimensional Smith Chart has become popular. However, the 2D format has some restrictions when the active impedances (oscillators) or stability circles (amplifiers) are represented, since these ones usually leave the polar chart. Traditionally, the Smith Chart has been used as 2-D polar form, centered at an unit radius circle. Developed by Phillip Smith in 1939, it has become the most popular graphic method for representing impedances and solving operations with complex numbers. The Smith Chart is a standard tool in RF design.
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