From basic electricity classes, you will remember that admittance is the inverse of impedance as such, an admittance chart makes sense for the complex parallel situation as all you will need to do is to examine the admittance of the antenna rather than the impedance and just add them up.
To allow the same simplicity, the admittance chart was developed.
The Impedance chart is great when dealing with load in series as all you need to do is simply add the impedance up, but the math becomes really tricky when working with parallel components( parallel inductors, capacitors or shunt transmission lines). The focus of today’s article will be on them so more details will be provided as the article proceeds.
The image below shows an impedance smith chart. They are the most popular, with all references to smith charts usually pointing to them and others being regarded as derivatives. The Impedance smith charts are usually referred to as the normal smith charts since they relate with impedance and works really well with loads made up of series components, which are usually the main elements in impedance matching and other related RF engineering tasks. While the impedance smith charts are the most popular and the others rarely get a mention, they all have their “superpowers” and can be extremely useful when used interchangeably. Based on this scaling, smith charts can be categorized into three different types Smith chart is plotted on the complex reflection coefficient plane in two dimensions and is scaled in normalised impedance (the most common), normalised admittance or both, using different colours to distinguish between them and serving as a means to categorize them into different types.
As a result of this, most RF Analysis Software and simple impedance measuring instruments include smith charts in the display options which makes it an important topic for RF Engineers. Smith chart can be used to display several parameters including impedances, admittances, reflection coefficients, scattering parameters, noise figure circles, constant gain contours and regions for unconditional stability, and mechanical vibrations analysis, all at the same time. However, the Smith charts method of displaying data have managed to retain its preference over the years and it remains the method of choice for displaying how RF parameters behave at one or more frequencies with the alternative being tabulating the information. The examples provided here are solved using graphical tools and a printed Smith chart, rather than the computer program, to emphasize the techniques and approximations involved.It was originally developed to be used for solving complex maths problem around transmission lines and matching circuits which has now been replaced by computer software. A computerized Smith chart can then be used to analyze conditions on lines. Naturally, any chart can also be implemented in a computer program, and the Smith chart has, but we must first understand how it works before we can use it either on paper or on the screen. Some measuring instruments such as network analyzers actually use a Smith chart to display conditions on lines and networks. Although the Smith chart is rather old, it is a common design tool in electromagnetics. As such, it allows calculations of all parameters related to transmission lines as well as impedances in open space, circuits, and the like. The Smith chart is a chart of normalized impedances (or admittances) in the reflection coefficient plane. This has been accomplished in a rather general tool called the Smith chart. Thus, the following proposition: Build a graphical chart (or an equivalent computer program) capable of representing the reflection coefficient as well as load impedances in some general fashion and you have a simple method of designing transmission line circuits without the need to perform rather tedious calculations. You may also recall, perhaps with some fondness, the complicated calculations which required, in addition to the use of complex variables, the use of trigonometric and hyperbolic functions. The reflection coefficient, in turn, was defined in terms of the load and line impedances (or any equivalent load impedances such as at a discontinuity). Voltage, current, and power were all related to the reflection coefficient. The reflection coefficient was used to find the conditions on the line, to calculate the line impedance, and to calculate the standing wave ratio. A look back at much of what we did with transmission lines reveals that perhaps the dominant feature in all our calculations is the use of the reflection coefficient.