RF electronic-design-automation programs use Smith charts to display the results of operations such as S-parameter simulation. 4), which is equivalent to the complex reflection coefficient G for single-port microwave Figure 1. The complex reflection coefficient (in the region, corresponding to passive loads) may be displayed graphically using a Smith chart. In essence, the Smith chart is a special plot of the complex S- parameter s 11 (Ref. Although the Smith chart can look imposing, it’s nothing more than a special type of 2-D graph, much as polar and semilog and log-log scales constitute special types of 2-D graphs. 3), Smith chart displays can provide an easy-todecipher picture of the effect of tweaking the settings in a microwave network in an EDA program (Figure 1), a Smith chart display can graphically show the effect of altering component values. 1, “From the time I could operate a slide rule, I’ve been interested in graphical representations of mathematical relationships.” It’s the insights you can derive from the Smith chart’s graphical representations that keep the chart relevant for today’s instrumentation and designautomation applications. Although calculators and computers can now make short work of the problems the Smith chart was designed to solve, the Smith chart, like other graphical calculation aids (Ref. ![]() 1) as a graph-based method of simplifying the complex math (that is, calculations involving variables of the form x + jy) needed to describe the characteristics of microwave components. By Rick Nelson, Senior Technical Editor The Smith chart appeared in 1939 (Ref. The Smith Chart, as it has been presented up to this point, is a plot of reflection coefficient for magnitudes either equal to or less than 1, thereby encompassing all real, positive values of resistance.Test & Measurement World, July 2001 How does a Smith chart work A venerable calculation aid retains its allure in a world of lightning-fast computers and graphical user interfaces. What is the significance of the Smith chart? smithplot (frequency,data) creates a Smith chart based on frequency and data values. A Smith chart is developed by examining the load where the impedance must be matched. Or, it is defined mathematically as the 1-port scattering parameter s or s11. The Smith chart is commonly used to display the relationship between a reflection coefficient, typically given as S11 or S22, and a normalized impedance. The Smith chart is a polar plot of the complex reflection coefficient (also called gamma and symbolized by ). Smithplot (data) creates a Smith chart based on input data values. How is a Smith chart a polar plot?Ī Smith chart is a polar plot of the reflection coefficient, overlaid on a set of imped- ance axes which have been distorted to show the reflection coefficient those imped- ances would produce. Where does the reflection coefficient begin on the Smith chart?Īs a result, the trace of input reflection coefficient will begin near the short circuit position on the left of the Smith chart and trace clockwise at constant radius (in this case, around the edge of the Smith Chart) as frequency goes higher. ![]() ![]() 2 the half plane with positive real part of impedance Z is mapped onto the interior of the unit circle of the Γ plane. Since it was invented in 1939 by the engineer Phillip Smith, it is simply known as the Smith chart. A transmission line terminated in its characteristic impedance will have all energy transferred to the load zero energy will be reflected and r = 0. The range of possible values for r is between zero and one. Reflection coefficient is the ratio of the reflected signal voltage to the incident signal voltage.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |