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RF Electronics Chapter 8: Amplifiers: Stability, Noise and Gain Page 278 2022, C. J. Kikkert, James Cook University, ISBN 978-0-6486803-9-0. adjust these reflection coefficients correctly, it is desirable to know both their magnitude and phase at different frequencies. The Smith Chart is a polar plot of reflection coefficient and allows both the magnitude and phase of the reflection coefficient to be plotted versus frequency. Such plots are very useful in visualising: the behaviour of the reflection coefficient, so that suitable action may be required to improve the matching of the devices. As shown later in this chapter, the Smith Chart is very useful in visualising the stability of amplifiers. The Smith Chart was developed by P. Smith [3, 4] in 1939. It is a polar plot of the reflection coefficient superimposed with circles for real and reactive normalised impedances. It allows a good visualisation of the impedance of RF networks as the frequency changes. Some prior knowledge of the Smith Chart is presumed here and only the equations 8.1 and 8.2 governing the Smith chart are stated here, for a more detailed discussion on the Smith chart please refer to D. M. Pozar [5] or similar books. The copyright of the Smith Chart has been released into the public domain by the copyright holder. The normalised reflection coefficient and the normalised impedance Z L of a network are related by: j r j L L j e Z Z 1 1 or L L L jX R Z 1 1 Eqn. 8.1 The Smith chart is a plot of ||e j and this also represents Z L and we can plot contours of Z L = R L + jX L . Solving for R L and X L gives: 2 2 2 2 ) 1 ( 1 j r j r L R and 2 2 ) 1 ( 2 j r j L X Eqn. 8.2 R L and X L form a family of circles, which are also plotted on the Smith Chart. = 0 is the centre of the Smith Chart. The Smith chart is a very useful tool for showing impedance values versus frequency. Paper versions of the Smith Chart are now seldom used for design calculations, but the Smith chart is an integral part of modern computer based design tools. Cadence AWR DE allows the results of the RF network simulation to be plotted on a Smith Chart, as well as rectangular and polar charts. In Cadence AWR DE, the centre part of the Smith chart can be expanded or compressed, by right clicking on the smith chart of the project file of figure 8.6 and selecting Options Grid and setting the Size to Normal, Expanded or Compressed. Compressed shows more of the area outside the = 1 region on the Smith Chart and is useful for plotting stability circles. Expanded provides a close up of the centre of the Smith Chart and is useful for visualising impedance matching. Scattering Parameters Revision Pozar [5] provides a more detailed description of S parameters than is presented here. Figure 8.4. S parameter definitions. RF Electronics: Design and Simulation 278 www.cadence.com/go/awr

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