8/29/2023 0 Comments Smith chart calculatorThe circles are centered at R/(R+1),0, with a radius of 1/(R+1), where R is the normalized value. With the resistances normalized to 50 ohms, we can draw these circles of constant resistance for 10, 20, 50, 100, and 200 ohms, or 0.2, 0.4, 1, 2, and 4 when normalized.įigure 4 – Polar Chart with Resistance Circles Using this equation, we could choose a real part of the impedance, the resistance, hold it constant, and then let the imaginary part, the reactance, go from -∞ to +∞ and draw the result on the polar plot. These reflection coefficients were calculated from Equation 1. These four reflections are plotted on the polar plot in Figure 3.įigure 3 – Polar Reflection Coefficients Building the Smith Chart For Z = 0, the reflection is 1∠0 or Cartesian 1,0.įor Z = ∞, the reflection is 1∠180 or Cartesian -1,0.įor Z = 23+j75, the reflection coefficient is 0.762∠64 or 0.333+j0.685 Where Z is the complex impedance R+jX and Z 0 is the characteristic impedance of the source.įor Z = Z 0, the reflection has a magnitude of zero, a dot at the center of the smith chart. The reflection coefficient of an impedance can be measured with a vector network analyzer.įigure 2 – Measured Reflection Coefficient It can be thought of as a polar reflection coefficient chart with overlaid impedance curves.įigure 1 – Smith Chart Reflection Coefficients It may also be used to solve impedance-matching problems. The Smith chart is a useful graphical tool to convert between impedances and reflection coefficients.
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