S 11 of this surface microstrip would plot as a dot in the centre of the Smith chart - no reflection In a perfect system Z 0 = Z L = 50 ohms, the network is exactly terminated, and there is no reflection. S-parameters of the network/black box can be obtained. The structure can be represented as a transmission line (terminated in Z L = 50 Ohms) and the
Unity, shows a perfect reflection at different phase angles. A point plotted anywhere on this circle, a reflection coefficient of unity reflection with no phase change, implying a transmission line terminated with an open circuit. Similarly, a point plotted at right-hand edge shows 100% +ve reflection, unity reflection with 180 degrees phase change, implying a transmission line terminated with a short circuit. a transmission line perfectly terminated.Ĭommonly, a point plotted at the left-hand edge shows 100% –ve reflection, i.e. SmithĬharts are constructed within the circle described when rho is unity.Ī point plotted at the origin shows no reflection, i.e. On the Smith Chart, that of reflection coefficient, rho.Ĭonsider the following graphs of reflection coefficient, rho. In this note we briefly consider an important scale, implied but not drawn S-parameters can be graphed in several ways one option is to use two graphs (magnitude v frequency and phase v frequency) to represent one s-parameter.Īnother popular method, described briefly here, is via the use of Smith Charts.Ī Smith Chart is a polar plot with several different scales/axis overlaid onto the graph.
comprising both magnitude and angle) because both the magnitude and phase of the signal are changed by the network. the voltage ratios of the waves) fully describing the behaviour of a device (in this example, a transmission line) under linear conditions at radio frequencies. S-parameters are the reflection and transmission coefficients between the incident and reflected waves (i.e.
Recall that a linear network can be characterised by a set of simultaneous equations describing the waves, b1 and b2, exiting from each port in terms of incident waves, a1 and a2, The Smith Chart displays reflection coefficient in terms of constant normalised resistance and reactance circles. The Si9000 v7 and later allows graphical representation of s-parameters S 11 and S 21 via a Smith Chart, a widely used tool for graphic solution of transmission-line networks.
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