![]() "\n`%matplotlib` prevents importing * from pylab and numpy" `%matplotlib` prevents importing * from pylab and numpy usr/local/lib/python3.5/dist-packages/IPython/core/magics/pylab.py:160: UserWarning: pylab import has clobbered these variables: If the loss increases with frequency the reflection coefficient becomes smaller and the plotted line spirals inwards.Populating the interactive namespace from numpy and matplotlib ![]() This plot shows this transmission line with a small amount of loss, as the 15GHz point is no longer sitting on the unity outer circle. The previous graphs plotted an ideal network with no loss. The S 21 graph starts at the right hand edge at 100Mhz and circles around with the last plot at 15GHz. Plotting the real response S 11 and S 21 of our 50 ohm surface microstrip shown above produces the following picture on the Si9000 (in this example If the frequency were increased, and other S 21 frequency readings obtained, the magnitude of S 21 would still be 1 but the phase shift would change.Īdding more S 21 readings at increasing frequencyĪs we plot more S 21 readings at increasing frequency we note that the plotted graph increases in a clockwise direction - typical of a transmission line. Where this dot is plotted would depend on the phase shift through the transmission line. The magnitude of b2 = magnitude of a1 and the magnitude of S 21 = 1.Ī single frequency reading of S 21 of our surface microstrip would plot as a dot somewhere on the outer circle of the Smith chart. In a perfect system there is no loss and the signal passes through the transmission line unattenuated: 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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