and any possible value for Y that you could think of, what is the resulting curve? The answer is shown in Figure 1: What would the curve corresponding to equation look like if we plotted it on the Smith Chart for all values of Y? That is, if we plotted z1 = 1 + 0*i, and z1 = 1 + 10*i, z1 = 1 - 5*i, z1 = 1. Now, suppose we have the normalized load impedance given by: Constant Resistance CirclesДЇor a given normalized load impedance zL, we can determine and plot it on the Smith Chart. It is just a convention that is used everywhere. To make the Smith Chart more general and independent of the characteristic impedance Z0 of the transmission line, we will normalize the load impedance ZL by Z0 for all future plots:Д®quation doesn't affect the reflection coefficient tow. Along this curve, all of the power is reflected by the load impedance. The outter ring of the Smith Chart is where the magnitude of is equal to 1. That is, this is the only point on the smith chart where no power is reflected by the load impedance. The center of the Smith Chart is the point where the reflection coefficient is zero. In Figure 2, plotting the set of all values for the complex reflection coefficient, along the real and imaginary axis. The complex reflection coefficient, or, must have a magnitude between 0 and 1.ДЄs such, the set of all possible values for must lie within the unit circle: Recall that the complex reflection coefficient () for an impedance ZL attached to a transmission line with characteristic impedance Z0 is given byДЇor this tutorial, we will assume Z0 is 50 Ohms, which is often, but not always the case. The Smith Chart displays the complex reflection coefficient, in polar form, for an arbitrary impedance (we'll call the impedance ZL or the load impedance).ДЇor a primer on complex math, click here. This section of the antenna theory site will present an intro to the Smith Chart basics. But for now, just admire the Smith Chart and its curvy elegance. In fact, we are going to learn an even more complicated version of the Smith Chart known as the immitance Smith Chart, which is twice as complicated, but also twice as useful. We will build up the Smith Chart from scratch, so that you can understand exactly what all of the lines mean. A larger version is shown here.ДЇigure 1 should look a little intimidating, as it appears to be lines going everywhere. With modern computers, the Smith Chart is no longer used to the simplify the calculation of transmission line equatons however, their value in visualizing the impedance of an antenna or a transmission line has not decreased. See, for instance, the input impedance equation for a load attached to a transmission line of length L and characteristic impedance Z0. Smith Charts were originally developed around 1940 by Phillip Smith as a useful tool for making the equations involved in transmission lines easier to manipulate.

The Smith Chart is used to display a real antenna's impedance when measured on a Vector Network Analyzer (VNA). Smith Charts are also extremely helpful for impedance matching, as we will see.

Smith Charts can be used to increase understanding of transmission lines and how they behave from an impedance viewpoint. The Smith Chart is a fantastic tool for visualizing the impedance of a transmission line and antenna system as a function of frequency. Upon clicking, a point is 'selected' and r and z will be populated with their correct values (and a change event is fired).Д¬licking the element again un-selects/unlocks the point.SMITH CHART, SOLUTIONS OF PROBLEMS USING SMITH CHART R and z will both be null when the element is 'unlocked', meaning the cursor will follow the mouse around the element. In the example above, the smith-chart element's z value will be, corresponding to the r-value of. R and z are automatically kept in sync (i.e., each is the correct value corresponding to the other on the Smith chart), and either can be set to change the selected point on the chart.

z: The corresponding normalized load impedance again a complex number represented in the same way.

Д¬orresponds to the (x, y) position selected on the smith chart

r: The reflection coefficient a complex number of magnitude no greater than 1, represented as an array of components.

The smith-chart element has two attributes: The custom element is now available and may be used in HTML directly as with: Import the library in your main entrypoint: import 'web-component-smith-chart' A web component for displaying or selecting points on a Smith Chart.

The smith chart