5/26/2023 0 Comments Using a smith chart![]() ![]() A larger version is shown here.įigure 1 should look a little intimidating, as it appears to be lines going everywhere. We will build up the Smith Chart from scratch, so that you can understand exactly what all of the lines mean. 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. But for now, just admire the Smith Chart and its curvy elegance. This section of the antenna theory site will present an intro to the Smith Chart basics. 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).įor a primer on complex math, click here. The complex reflection coefficient, or, must have a magnitude between 0 and 1.Īs 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 byįor this tutorial, we will assume Z0 is 50 Ohms, which is often, but not always the case. In Figure 2, plotting the set of all values for the complex reflection coefficient, along the real and imaginary axis. The center of the Smith Chart is the point where the reflection coefficient is zero. That is, this is the only point on the smith chart where no power is reflected by the load impedance. The outter ring of the Smith Chart is where the magnitude of is equal to 1. Along this curve, all of the power is reflected by the load impedance. 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:Įquation doesn't affect the reflection coefficient tow. It is just a convention that is used everywhere. Now, suppose we have the normalized load impedance given by: Constant Resistance Circlesįor a given normalized load impedance zL, we can determine and plot it on the Smith Chart. 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. In Figure 1, the outer blue ring represents the boundary of the smith chart. The black curve is a constant resistance circle: this is where all values of z1 = 1 + i*Y will lie on. Several points are plotted along this curve, z1 = 1, z1 = 1 + i*2, and zL = 1 - i*4. Suppose we want to know what the curve z2 = 0.3 + i*Y looks like on the Smith Chart. In Figure 2, the black ring represents the set of all impedances where the real part of z2 equals 0.3. ![]()
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