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:Ĭonstant 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. A few points along the circle are plotted. We've left the resistance circle of 1.0 in red on the Smith Chart. These circles are called constant resistance curves. The real part of the load impedance is constant along each of these curves. We'll now add several values for the constant resistance, as shown in Figure 3: In Figure 3, the zL=0.1 resistance circle has been added in purple. The zL=6 resistance circle has been added in green, and zL=2 resistance circle is in black. look at the set of curves defined by zL = R + iY, where Y is held constant and R varies from 0 to infinity. The curve defined by this set of impedances is shown in Figure 1: Since R cannot be negative for antennas or passive devices, we will restrict R to be greater than or equal to zero. The resulting curve zL = R + i is plotted in green in Figure 1.
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