Immittance Smith chart showing a normalized load and target. With a normalizing impedance of Z 0 50, we locate the normalized load and target impedance (z L 1, z In 1 + j2) on the immittance Smith chart (Figure 4). The dashed-line circle in each plot is the demarcation circle of return loss as mentioned in Chapter 3, where S 11 or S 22 = − 10 dB. Using an immittance Smith chart, design a matching network to transform Z L 50 to Z In 50 + j100. (The methodology of impedance matching in the wideband case introduced and discussed in this chapter was developed in 2005 by the author specially for a UWB (ultra wideband) system and has not been made public until now).įigure 4.1 shows the difference of the return loss or impedance on the Smith Chart between the narrow and wideband cases. In this chapter, we will apply the same process of impedance matching as in the narrowband case, but the main effort will to expand the skill from narrow to wide bandwidth. If we are dealing only with impedances with non-negative resistive components, our interest is focused on the area inside the circle. Those with negative real parts map outside the circle. Complex numbers with positive real parts map inside the circle. In the wideband case, instead of a single frequency, the entire wide bandwidth must be taken care of, which makes impedance matching somewhat difficult. The Smith chart is a mathematical transformation of the two-dimensional Cartesian complex plane. However, in the narrowband case, only one frequency needs to be taken care of in the process of impedance matching because a narrow bandwidth can be represented approximately by the central frequency. That is, if we add a parallel inductor with a susceptance of -i3, the impedance will be translated to the center of the Smith Chart, shown in Figure 2: Figure 2. To complete the impedance matching, we just need to cancel out the susceptance. The normalized source impedance, rS, is Point A, and the normalized load impedance, rL, is Point C. The methodology of impedance matching is basically the same between narrow and wideband cases. Using a Series Capacitor to Move zA to the Re y1 circle. The load and source resistances are plotted on the Smith chart in Figure 6.7.4 (a) after choosing a normalization impedance of Z0 50 (and so rS RS / Z0 0.5 and rL RL / Z0 4 ). Impedance Matching in the Wideband Case 4.1 Appearance of Narrow and Wideband Return Loss on a Smith Chart

Smith chart impedance matching