You can do a lot of algebra to find these circles’ centers and radii, or you can just flip the impedance circles horizontally.Ĭonsider a 1-GHz generator with a 25-Ω source impedance driving a 400-Ω load, for a horrendous Γ=0.882. But I can add some admittance circles to form an immittance chart ( Figure 3), where admittance Y= g+j b=1/ Z. Your chart isn’t as elaborate as some I’ve seen. An immittance chart includes admittance (blue) and impedance (red) circles. Similarly, an impedance of 2+j1 is located where the red r=2 circle crosses the blue x=1 circle (point B), where Γ= 4+j2. A resistance of 2 appears where the red r=2 resistance circle crosses the horizontal axis (point A), where you can see that Γ=0.333. Figure 2 shows some of these circles plotted on a grid representing Γ. Similarly, a locus of points representing constant reactance is a circle of radius 1/ x centered at 1, 1/ x. Noting that Z L is a complex number in the form of r+j y, you can manipulate the equation for Z L to determine that a locus of points representing constant resistance is a circle of radius 1/( r+1) centered at r/( r+1). In a Smith chart, resistance (red) and reactance (blue) are plotted on a grid representing Γ. You’ll also see it represented as the scattering parameter S 11. It’s the reflection coefficient (sometimes denoted as ρ), which we discussed in part 1. Normalization lets one Smith chart work with any characteristic impedance. This part elaborates on the Smith chart’s construction and provides an impedance-matching example. Part 1 of this FAQ looked at why you might use a Smith chart. The Smith chart remains valuable in helping to visualize how such circuits perform. A typical RF/microwave circuit includes a source, transmission line, and load. That circuit includes a source with impedance Z s, transmission line with characteristic impedance Z 0, and load with impedance Z L. Take a journey around a Smith chart to find capacitance and inductance values in a matching network.īefore computers became ubiquitous, the Smith chart simplified calculations involving the complex impedances found in RF/microwave circuits such as the one shown in Figure 1.

Smith chart impedance matching