![]() I’m choosing 100 Ω as our normalization impedance because, with the values in Figure 4, the map will spread out on the chart and be easy to follow. We’ll map a journey on the Smith chart and compile a travelogue along the way. You can find L and C using a Smith chart. I propose a simple LC circuit ( Figure 4). Because we’re not building an electric heater, we will use purely reactive components. 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.
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