Read a Smith chart: resistance circles, reactance arcs, the matched center, SWR circles and wavelength scales, and use it to place a stub.
Syllabus: The Smith chart
Compendium articles on the ideas in this lesson, beyond what the exam asks.
Practise the 11 pool questions for this group. Answers are shuffled, and every one comes with a one-line "why".
Two families of curves cross to fix a point: resistance circles (constant r) and reactance arcs (constant x). Left edge is a short, right edge is an open, center is a perfect match.
The horizontal line is the resistance axis (x = 0), the only straight line. The outer circle is the reactance axis (r = 0): every arc ends on it.
RememberCircles = constant resistance. Arcs = constant reactance.
Divide every impedance by the line's Z₀. The center is then 1 + j0 for any line. A 50 Ω chart and a 75 Ω chart are the same picture: reassign the center's value and the labels follow.
RememberCenter = 1 + j0 = Z₀. Match is always the middle.
SWR doesn't change along a lossless line, so the point stays on a constant-SWR circle (added to the chart when you design a match). Moving toward the generator turns it clockwise. The rim scales count fractions of a wavelength on that line, ½ λ per lap.
RememberLonger line = clockwise walk on the same SWR circle. Scales are in line wavelengths.
The chart gives impedance and SWR along a line. Its classic job: find where to attach a stub and how long to make it. Read as admittance, slide along the SWR circle to the g = 1 circle, then add a stub whose susceptance cancels the rest.
RememberPosition gets you to the g = 1 circle. Stub length cancels what is left.