Extra Class question of the day: Smith Chart

September 27, 2012 Dan KB6NU

NOTE: This is the last installment of the Extra Class question of the day. I’m going to be compiling all of these into the No-Nonsense Extra Class Study Guide. Watch for it real soon now.


Figure E9-3A Smith chart is shown in Figure E9-3 above. (E9G05) It is a chart designed to solve transmission line problems graphically. While a complete discussion of the theory behind the Smith Chart is outside the scope of this study guide, a good discussion of the Smith Chart can be found on the ARRL website.

The coordinate system is used in a Smith chart is comprised of resistance circles and reactance arcs. (E9G02) Resistance and reactance are the two families of circles and arcs that make up a Smith chart. (E9G04)

The resistance axis is the only straight line shown on the Smith chart shown in Figure E9-3. (E9G07) Points on this axis are pure resistances. In practice, you want to position the chart so that 0 ohms is at the far left, while infinity is at the far right.

The arcs on a Smith chart represent points with constant reactance. (E9G10) On the Smith chart, shown in Figure E9-3, the name for the large outer circle on which the reactance arcs terminate is the reactance axis. (E9G06) Points on the reactance axis have a resistance of 0 ohms. When oriented so that the resistance axis is horizontal, positive reactances are plotted above the resistance axis and negative reactances below.

The process of normalization with regard to a Smith chart refers to reassigning impedance values with regard to the prime center. (E9G08) The prime center is the point marked 1.0 on the resistance axis. If you’re working with a 50 ohm transmission line, you’d normally divide the impedances by 50, meaning that a 50 ohm resistance would then be plotted on the resistance axis at the point marked 1.0. A reactance of 50 + j100 would be plotted on the resistance circle going through the prime center where it intersects the reactance arc marked 2.0.

Impedance along transmission lines can be calculated using a Smith chart. (E9G01) Impedance and SWR values in transmission lines are often determined using a Smith chart. (E9G03) Standing-wave ratio circles are often added to a Smith chart during the process of solving problems. (E9G09)

The wavelength scales on a Smith chart calibrated in fractions of transmission line electrical wavelength. (E9G11) These are useful when trying to determine how long transmission lines must be when used to match a load to a transmitter.

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