Use a Smith chart for component characterizations

Article By : John Dunn

Applicability of the Smith chart also applies to component characterizations, sometimes with intuitively surprising results.

In response to the prior Smith chart essay, several comments were offered via LinkedIn groups. One comment in particular, from Dan Bullard, caught my attention: “One of my interview questions is, what does a quartz crystal look like on a Smith chart? That throws most people.” The question is worth a look-see. The equivalent circuit of a crystal is taken as follows.

circuit diagram for quartz crystalFigure 1 Here is the equivalent circuit of a quartz crystal.

Doing a Smith chart plot of this circuit yields the following result.

quartz crystal Smith chartFigure 2 This is a Smith chart plot for the circuit in Figure 1.

The left side of Figure 2 is simply the Smith chart for limited ranges of the real and imaginary coefficients based on the previously-presented equations. The right side of Figure 2 includes in red going clockwise as frequency is swept upward through series resonance, the crystal's Smith chart track for ESR = 6 ohms, L = 10 mHy, C1 chosen for series resonance at 10 MHz, and for C2 = 30 pF. I don't know for sure that these L1, C1, and C2 values are real-world proper, but lowering L1 to only 1 mHy yields a Smith chart result that is visually indistinguishable from the track shown. This article was originally published on EDN. John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE). Related articles:

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