A Smith chart should go round in circles

An online expert recently offered the following Smith chart graphic to help explain the mysteries of the Smith chart.

Instantly something looks wrong.

The usual shape of a Smith chart plot of a passive circuit is that in any set of nearby points, the locus of the points forms an arc and with increasing frequency, the points are located clockwise about the centre of that arc. Nothing in that statement constrains the location of the centre of that arc, it is not necessarily the middle of the chart. It is very rare that otherwise is observed.

Above is an example that obeys that rule. The highest frequency is the point marked X, and the lowest is marked O. In any set of nearby points, the locus forms an arc, and points of increasing frequency are located clockwise about the centre of the arc.

Experienced analysts use this property to navigate around the curve when there is no frequency axis to the chart.

So what is phoney about the original chart?

The problem is that implied under that rule:

  • frequency increases from B to C and B to A; and
  • frequency decreases from D to C and D to E.

Here is another example of an implausible Smith chart.

Again the locus of the plot breaks the ‘arcs' rule of real systems, this time as a result of poor guesses by software of the sign of reactance from unsigned reactance data from a low end analyser.

Try this one…

Is the low frequency end the X or the O?