Advanced Smith Charting

Smith Charts are a beautiful way of visualizing what's going on with a circuit.  The importance of Smith Charts in the design process has (arguably) waned- few professionals still design matching networks using Smith Charts outside of school.  The RF design tools (with optimizers) are generally good enough to solve most problems.  Unfortunately, this means many designers have forgotten or were never taught some important features of the Smith Chart.  

Neat Smith Chart Fact

For circuits using only passive components (and often even those with active components), curves on the Smith Chart spin clockwise with increasing frequency.

Constant Q Lines

Smith Charts all about lines of constant... something.  Smith Charts themselves are lines of constant resistance and reactance.  Most people are probably familiar with lines of constant SWR, any point on the Smith Chart the same distance from the center has the same mismatch.  One of the lesser known features of the Smith Chart is the lines of constant Q.

The Q of a circuit can be defined in multiple ways, often as the ratio of the frequency to the bandwidth.  High Q translates into a narrow band circuit- in this case a narrow band match.  

Q can also be defined as the ratio of the reactance to the resistance.  

This simple relationship means that lines of constant Q can be drawn on a Smith Chart. The relationship is simple: the arc starts at R=X=0; ends at R=X=infinity; and is centered at the Cartesian coordinates of X=0, Y= +/-(1/Q).

Consider the Smith Chart below with four Q contours, Q equal to 1, 2, 5, and 10.  The (admittedly crudely) drawn matching path is meant to illustrate several points:

Click image to enlarge

As always, certain Caveats exist.  For this particular scenario, I have assumed Foster components (no negative capacitors or inductors, just passive components).

Copyright 2010, Gregory Kiesel