Operating power gain circles

Recall operating power gain equation


 
(156) can be rearranged as an equation of circle on plane

For each value of , we have a corresponding circle with

Note that the centers of circles are always on the line drawn between and the origin of the plane. The radius of circle is getting smaller for a larger . In case of an unconditionally stable device, when , reaches its maximum.

so as

In case of a potentially unstable device, when , i.e., , the circle equals to input stability circle.

Example In a 50 system, a transistor has the following S-parameter at 1.3 GHz. Plot a few constant operating power gain circles.

Solution dB.

At maximum operating power gain, the constant gain circle becomes a point with , and the load reflection coefficient is

We can calculate the corresponding input reflection coefficient for this load.

Hence, if the source is conjugately matched with the amplifier, then the source reflection coefficient becomes

Note that the results are the same as the optimum terminations ,.

 
Figure 19: A set of constant operating gain circles plotted on a Smith chart