Unilateral power gain circles

Recall unilateral transducer power gain

For a given device, is fixed, the values of and depend on , . Let's say, we want to investigate the effect of on . Notice that is maximum when

 

Note that equation of a circle on the complex plane is

(145) can be rearranged in the following form

for given value of , this equation provides the corresponding values of which are in a form of a circle with

This set of circles is called constant circles. Note that

1. the centers of circles are always on the line drawn between and the origin,
2. when or , we have the maximum gain. Then the circle becomes a point at which corresponded to conjugated match at the input port.
3. when or , we have . This indicates that the circle passes through the origin. This is also the boundary of the input network for providing gain, any values beyond this circle represent loss.

Similarly, a set of constant gain circles can be drawn for the output port.

The constant circles can be drawn on the plane with

Example In a 50 system, a transistor has the following S-parameter at 1.3 GHz.



Plot a few constant unilateral power gain circles.

Solution Because , and have the same set of constant gain circles. Let







The parameters of a set of constant gain circles are listed in the following table

 
Figure 18: A set of constant unilateral gain circles plotted on a Smith chart