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

- the centers of circles are always on the line drawn between and the origin,
- when or , we have the maximum gain. Then the circle becomes a point at which corresponded to conjugated match at the input port.
- 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