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Operating power gain circles

Recall operating power gain equation
equation1189

 eqnarray1195
(156) can be rearranged as an equation of circle on text_wrap_inline2885 plane
equation1206

For each value of text_wrap_inline3235, we have a corresponding text_wrap_inline2925 circle with
equation1218

equation1224

Note that the centers of text_wrap_inline2925 circles are always on the line drawn between text_wrap_inline3241 and the origin of the text_wrap_inline2885 plane. The radius of text_wrap_inline2925 circle is getting smaller for a larger text_wrap_inline3235. In case of an unconditionally stable device, when text_wrap_inline3249, text_wrap_inline3235 reaches its maximum.
equation1238
so as text_wrap_inline2925
equation1245
In case of a potentially unstable device, when text_wrap_inline3255, i.e., text_wrap_inline3257 , the text_wrap_inline2925 circle equals to input stability circle.
equation1251

equation1256

Example In a 50 text_wrap_inline2807 system, a transistor has the following S-parameter at 1.3 GHz. Plot a few constant operating power gain circles.
displaymath3052

displaymath3053

Solution text_wrap_inline3263 dB.
displaymath3223
At maximum operating power gain, the constant gain circle becomes a point with text_wrap_inline3249, and the load reflection coefficient is
displaymath3224
We can calculate the corresponding input reflection coefficient for this load.
displaymath3225
Hence, if the source is conjugately matched with the amplifier, then the source reflection coefficient becomes
displaymath3226
Note that the results are the same as the optimum terminations text_wrap_inline3139,text_wrap_inline3141.


tabular1289

 figure1295
Figure 19: A set of constant operating gain circles plotted on a Smith chart