Global stability analysis of automatic gain control circuits

Behavior of Automatic Gain Control Circuits (AGC's) is studied in a general nonlinear setting. Both noncoherent and coherent AGC's are addressed, and it is shown that AGC's are globally stable. When
x(t)
is the AGC input and
y(t)
is the AGC output, there is an a priori desired gain
\bar{g}(t)
such that one solution of the AGC equations is
y(t) =
\bar{g}(t)x(t)
. Further, all other solutions
g(t)
of the AGC equation satisfy
g(t) \rightarrow \bar{g}(t)
as
t \rightarrow \infty
. The conclusions are reached after placing very general conditions upon the two nonlinear circuit elements: the gain controlled amplifier and the detector. The conditions are very weak and are the minimum expected for these circuit elements. The tools used to reach the conclusion are basic theorems governing the qualitative behavior of nonlinear ordinary differential equations.