Nonlinear Distortion in Feedback Amplifiers

Consider a feedback amplifier
F
with a nonlinear output device
T_0
and an open-loop amplifier A having the same gain and the same output device
T_0
. If the gains of the forward amplifier
u
and feedback network
\beta
are independent of frequency, it is well known that under the usual conditions the nonlinear distortion
\zeta
of
F
due to
T_0
is related to the nonlinear distortion
\hat{\zeta}
of
A
by
\zeta = \hat{\zeta}/(1 + u \beta)
. In this paper conditions are determined under which a similar formula, namely
\zeta = (1 + u \beta)^{-1 \ast}
, applies when
u
and
\beta
are strictly stable linear time-invariant amplifiers. The interpretation of the formula is the following:
\zeta
is the function of time which is output of an amplifier whose gain is
1/(1 + u \beta)
when
\hat{\zeta}
is its input, and
\hat{\zeta}
is the nonlinear distortion of the open-loop amplifier A.