Blackman's theorem is a general procedure for calculating the change in an impedance due to feedback in a circuit. It was published by
Ralph Beebe Blackman
Ralph Beebe Blackman (August 29, 1904 – May 24, 1990) was an American mathematician and engineer who was among the pioneers of the information age along with Claude E. Shannon, Hendrik Wade Bode, and John Tukey.
Blackman graduated from the ...
in 1943,
was connected to
signal-flow analysis by
John Choma, and was made popular in the
extra element theorem The Extra Element Theorem (EET) is an analytic technique developed by R. D. Middlebrook for simplifying the process of deriving driving point and transfer functions for linear electronic circuits.
Much like Thévenin's theorem, the extra element t ...
by
R. D. Middlebrook
Robert David Middlebrook (May 16, 1929 – April 16, 2010) was a professor of electrical engineering at the California Institute of Technology (Caltech). He is most well known in the field of power electronics and as a proponent of design-oriented ...
and the
asymptotic gain model
In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...
of
Solomon Rosenstark.
[ Blackman's approach leads to the formula for the impedance ''Z'' between two selected terminals of a negative feedback amplifier as Blackman's formula:
:
where ''ZD'' = impedance with the feedback disabled, ''TSC'' = loop transmission with a small-signal short across the selected terminal pair, and ''TOC'' = loop transmission with an open circuit across the terminal pair.][ The loop transmission also is referred to as the return ratio.][ Blackman's formula can be compared with Middlebrook's result for the input impedance ''Zin'' of a circuit based upon the extra-element theorem:][
:]