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 in 1943,[1] was connected to signal-flow analysis by John Choma, and was made popular in the extra element theorem by R. D. Middlebrook and the asymptotic gain model of Solomon Rosenstark.
[2][3][4][5] 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.
[7][8] Blackman's formula can be compared with Middlebrook's result for the input impedance Zin of a circuit based upon the extra-element theorem:[4][9][10] where: Blackman's formula also can be compared with Choma's signal-flow result:[11] where
under the condition that a selected parameter P is set to zero, return ratio