Blackman's Theorem
   HOME

TheInfoList



OR:

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, 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 ...
by R. D. Middlebrook and the asymptotic gain model of
Solomon Rosenstark Solomon (), also called Jedidiah, was the fourth monarch of the Kingdom of Israel and Judah, according to the Hebrew Bible. The successor of his father David, he is described as having been the penultimate ruler of all Twelve Tribes of Israel ...
. Blackman's approach leads to the formula for the impedance ''Z'' between two selected terminals of a negative feedback amplifier as Blackman's formula: :Z = Z_D \frac \ , 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: :Z_ = Z^_ \left \frac\right/math> where: :Z\ is the impedance of the extra element; Z^_ is the input impedance with Z\ removed (or made infinite); Z^0_ is the impedance seen by the extra element Z\ with the input shorted (or made zero); Z^_ is the impedance seen by the extra element Z\ with the input open (or made infinite). Blackman's formula also can be compared with Choma's signal-flow result: :Z_=Z_\left frac\right\ , where Z_\ is the value of Z_\ under the condition that a selected parameter ''P'' is set to zero, return ratio T_Z\ is evaluated with zero excitation and T_I\ is T_Z\ for the case of short-circuited source resistance. As with the extra-element result, differences are in the perspective leading to the formula.


See also

*
Mason's gain formula Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, for whom it is named. MGF is an alternate method to finding the transfer function alg ...


Further reading

* * *


References

Electronic feedback Signal processing Electronic amplifiers Control engineering {{Engineering-stub