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The Miller theorem may be proved by using the equivalent two-port network technique to replace the two-port to its equivalent and by applying the source absorption theorem. [3] This version of the Miller theorem is based on Kirchhoff's voltage law; for that reason, it is named also Miller theorem for voltages.
Figure 2B shows a circuit electrically identical to Figure 2A using Miller's theorem. The coupling capacitor is replaced on the input side of the circuit by the Miller capacitance , which draws the same current from the driver as the coupling capacitor in Figure 2A. Therefore, the driver sees exactly the same loading in both circuits.
In electrical circuits, reactance is the opposition presented to alternating current by inductance and capacitance. [1] Along with resistance, it is one of two elements of impedance; however, while both elements involve transfer of electrical energy, no dissipation of electrical energy as heat occurs in reactance; instead, the reactance stores energy until a quarter-cycle later when the energy ...
Miller's theorem can be used to effect this replacement: it states that, if the gain ratio of two nodes is 1 / K , then an impedance of Z connecting the two nodes can be replaced with a Z / 1 − K impedance between the first node and ground and a KZ / K − 1 impedance between the second node and ground.
Miller's theorem generalizes to a version of Sullivan's conjecture in which the action on is allowed to be non-trivial. In, [ 3 ] Sullivan conjectured that η is a weak equivalence after a certain p-completion procedure due to A. Bousfield and D. Kan for the group G = Z / 2 {\displaystyle G=Z/2} .
In electronics engineering, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback.It usually has two primary goals: To avoid the unintentional creation of positive feedback, which will cause the amplifier to oscillate, and to control overshoot and ringing in the amplifier's step response.
The field was founded by Wilhelm Cauer after reading Ronald M. Foster's 1924 paper A reactance theorem. Foster's theorem provided a method of synthesising LC circuits with arbitrary number of elements by a partial fraction expansion of the impedance function.
The horizontal top section of a 'T'-antenna can also reduce the capacitive reactance at the feedpoint, substituting for a vertical section whose height would be about 2 / 3 its length; [9] if it is long enough, it completely eliminates reactance and obviates any need for a loading coil at the feedpoint.