Article

# Network theoretical and physical limitations of amplifier noise performance

Il Nuovo Cimento 08/1959; 13:416-429. DOI:10.1007/BF02724676

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**ABSTRACT:**At any single frequency, every n -terminal-pair noisy linear network has at most n real parameters that are invariant with respect to all lossless "imbeddings" of that network. Such an "imbedding" is defined by constructing an arbitrary lossless 2n -terminal-pair network, n of whose terminal pairs are connected to those of the original network, and the remaining n of which form a new set of n terminal pairs. Moreover, by a suitable choice of this imbedding structure, the original network can always be reduced to a canonical form which places clearly in evidence its n invariants. The canonical form consists of n isolated one-terminal-pair networks each of which comprises a (negative or positive) resistance in series with a noise voltage generator, and these various noise generators are mutually uncorrelated. The n exchangeable powers from the n isolated terminal pairs are the n invariants of the original network. The invariants have other physical meanings. Each meaning is best brought out by a corresponding particular matrix description of the network. Transformations between matrix descriptions are studied and applied to show that the invariants are interpretable as the n stationary values of the exchangeable power obtainable from any one of the new terminal pairs created by a lossless imbedding, as the imbedding network is varied through all lossless forms. Finally, the two invariants of a two-terminal-pair network are shown to fix the extrema of its noise measure, one of which is known to represent, for an amplifier, the minimum excess noise figure achievable at high gain.IRE Transactions on Circuit Theory 10/1958; - [show abstract] [hide abstract]

**ABSTRACT:**A matrix description of microwave amplifiers such as klystrons, traveling-wave tubes, and backward-wave amplifiers, in which an electron beam interacts with longitudinal RF fields, is developed. Certain relations between the matrix elements are derived as a consequence of the conservation of energy and these relations set a lower limit to the noise figure attainable with amplifiers of this class. It is shown that the minimum noise figure of any amplifier of this type with lossless RF structures is identical with that already found by several authors for the traveling-wave tube and is entirely determined by the noise parameters of the beam. These in turn depend only on conditions in the immediate neighborhood of the cathode. Special cases involving lossy structures are investigated and in each case the presence of loss is shown to increase the noise figure. The method is also applied to calculate the minimum noise figure of a double-stream amplifier.Proceedings of the IRE 09/1955; - [show abstract] [hide abstract]

**ABSTRACT:**A single quantitative measure of amplifier spot noise performance is established. It removes difficulties heretofore associated with the effect of feedback upon spot noise performance. This measure, (Me)opt, is a function of the amplifier noise and circuit parameters alone. It determines the lowest spot noise figure achievable at high gain with a given amplifier, which is used either alone or in a passive interconnection with other amplifiers of the same (Me)opt. Moreover, passive interconnection of amplifiers with different (Me)opt cannot lead to a spot noise figure at high gain better than that obtainable by using only amplifiers of the smallest (Me)opt. (Me)opt is, therefore, a valid measure of the absolute quality of amplifier noise performance. In many important cases the best noise performance attainable with a particular type of amplifier is actually achieved by a simple cascade in which the input of each stage is properly mismatched. The mismatch conditions for each stage do not in general coincide with those normally used to "minimize" its noise figure. In the case of a two-terminal-pair negative resistance amplifier, a limiting form of which is the maser, optimization may always be obtained using an ideal circulator.Proceedings of the IRE 09/1958;

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