By Hermann A Haus, Richard B Adler
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Additional info for Circuit Theory of Linear Noisy Networks
Mixed voltage-current representation of 2m-terminal-pair network. Returning to the general expression (Eq. 2 ) , ,ve note that it also can be written in a form similar to Eq. 5. 1 . 6 ) The analysis in Sec. 2 shows how transformations are performed from one matrix representation to another. Then the transformation of the power expression will be studied. Combining the results of these two studies, we shall be able to define a characteristic-noise matrix for every formalism and to show its relation to the characteristic-no\se matrix de fined in Eq.
4. 1 . This is accomplished by a lossless network transformation, and results in an arrangement like Fig. 2 but with 411 separate resistances and un correlated noise generators. These resistances are arranged in the way shown at the bottom of Fig. 8.
The conclusion is immediate . The eigenvalues of the characteristic-noise matrix of an n-terminal-pair network constructed by lossless interconnection of independently noisy com ponent networks having m terminal pairs in all, m > n, must lie 'within the range defined by the most extreme eigenvalues of the component networks. Linear Noisy Networks in Other Representations In the foregoing analysis we have found all the invariants of a linear noisy network with respect to lossless imbeddings that preserve the number of terminal pairs.
Circuit Theory of Linear Noisy Networks by Hermann A Haus, Richard B Adler