68 NETWORK REALIZATION OF OPTIMUM PERFORMANCE [Ch. 7 



With these specific values we obtain for the optimum noise-measure 

 expression of the triode 



Mont 



—^ + ylRn^ + RlRn H T — ^ ~l 





(7.37) 



For large values of m, the minimum noise measure is effectively equal 

 to the minimum excess-noise figure, and all terms in Eq. 7.37 divided by 

 II can be disregarded. We obtain in the limit ju — ^ °° 



/^min = 1 + — (i?n + Vi?^^ + R^R^) 



This result is well known.^ 



7.4. Optimization of Negative-Resistance Amplifiers, 

 Definite Case 



There remains the problem of achieving the optimum noise measure of 

 negative-resistance amplifiers, that is, the class illustrated in Fig. 7.1c. 

 This problem we now wish to solve, employing a positive source imped- 

 ance and guaranteeing that a positive output impedance results. 



While it is actually possible to accomplish our purpose by performing 

 a consecutive series of lossless reciprocal imbeddings, starting from the 

 specific amplifier form given in Fig. 7.1c, the particular method we found 

 for doing it was rather involved. It was also of little interest beyond its 

 application to the present proof. 



Fortunately, there exists another method of optimizing the noise per- 

 formance of any nonpassive network, including negative-resistance 

 networks. This method is not only simple analytically but has a practical 

 bearing upon the noise optimization of the new maser amplifier. We 

 shall present this solution and its relation to the maser. 



We have shown in Chap. 4 that every two-terminal-pair network can 

 be reduced by lossless nonreciprocal imbedding to the canonical form of 

 Fig. 7.2, comprising two isolated (positive or negative) resistances in 

 series with uncorrelated noise voltage generators. Moreover, the open- 

 circuit noise voltages Eni and En2 and the two eigenvalues Xi and X2 of 

 the characteristic-noise matrix N are directly related: 



J^nl ^ _x^; ^ ^ _X2 (7.38) 



4i?i ^' 4i?2 



2 A. van der Ziel, Noise, Prentice-Hall, New York (1954) 



