viii PREFACE 



for any linear amplifier could be made without referring again to some 

 detailed physical mechanism. In order to detach the study of noise 

 performance from specific physical mechanisms, one had to have recourse 

 to general circuit theory of active networks. Such a theory had grown 

 up around the problems associated with transistor amplifiers, and im- 

 portant parts of it were available to us through the association of one of 

 us with Professor S. J. Mason. This combination of circumstances led 

 to the collaboration of the authors. 



Two major guiding principles, or clues, could be drawn from the 

 experience on microwave tubes. One such clue was the general form of 

 the probable appropriate noise parameter. The other was the recog- 

 nition that matrix algebra and a proper eigenvalue formulation would be 

 required in order to achieve a general theory without becoming hope- 

 lessly involved in algebraic detail. 



Essentially by trial and error, guided by some power-gain theorems in 

 active circuit theory, we first found a few invariants of noisy networks. 

 Afterward, while we were trying to decide around which quantities we 

 should build a matrix-eigenvalue formulation leading to these same 

 invariants, we were aided by the fact that Mr. D. L. Bobroff recognized 

 a connection between the invariants which we had found and the problem 

 of the available power of a multiterminal-pair network. 



Armed with this additional idea, we consulted extensively with Profes- 

 sor L. N. Howard of the Massachusetts Institute of Technology, Depart- 

 ment of Mathematics, in search of the appropriate matrix-eigenvalue 

 problem. As a result of his suggestions, we were able to reach substan- 

 tially the final form of the desired formulation. 



Once the proper eigenvalue approach was found, additional results 

 and interpretations followed rapidly. In particular, the idea that the 

 eigenvalue formulation should be associated with a canonical form 

 of the noisy network was suggested in a conversation with Professor 

 Shannon. 



One of the principal results of the work is that it furnishes a single 

 number, or tag, which may be said to characterize the amplifier noise 

 performance on the basis of the signal-to-noise-ratio criterion. The novel 

 features of this tag are two in number: First, it clears up questions of 

 the noise performance of low-gain amplifiers or of the effect upon noise 

 performance of degenerative feedback; second, it provides for the first 

 time a systematic treatment of the noise performance of negative-resist- 

 ance amplifiers. The latter results were not expected in the original 

 motivation for the study but grew from insistent demands upon the 

 internal consistency of the theory. It is interesting that the negative- 

 resistance case will probably turn out to be one of the most important 

 practical results of our work. 



