74 CONCLUSIONS [Ch. 8 



noise characteristics. In parametric amplifiers correlation between signal 

 sidebands often occurs and must be taken into account in the mathe- 

 matical analysis. For such an analysis a systematic theory of noise in 

 multiterminal-pair networks involving correlation between signal and/or 

 noise sidebands is required. It is also probable that, because of these very 

 same signal correlations between sidebands, the appropriate theory for 

 the parametric case may not be merely the theory of the generalized noise 

 parameter pT introduced in this work. We have not had the opportunity 

 to pursue this interesting question in much detail. But we have studied 

 the question sufficiently to be convinced that the general matrix methods 

 of dealing with power and power ratios employed in the present study 

 will help greatly in the analysis and understanding of these somewhat 

 more difficult problems. 



The remarks of the previous paragraphs do not, of course, imply that 

 multiterminal-pair networks have been neglected completely. Indeed, in 

 the impedance-matrix formulation we have given extensive attention to 

 the exchangeable-power interpretations of the network invariants in the 

 multiterminal-pair case. As a practical application of these ideas, we may 

 refer again to the work of Granlund^ regarding the problem of combining 

 a multiplicity of antenna outputs into a single receiver, when the inputs 

 to the antennas are statistically related. Furthermore, from the imped- 

 ance formulation we have been able to develop a canonical form for the 

 multiterminal-pair network. The merit of this form is that it leads to a 

 simplification in thinking about single-frequency noise and gain char- 

 acteristics of linear networks. 



The problem of considering noise performance over a broad band, 

 rather than at a single frequency, appears to be covered by the spot-noise 

 discussions that we have conducted. Certainly, in a two-terminal-pair 

 amplifier one could adopt the position of optimizing the noise measure at 

 each frequency in the band. Although such a procedure might involve 

 complicated feedback variations with frequency and/or intricate match- 

 ing systems, these are principally network-synthesis problems that pre- 

 sumably could be solved on the basis of suitable approximations, if it 

 appeared desirable to do so. There is no doubt that such a solution would 

 give the "optimum noise performance" of the amplifier. By this we mean 

 that the optimum is to be interpreted as the "best signal-to-noise ratio at 

 high gain, at each frequency within the band." It is by no means obvious 

 that, with the over-all system in mind, such a solution is always the 

 best. There are many other considerations besides noise performance 

 which enter into the design of wideband amplifiers, such as the behavior 



^ J. Granlund, Topics in the Design of Antennas for Scatter, M.I.T. Lincoln Labora- 

 tory Technical Report 135, Massachusetts Institute of Technology, Cambridge, Mass. 

 (1956). 



