Ch. J] INTRODUCTION 7 



matrix description leads to a different interpretation of the invariants. 



In the case of an active two-terminal-pair network, a particularly- 

 important interpretation of the invariants is brought out by the general- 

 circuit-parameter-matrix description. This interpretation relates directly 

 to the optimum "noise measure" of the network used as an amplifier and, 

 therefore, to the minimum noise figure of the amplifier at arbitrarily high 

 gain. Chapter 6 is devoted to this noise-measure concept and to the 

 range of values that the noise measure may assume for a two-terminal- 

 pair ampKfier subjected to arbitrary passive network transformations. 

 In particular, the minimum value of the noise measure of the amplifier is 

 found to be directly proportional to one of the two invariants of the 

 amplifier. 



A study is made of those arbitrary passive interconnections of two- 

 terminal-pair amplifiers which result in an over-all two-terminal-pair 

 amplifier. The conclusion is that the noise measure of the composite 

 amplifier cannot be smaller than the optimum noise measure of the best 

 component ampHfier, namely, the amplifier with the smallest optimum 

 noise measure. 



The general theorems having established the existence of an optimum 

 value of the noise measure of amplifiers, it remains in Chapter 7 to discuss 

 in detail the network realization of this optimum for two-terminal-pair 

 amplifiers. Some practical ways of achieving it are presented. Among 

 these, the realization of optimum noise performance for a maser may be 

 of greatest current interest. 



With proof of the existence and realizability of a lower limit on the 

 noise measure, and therefore of the noise figure at high gain, the major 

 objective of the present work is accomplished. It is demonstrated that 

 the quality with regard to noise performance of a two-terminal-pair 

 amplifier can be specified in terms of a single number that includes the 

 gain and that applies adequately to low-gain amplifiers. 



We have previously published various separate discussions of some of 

 these topics in different contexts.®~^° Each of these discussions has 

 suffered from unnecessary complications because space limitations forced 



® H. A. Haus and R. B. Adler, "Invariants of Linear Networks," 19S6 IRE Con- 

 vention Record, Part 2, 53 (1956). 



^ H. A. Haus and R. B. Adler, "Limitations des performances de bruit des ampli- 

 ficateurs lineaires," L'Onde Electrique, 38, 380 (1958). 



^ H. A. Haus and R. B. Adler, "Optimiim Noise Performance of Linear Amplifiers," 

 Proc. I.R.E., 46, 1517 (1958). 



^ R. B. Adler and H. A. Haus, "Network Realization of Optimum Amplifier Noise 

 Performance," IRE Trans, on Circuit Theory, CT-5, No. 3, 156 (1958). 



^"H. A. Haus and R. B. Adler, "Canonical Form of Linear Noisy Networks," 

 IRE Trans, on Circuit Theory, CT-5, No. 3, 161 (1958). 



