Sec. 7.1] CLASSIFICATION OF AMPLIFIERS 59 



Chap. 1. The excess-noise figure of the high-gain cascade is equal to the 

 optimum noise measure of the cascade, and thus in turn equal to Me, opt 

 of the individual amplifiers. This arrangement therefore accomplishes 

 the realization of the lower limit of the excess-noise figure at high gain. 



Since Me, opt of any given amplifier determines the lowest (excess-) 

 noise figure that can be achieved at high gain with the amplifier, either 

 singly or in interconnection with other amplifiers of the same type, we 

 may conclude from the criterion chosen in Chap. 1 that Me, opt is an 

 absolute measure of the quality of noise performance of a given amplifier. 



7.1. Classification of Two-Terminal-Pair Amplifiers 



The noise-performance optimization problem is solved conveniently by 

 referring to a detailed classification of nonpassive two-terminal-pair net- 

 works (that is, amplifiers). Mason^ has shown that every such network 

 can be reduced by lossless reciprocal imbedding to one of the three basic 

 t)^es shown in Fig. 7.1. His classification is based primarily upon the 

 range of values of the unilateral gain U 



U = ^^ ^ (7.1) 



4(i?ni?22 — ^12^21) 



where the i?'s are the real parts of the impedance-matrix elements. Since 

 the numerical value of U is invariant to lossless reciprocal transforma- 

 tions,^ none of the three types can be carried into any other type by such 

 transformations. 



The first type (Fig. 7.1a), with C/ > 1, is by far the most common. 

 The majority of vacuum-tube and transistor amplifiers belong to this 

 class. The second type (Fig. 7.1&), with C/ < 0, is less common. It does, 

 however, share one important property with the first ; namely, both have 



det (P - TPT+) < (7.2) 



which means that they can absorb as well as deliver power. It is perhaps 

 not surprising, therefore, that with lossless nonreciprocal transformations 

 amplifiers of the type of Fig. 7,16 can be carried into the form shown in 

 Fig. 7.1a. This we now show. 

 The network of Fig. 7.16 has a unilateral gain 



U = -\u\^ <0. 



By connecting the network in series with a lossless gyrator with the 



^ S. J. Mason, "Power Gain in Feedback Amplifiers," Trans. IRE, Professional 

 Group on Circuit Theory, CT-1, No. 2, 20 (1954). 



