Ch. 1\ INTRODUCTION 3 



simple cascade become important in amplifier applications. The question 

 of the quality of noise performance then becomes much more complicated. 

 For example, when degenerative feedback is applied to an amplifier, its 

 noise figure can be reduced to as close to unity as desired (for example, 

 bypassing the entire amplifier with short circuits yields unit noise figure). 

 But its gain is also reduced in the process. Indeed, if identical stages 

 with the feedback are cascaded to recover the original single-stage gain 

 before feedback, the resulting noise figure of the cascade cannot be less 

 than that of the original amplifier.^ Moreover, with degenerative feed- 

 back the gain may easily be so greatly reduced that, as a first stage in a 

 cascade, this amplifier alone no longer determines the over-all noise 

 figure of the cascade. The minimum-noise-figure criterion considered 

 above as a measure of amplifier noise performance breaks down. It 

 appears that an absolute measure of amplifier noise performance must 

 include, in addition to the specification of noise figure and source im- 

 pedance, at least the specification of the gain. 



The foregoing reasoning led us to the investigation presented in this 

 study. Taking our clues from the results previously found by Haus and 

 Robinson^ for microwave amplifiers, and the method of active-network 

 description presented by Mason,^ we searched for a measure of amplifier 

 noise performance that would not only include the gain explicitly, as 

 discussed earlier, but could also be minimized by external circuitry in a 

 nontrivial way. Moreover, we believed that the minimum thus obtained 

 should be a quantity characteristic of the amplifier itself. It should, for 

 example, be invariant under lossless feedback, a type of feedback that 

 does not appear to change the essential "noisy" character of the amplifier 

 because it certainly adds no noise and can always be removed again by 

 a realizable inverse lossless operation. 



The precise form of a suitable noise-performance criterion has actually 

 been known for many years, although its deeper significance somehow 

 escaped attention. Indeed, the most glaring example of the correct 

 criterion arises from the familiar problem of cascading two (or more) 

 low-gain amplifiers having different noise figures Fi and F2 and different 

 available gains Gi ( > 1 ) and G2 ( > 1 ) . 



The question is : If the available gain and noise figure of each amplifier 

 do not change when the order of cascading is reversed, which cascade 

 order leads to the best noise performance for the pair? Usually, "best 

 noise performance" has been taken to mean "lowest noise figure" for the 



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



* H. A. Haus and F. N. H. Robinson, "The Minimum Noise Figure of Microwave 

 Beam Amplifiers," Proc. I.R.E., 43, 981 (1955). 



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

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



