52 



NOISE MEASURE 



[Ch. 6 



of Nr. By making use of Table 5.1 and Eq. 5.28 in the special case of a 

 two-terminal-pair network, we see that the following three cases have to 

 be distinguished: 



LP — TPT"*" is negative definite; T is the general circuit matrix of a 

 passive network, Mj < 0. 



2. P — TPT^ is positive definite; T is the general circuit matrix of a 

 negative-resistance network, Mj > 0. 



3. P — TPT""" is indefinite; T is the general circuit matrix of a network 

 capable of absorption, as well as delivery of power, Mj < 0. 



M^ 



Mp 



-m: = 



kTQ^f 



X2 



kTQ^f 



Mi 



kToAf 



kToAf 



-m; = o 



kTo^f 



■MJ = 



kToAf 



P - TPTt negative definite P - TPTt positive definite 

 (a) (b) 



P - TPTT indefinite 

 (c) 



Fig. 6.6. Schematic diagram of permitted values of Me' for two-terminal-pair networks. 



When C in Eq. 6.30 is varied through all possible values, M/ reaches two 

 extrema, which are the two eigenvalues of the characteristic-noise matrix 

 Nr divided by kTo A/. Now, we have pointed out that in practical 

 situations amplifiers are driven from sources having an internal im- 

 pedance with positive real part. According to Table 6.1, the noise meas- 

 ure is positive when i?^ > in all cases except Rq > 0,0 < Ge < 1. 

 This case does not correspond to an amplifier. Hence we shall be inter-" 

 ested in achieving only positive values of Mj , which occur in Cases h and 

 c of Fig. 6.6. These cases both have an available gain, G, in the con- 



