Sec. 5.4] THE GENERAL CHARACTERISTIC-NOISE MATRIX 41 



It is easily checked that P has the properties 



p-i = pt = p (5.27) 



Substituting the particular form of Qr from Eq. 5.26a into the matrix in 

 column 2 of Table 5.1, we obtain the matrix of 2wth order 



[l I -t] Qt-' [l ; -t]^ = 2(P - TPT^) (5.28) 



Thus, from Eq. 5.19 we have for Nr 



Nr = i(P - TPT+)-^85^ (5.29) 



With the introduction of the specific expression Eq. 5.28 into Eq. 5.25 

 for the noise parameter pr, we find that it reduces to 



^^ = 2y + (P - TPT+)y ^^-^"^ 



The preceding development shows how each matrix representation T 

 has associated with it a particular noise parameter pr, of which the 

 extrema are determined by the eigenvalues of its characteristic-noise 

 matrix. In the next chapter we shall develop in detail the significance of 

 pT for two-terminal-pair amplifiers represented in terms of their general 

 circuit constants. 



