14 



IMPEDANCE REPRESENTATION 



[Ch.2 



and 



E = Zj,a(Z + Zaa) E 



(2.10) 



Equation 2,8 is the matrix relation for the new w-terminal-pair network 

 obtained from the original one by imbedding it in a 2w-terminal-pair 

 network. Here Z' is the new impedance matrix, and E' is the column 

 matrix of the new open-circuit noise voltages. Conditions 2.5 must be 

 appHed to Eqs. 2.9 and 2.10 if the transformation network is to be lossless. 



2.3. Network Classification in Terms of Power 



In the course of our general study of noise performance of linear am- 

 plifiers, it will be necessary to generalize the definition of available power. 

 The need arises from situations involving negative resistance. 



Normally, the available power Pav of a one-terminal-pair source is 

 defined as : 



Pg^y = the greatest power that can he drawn from the source by 

 arbitrary variation of its terminal current (or voltage) 



E 



Fig. 2.3. The Th6vemn equivalent of a one-terminal-pair linear network. 



If the Thevenin representation of the source (Fig. 2.3) has the 

 complex open-circuit voltage E and internal impedance Z, with R = 

 Re (Z) > 0, this definition leads to 



P = - 



\EE^ 



1 EE^ 



4 R 



2Z + Z^ 



> 0, for i? > 



(2.11fl) 



If the source is nonrandom, the bar in Eq. 2.11(1 may be omitted. No 

 other changes are necessary because E is then understood to be a root- 

 mean-square amplitude, as remarked in Sec. 2.1. In Eq. 2.11a, Pav is 

 also a stationary value (extremum) of the power output regarded as a 

 function of the complex terminal current /. Moreover, the available 

 power (Eq. 2 Ala) can actually be delivered to the (passive) load Z*. 



