Linear Noisy Networks 



m the Impedance Representation 



The discussion of the invariants of a linear noisy network under the 

 group of lossless transformations is most simply carried out by using the 

 impedance description of the network. We shall start by describing 

 the effect of a lossless transformation on a general w-terminal-pair net- 

 work. Such a network has to be classified with respect to its passive- 

 active character, which depends upon its ability to deliver or absorb 

 power. The examination of power delivered or absorbed by a multi- 

 terminal-pair network raises some interesting questions leading to a 

 generaKzation of the available-power concept: the exchangeable power. 

 In Chap. 3, the exchangeable-power concept in turn leads to the discovery 

 of the invariants mentioned in Chap. 1. 



2.1. Impedance-Matrix Representation of Linear Networks 



At any frequency, a linear w-terminal-pair network containing internal 

 prescribed signal or noise generators is specified completely with respect 

 to its terminal pairs by its impedance matrix Z and the complex Fourier 

 amplitudes of its open-circuit terminal voltages £i, E2, • • • , En (Fig. 2.1). 

 In matrix form, Z denotes a square n-hy-n array 



Z = 



