10 



IMPEDANCE REPRESENTATION 



lCh.2 



Fig. 2.1. Equivalent representation of linear network with internal noise sources. 



The cases in which the Z matrix does not exist in a formal sense can be 

 handled by suitable perturbations, for example, slight frequency changes 

 or the addition of perturbing circuit elements. The complex amplitudes 

 of the open-circuit terminal voltages are represented conveniently by a 

 column matrix E: 



'El 



E = 



E 



E 



En. 



If the internal generators are random-noise sources, the Fourier ampli- 

 tudes El • ' • En are complex random variables, the physical significance 

 of which usually appears in their self- and cross-power spectral densities 

 EiEk*} The bar indicates an average over an ensemble of noise processes 



^ W. B. Davenport and W. O. Root, Random Signals and Noise, McGraw-Hill 

 Book Company, New York (1958). 



