46 



NOISE MEASURE 



[Ch. 6 



the network equations are expressed in matrix form as 



V = Tu (6.13) 



When the network of Fig. 6.2 is driven by the source of Fig. 6.1, the 

 exchangeable output power Peo from terminal pair 2 can be obtained at 



Fig. 6.2. The general-circuit-matrix representation of a source-free two-terminal-pair 



network. 



once from a source equation in the form of Eq. 6.8 written with u as 

 the voltage-current column variable. Multiplication of Eq. 6.13 by y^, 

 with the use of Eq. 6.8, yields this new relation, 



(y^T)u = 7 



(6.14) 



Accordingly, by applying the steps of Eqs. 6.8, 6.10, and 6.11 to Eq. 6.14, 

 we_find that 



|2 



PeO = 



T 



2ytxpTV 



and with Eq. 6.10, and Eq. 6.1a for the exchangeable gain, we have 



y^Py 



(6.15) 



G. = 



(6.16) 



ytXPXV 



Extended Noise Figure. To apply the matrix formulation of ex- 

 changeable power to the calculation of the (extended) noise figure of a 

 two-terminal-pair noisy network, we still describe the network by its 

 general-circuit constants, but we also allow for noise voltages or currents 

 at the terminals in the absence of external sources. With reference to 

 Fig. 6.3, the network equations for the dotted box^'^ would be 



V = Tu -f 8 (6.17) 



2 A. G. Th. Becking, H. Groendijk, and K. S. Knol, "The Noise Factor of 4 Termi- 

 nal Networks," Philips Research Repts. 10, 349-357 (1955). 



"H. Rothe and W. Dahlke, "Theory of Noisy Four Poles," Proc. I.R.E., 44, 

 811-817 (1956). 



