44 



NOISE MEASURE 



[Ch.6 



only the effect of internal network noise sources. The term kTo Af in 

 Eq. 6.3 represents the available noise power from the input source im- 

 pedance held at equilibrium at standard temperature Tq, provided this 

 impedance is passive (that is, has a positive real part). In the case of a 

 source impedance with a negative real part, kTo Af merely represents an 

 arbitrary but convenient normalization factor. 

 From Eqs. 6.1, 6.2, and 6.3, it is clear that 



Fe-1>0 

 Fe- KO 



if Rs>0 

 if Rs <0 



(6.4a) 

 (6.4&) 



li Rs > and Ro > 0, Fe becomes the standard noise figure F. 



E, 



Zs 



■AAAAAr 



-o + 



o 



Fig. 6.1. Thevenin equivalent of two- terminal source. 



6.2. Matrix Formulation of Exchangeable Power and Noise Figure 



The parameter pr of Eq. 5.30, whose relation with the noise figure we 

 are going to investigate, is expressed in matrix notation. Accordingly, 

 to facilitate comparison, we must express the (extended) noise figure and 

 the related parameters in the same manner. 



Exchangeable Power. A linear two-terminal source of power can be 

 represented by its Thevenin rms open-circuit voltage Es, in series with 

 its internal impedance Zs. Let Vi and /i be the terminal voltage and 

 current of the source, respectively, as shown in Fig. 6.1, so that 



Fi + Zsh = E, 



(6.5) 



To express Eq. 6.5 in matrix form suitable for cascade applications, we 

 define column vectors (matrices) v and x as 



Then, for Eq. 6.5, we have 



xV = Ei 



(6.6) 

 (6.7) 



