50 NOISE MEASURE [Ch. 6 



suppose that the input terminal pair of this network is connected to a 

 source with the internal impedance Zs. The noise measure of the net- 

 work as measured at its output terminal pairs is then given by Eq. 6.25, 

 where the column vector y satisfies the relation 



^ = Zs* (6.9) 



Next, we suppose that the original network is imbedded in a four-termi- 

 nal-pair, lossless network (Fig. 6.5) before we connect it to the source. 

 A new network results, with the noise column vector 5' and the matrix T'. 

 If one of the terminal pairs of the resulting network is connected to the 

 same source, a new noise measure M/ is observed at the other terminal 

 pair: 



, y+8'8'V 1 



We shall now determine how the primed matrices in Eq. 6.26 are related 

 to the unprimed matrices of the original network. First, from Eqs. 3.3 

 and 3.6 we know that after a lossless transformation 



E^E^ = T^EE^T (3.3) 



and 



Z' + Z'+ = T^(Z -h Z+)t (3.6) 



However, from Eqs. 5.22, 5.23, and 5.28 we have 



W^ = M' E^E^M't = M VEE^tM'"^ 

 = (mVM-i)88^(mVm-i)'^ 

 = CWC (6.27) 



and 



(P - T'PT't) = M'iZ' + Z'+)M'^ = -MV(Z + Z+)tM'+ 

 = (mVm-^)(p - tptO(m t"^M-i)+ 

 = Ct(P - TPTt)C (6.28) 



where 



C^ = MVm-1 (6.29) 



The matrix C involved in the colinear transformations of 88^ and 

 P — TPT^ can be adjusted arbitrarily by arbitrary changes in the im- 

 bedding network, on account of the matrix t of the lossless transformation 

 that appears in C. 



Introducing the explicit transformations, Eqs. 6.27 through 6.29, into 



