FORMAL REALIZAIULITV THKOUV — II 



2, 1 + 2 + 3). This verifies the statements on the third hue of the 

 Table 4.04, and the fourth by duality. 



That N is pliysically realizable if Ni is, is the gist of (I, 8.11) and (I, 

 8.4). We prove it here by noting that Zf (p) is the matrix of a 2n-pole 

 N2 which obtains by adjoining /( — tii > pairs of shorted terminals 

 to Ni . Then (1) shows that N obtains from N2 by the use off deal trans- 

 formers (I, 9.1). 



Fig. 4 shows in schematic form the effects of the operation II) and 

 AD. In each case, it is emphasized that Ni has a matrix dual to that of 

 N. We have shown n = 5, th = 3. 



4.21 No reactive elements are used in this construction, so 4.07 is 

 satisfied. 



4.3 Consider now a 2n-pole N in (1, 1). Then its impedance matrix 

 Z(p) is finite for every p = ico, and not constant. 



Let R(p), Hp), respectively, be the real and imaginary parts of Z(p): 



2R(p) = Zip) + Zip) = Zip) + Zip) = Zip) + Z*ip); 

 2ilip) = Zip) -W) = Zip) - Zip) = Zip) - Z*ip); 

 Zip) = Rip) + Hip). 



00 K 



STRUCTURE RESULTING FROM IP 



N, 







STRUCTURE RESULTING FROM AP 



Fig. 3 — Structure resuUing from IP, above and AF, below. 



