654 DELL SYSTEM TECHNICAL JOURNAL 



consisliiij; iif ifsislaiu'fs, caparitics, and inductances can be reijlaced, 

 in so far as ihe impedance between terminals is concerned, by any 

 one of the elc\in networks shown by Fig. 1, upon assigning the proper 

 values to the elements. Kach of these networks consists of two 

 resistances, two capacities, and two self-inductances with miiuial 

 inductance between them. 



l-'ach nf tiiese elexen neiworUs realizes impedances wiili arhiirariK- 

 assigned roots and with poles an\-where in the entire domain ol pos- 

 sibilities, subject to the general conditions stated in Theorem I. 

 Special cases of these networks realize, for arbitrarily assigned roots, 

 only critical lines and points in the domain. .\\\ these special cases 

 are listed in Table III, with a specification of the lines or points in 

 the dcim.iin reali/alile ii\ each, as illustrated by Figs. 4 and .'). 



Certain liniiti'd regions of the <l(imaiii cm he realized by networks 

 which cont.iin no mutual induct. mce and whiiii are not si)ecial cases 

 (if liu- networks gi\eii b\' TlK'nrem II. Tiif.-i' nclworks are ;4i\en 

 i)\ the following theori-m : 



Theorem III. Any ilrivini^-poiiil iinpcdaiuc of a tz^-o-Diesli circuit 

 consisting of resistances, capacities, and self-inductances can be realized 

 by at least three and not more than five of the tu<elve networks shown by 

 /•('g. 2, upon assigning to the elements of each network the values given 

 by Table II. These twelve networks are the only networks without mutual 

 inductance and without superfluous elements by which any impedance 

 can, in general, be realized. 



These tweKe networks, taken together, cover that portion of the 

 domain realizable without mutual inductance. Networks with mutual 

 inductance are needed In order to co\er the entire domain. Tliisc 

 twelve are the oni\ netwurks, without superfluous elements, rc.ili/ini; 

 limited regions in the domain. Kach of these networks n insists ol iwd 

 resistances, two capacities, two self-inductances, and one additional 

 resistance, ca|)acit>', or self-indurt.inre. 'V\\v twiKe networks, with 

 their special cases, are ail listed in Taiiit' 111, wiiii a specification of 

 till' regions, lines, or points reali/abie i)\' each. 



In .iddiiion to the specilic formulas for the networks of Figs. 1 and 2. 

 it i> (onvenieiii to iia\e general formulas for the computation ol all 

 networks meeting the given conditions, including those networks 

 with superfluous elements as well as all special cases. The most 

 general two-mesh circuit is shown by Fig. (i; accordingly, the most 

 general network under consitleration is that shown by Fig. 7, I'ornnilas 



