76 nr.i.i. SrSTLM it.ciisical jolrxal 



Fig. 1.')1H, tlir imagi- imi)r<laiui-, Z/,. at tlif 1 — 2 terminals has rliar- 

 acterisiic No. 2 of V\^. X, wiiilo llie image imix^dancc, Z/,, at the 

 3 — 4 terminals lias characlerisiie No. 4 of Fig. 8. 



Electrically luiiiivalenl Xelworks. Reference lias been made to 

 the fact that any passive tiehcork having one pair of input terminals 

 and one pair of output terminals may be adequately represented, at any 

 frequency, by an equivalent T or ir network. In general, this represen- 

 tation is a mathematical one antl the arms of the T or ;r network 

 cannot be represented, at all fre(|uencies, by physically realizable 

 impedances. 



Furthermore, any concealed network, containing no impressed electro- 

 motive forces, and having N accessible terminals is always capable of 

 mathematical representation, at a single frequency, by a network having 

 not more than N (A'— l)/2 impedances, which impedances are determin- 

 able from the voltage and current conditions at the accessible terminals. 

 For networks having three or more terminals, this arbitrary mesh of 

 impedances may possess a number of variant configurations. It is 

 also true that the equivalence of the arbitrary mesh to the concealed 

 network holds, at any single frequency, for any and all sets of e.\- 

 ternal or terminal conditions, and that the magnitudes of the imped- 

 ances of the arbitrary mesh are determinable, at will, on the assump- 

 tion of the most convenient set of terminal conditions for each in- 

 dividual case. Familiar instances are the impedance equations 

 derivable under various short-circuit and open-circuit conditions. 



In specific cases, which arc of particular interest, one network may 

 be shown to be capable of representation, as far as external circuit con- 

 ditions are concerned, by another network which is physically realizable, 

 and the latter may be substituted for the former, indiscriminately, in any 

 circuit without consequent alteration, at any frequency, in the circuit 

 conditions external to the interchanged networks. 



F«iuivalent meshes having two accessible terminals and employ- 

 ing respectively, three or four impedances in each mesh have been 

 discussed by O. ]. Zobel." In filter design, two-terminal meshes are 

 of importance only in those cases where the iinjHxlances arc essentialK' 

 reactances. Figs. 17A, B, C and I) illustrate the physical configura- 

 tions which reactance meshes emplojing not more than four elements 

 may t.ike. We are not generalK- interested in meshes ha\ ing more 

 than four olenu-nts for practical reasons which have previously been 

 discussed. Wheneicr any of the reactance meshes shown in Fig. 17 

 occur, we may, with proper design, substitute for it an equivalent mesh 

 "Sec .'\|>|M-nilix III <>( Hil>liu)(ru|>liy U. 



