FORMAL REAIJZABILITY THEORY — I 219 



formance" here must be construed to mean performance as viewed from 

 the accessible terminals only. Were all branch currents and node poten- 

 tials in a network available to observation, a mathematical statement 

 of performance would be equivalent to stating the full system of dif- 

 ferential equations governing these quantities, i.e., equivalent to giving 

 the detailed network diagram. 



2.1 With a few important exceptions, the converse kind of problem in 

 realizability theory docs not lead to a strict implication from fimctional 

 limitations to structural features, because the held of equivalent struc- 

 tures for a specified performance is very broad. Typically, it is only by 

 imposing some general a priori limitations on structure that fiu-ther 

 conclusions can be firmly drawn from a functional limitation. In study- 

 ing this kind of problem one is rapidly led from those basic issues which 

 are clearly part of realizability theory toward general, diflRcult, and 

 usually unsolved problems of network synthesis. One cannot, and should 

 not, draw a sharp boundarj'^ here, but Nature so far has provided a 

 fairly definite one for us, in that most of these problems have proved 

 too difficult of solution. 



2.2 Th^ direct realizability problems, the passage from structural prop- 

 erties to functional properties, have been somewhat more tractable. 

 Here, again, there is no clear dividing line between general realizability 

 theory and the sort of design theory in which, for example, one specifies 

 a particular filter structure depending on a limited number of param- 

 eters and examines the performance of the structure as a function of 

 these parameters. There is an extensive literature at or near this latter 

 level of generality, most of it relating to filters or filter-like structures 

 (e.g., interstage couplers in amplifiers). 



At a more basic level, the limitations on a network's structure which 

 are commonly met in practice are of the following kinds: 



a. Limitations on the kind of elements appearing, e.g., to passive 

 networks, networks without coupled coils, networks whose elements 

 have specified parasitics, etc; 



b. Limitations on the general form of the network diagram, e.g., to 

 ladder or lattice structures, without limitation to a specified number of 

 elements or parameters. 



Here the problems are varied and difficult. We survey briefly the 

 l)resent status of some of them. 



2.3 Networks with two accessible terminals, two-poles, are basic in 

 network technology. Fortunately, also, two-poles are unique among 

 networks in that there is always a simple way to describe their perform- 



