Conditions for Network-Element-Value Solvability

The concept of network-element-value solvability is introduced and its importance in the establishment of methods of automatic trouble-shooting of electronic equipment is pointed out. First, a set of definitions is given which enables an objective discussion to be made of network solvability of arbitrary passive, linear, lumped parameter networks with respect to a restricted set of external terminals (available and partly available). Next, a relation is obtained connecting the number of available and partly available terminals of a network with the number of admittance functions determining the measurable behavior of the network. Theorems A, B and C then give solvability conditions for purely resistive networks. It is shown that the theory developed can be extended to include networks with internal energy sources (Theorem D). A general necessary condition for network-element-value solvability is then obtained (Theorems E and F). Finally, examples are given showing applications and limitations of the theorems obtained.