Identifications of Hasler´s classes of linear resistive circuit structures

A simplified variant of the classical Shannon Hagelbarger theorem on the concavity of the resistance function is used to derive separate necessary and sufficient conditions characterizing always well posed, sometimes ill posed and always ill posed classes of linear resistive circuit structures introduced and characterized by Haster, new both in formulation and proof. This reveals that the form of the second partial derivative of the resistance function is responsible for various kinds of the structural solvability of linear circuits. Next, alternative “if and only if” criteria for these classes are established. They involve replacements of reciprocal circuit elements by combinations of contractions and removals leading to pairs of complementary directed nullator and directed norator trees with appropriately defined signs, and resemble therefore earlier famous Willson Nielsen feedback structure and Chua-Nishi cactus graph criteria for circuits containing traditional controlled sources