Network Analysis by the Chain-Relaxation Method

A new approach to the analysis of electrical networks, the Chain-Relaxation method, is developed. Essentially the method consists: (a) in selecting a certain number of branch currents and considering them as unknowns to which arbitrary values are assigned, (b) in expressing all other branch currents, node potentials, given e.m.f.´s of voltage-generators, and given currents of current-generators in terms of the selected branch currents, (c) in providing for additional ¿residual¿ external node currents in order to make the resulting voltage and current distribution physically possible, (d) in solving simultaneous linear equations for the initially selected branch currents as unknowns. A special technique is used, which is based on the superposition theorem, and which obviates the unnecessary repetition of algebraic symbols and reduces the possibility of errors. The new method leads in general to simultaneous equations with a smaller number of unknowns than the usual methods of network analysis: in many cases the number of unknowns is two only.