On the problem of LC-circuits eigenvalues multiplicity

Abstract

Weinstein method of intermediate problems has been modified for a system with concentrated parameters – electrical circuits. Basis (initial)
problem for this case of the intermediate problems method is defined. A relationship between eigenvalues (proper frequencies) of impedances
of separate branches of the circuit and loop impedances are established. A simple technique of separating the roots of characteristic polynomials
is elaborated. Finite steps recurrent process of intermediate problems of eigen values is determined. The latter leads to the important
result conserning LC-circuit eigenvalues multiplicity, in the synthesis of circuits with a given range of eigenfrequencies by simply choosing the
required number of elements (impedances) of the same kind in a primitive circuit.