Synthesis of passive fractional-order LC n-port with three element orders

Fractional-order circuits find a widespread use in different engineering applications. The problem of realising fractional-order circuits has been discussed by several authors, however, it is far from being solved. Realising fractional-order resistorless passive network with three element orders is been studied. At first, this study extends the two-variable reactance matrix synthesis method to three-variable case, and then proposes a synthesis method of fractional-order reactance matrix with three element orders by variable substitution. The process in above methods mainly involves variable substitution, decomposition of three-variable reactance matrix, extraction of unit inductors, Laurent series expansion, spectral factorisation of two-variable positive semidefinite Hermitian matrix and synthesis of univariable reactance matrix. Then the above-mentioned synthesis process is illustrated by two examples.