Fractional-order multiple RLαCβ circuit

Since the RLC circuit is a basic circuit, attention is directed to the generalization of the fundamentals of fractional multiple RL alpha C beta circuit. Compared with the conventional multiple RLC circuit, the effects of fractional orders, alpha and beta, is the key factor for extra freedom, more flexibility and novelty. First, we study the basic features including the admittance and phase. Then, the conditions for fractional-order multiple RL alpha C beta circuit to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. As a peculiar phenomenon-resonance, the relationships among resonance frequency, fractional order and LC are studied in detail. In addition, sensitivity analysis including some interesting rules is illustrated. Finally, numerical simulations are carried out to validate the above studies.