Fractional-order elements of complement order

The design of analogue fractional-order systems requires the presence of fractional-order elements (FOEs), capacitive and/or inductive, featuring fractional order α (0 < α < 1). As currently FOEs are not available as discrete elements, suitable RC networks are used to overcome this obstacle. In this paper we primary propose the transformation of fractional-order elements to cover the whole span of α by a reduced number of RC networks or later readily available discrete FOEs. Using this approach, FOEs can be designed featuring complementary fractional order β, i.e. β = 1 - α. Analysing the transformation possibilities, we also discuss the design of fractional capacitance multiplier.