Passive Synthesis of Fractional Order Immittance of Three-Element-Kind

For the actual circuit with fractional order characteristics, the fractional order circuit model is more concise and precise than the classical circuit model. So studying the synthesis of fractional order immittance is of great significance. This paper investigates the passive synthesis method of the three-element-kind fractional order immittance function. It means designing a network with three kinds of passive fractional-order elements that exhibit a specific impedance function. This paper proposes a variable substitution method to solve this problem. The method consists of three steps: The first step of the process is to establish the correspondence between the fractional order and lossy reactance. This way, the fractional order immittance function is transformed into an integer order immittance function. Then the Brune procedure realizes the immittance function as a network with lossy reactance. Finally, a fractional order network is obtained by replacing the lossy reactance with the corresponding fractional reactance. A simulation example and an experiment are also given for verification. This method applies to all three-element-kind network impedance functions that meet the passive condition.