HP-NGD Circuit Theory With Generalized Exponential Kernel Fractional Derivative-Based Impedances

In this work, we propose a novel passive circuit theory on fractional High-Pass (HP) Negative Group Delay (NGD) topology by using the fractional order reactive impedance and admittance. The fractional order reactive networks are derived from the generalized exponential kernel fractional derivative function. We analytically show that the proposed fractional order topology is capable to satisfy the existence conditions of the HP-NGD function. The design equations of HP-NGD function were derived with respect to the targeted specifications. The established synthesis methods are compared with those of the state-of-the-art on the HP-NGD circuit specifications. The proof of concept (POC) of generalized exponential Kernel fractional HP-NGD circuit is identified from Oustaloup approximation-based impedance and admittance. Study cases of POCs confirm the feasibility of the established HP-NGD circuit theory by means of simulations with a commercial tool. The calculated model and simulation outcomes confirm the HP-NGD behavior and specifications as expected from the proposed theoretical design. The obtained results present NGD minimal values and HP-NGD cut-off frequency of about (−32.9 ns, 45.3 kHz) and (−650 ns, 2.2 kHz) with low-attenuation less than 1 dB from the POC circuits of the fractional-capacitor and fractional- inductor based NGD circuits, respectively. To the best of our knowledge, this is the first time that the fractional order capacitor and inductor whose impedance and admittance were derived based on the generalized exponential kernel fractional derivative is applied to the NGD circuit.