Double‐order negative group delay filtering function: A brilliant capability of the bilinear double‐order transfer function

Abstract

In this work, the capability to generate the negative group delay (NGD) phenomenon at those frequencies higher than a certain value, that is, the NGD high‐pass (HP) filtering function, of the bilinear double‐order transfer function has been demonstrated. Based on the Type‐I bilinear double‐order filter circuit, our theory has been verified by strong agreements between the formulae and their proof‐of‐concept (POC) circuit‐based simulation results. Both formula‐based and POC circuit‐based simulations give the minimum group delay of −5 ms yet the cut‐off frequency of 10 and 9 rad/s, respectively. Such slight deviation is caused by the approximation error of the bilinear double‐order impedance. By employing two orders, the bilinear double‐order transfer function has been found to be the basis transfer function for the NGD filtering function with the highest degree of freedom. Based on our design equation for the NGD filtering function, it can be seen that the distances between zero and pole and the characteristic frequency of the bilinear double‐order transfer function are governed by such characteristic frequency itself, the cut‐off frequency of the NGD filtering function, and the fractional order of the Laplacian operator. In addition, the effects of the fractional order of the Laplacian operator, the fractional order of the transfer function, and the ratio of the abovementioned distances to the characteristics of the newly found double‐order NGD filtering function have been studied in detail.