volume | PIER Journals

Abstract

A Negative Group Delay (NGD) prototype filter design, based on the ratio of two Chebyshev filter transfer functions, is presented. The two transfer functions are of the same order, but with different in-band ripple amplitudes and different 3 dB-bandwidths. The overall transfer function exhibits both an in-band ripple and an out-of-band steep-slope magnitude transition characteristic of a Chebyshev filter, while also exhibiting an in-band NGD. For high-order designs and in the upper asymptotic limit, the NGD-bandwidth product of the filter is shown to be a linear function of out-of-band gain in decibels. A resonator-based methodology is used to show how frequency upshifted filter designs can be implemented in a Sallen-Key topology or in an all-passive ladder topology. An in-band combined magnitude/phase distortion metric is evaluated for examples of the NGD filter. It is shown that the distortion metric is proportional to the design order, the in-band ripple amplitude, and the out-of-band gain. For a prescribed distortion metric value, it is demonstrated that the proposed design can achieve a higher NGD-bandwidth product than an equivalent Butterworth design, which has a flat in-band magnitude characteristic. Additionally, input waveforms with bandwidths extending to the entire frequency range where the group delay is negative (typically larger than the 3dB-bandwidth) should not be applied to this filter design as it results in strong levels of distortion.

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37. United States Patent Office (USPTO) application number: 18/491922.

Dr. Miodrag Kandic

Prof. Greg E. Bridges