volume | PIER Journals

Abstract

A Negative Group Delay (NGD) prototype filter design based on the reciprocal transfer function of a low-pass Butterworth filter of a given order, is presented. The out-of-band gain of the prototype transfer function is capped at a finite constant value via multiplication by a transfer function of a low-pass Butterworth filter with 3 dB bandwidth that is wider than the reciprocal function bandwidth. Such synthesized transfer function exhibits maximal magnitude characteristic flatness within the 3 dB bandwidth (Butterworth-like property), while it also exhibits NGD and satisfies Kramers-Kronig relations (causal transfer function). The prototype design achieves an NGD-bandwidth product that in the upper asymptotic limit as the design order increases, is a linear function of out-of-band gain in decibels. This is an improvement compared with previously reported cascaded first-order and second-order designs, which have NGD-bandwidth functional dependency of out-of-band gain in decibels to the power of 1/2 and 3/4, respectively. It is shown that the transfer function of the corresponding design transformed to a non-zero center frequency can be exactly implemented with a Sallen-Key topology employing parallel resonators, or approximately implemented with an all-passive ladder topology. An in-band magnitude/phase distortion metric is applied to the prototype designs, evaluated for Gaussian and sinc pulse input waveforms, and compared with values obtained for a well-known commonly used medium. It is also shown that when the specified bandwidth corresponds to the entire bandwidth over which the group delay characteristic is negative, the magnitude characteristic variation approximately equals half the out-of-band gain value in decibels. Therefore, for any NGD design with large out-of-band gain (typically higher than 6 dB), using the entire bandwidth where group delay is negative can result in strong levels of distortion and should be checked for applied waveforms.

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Dr. Miodrag Kandic

Prof. Greg E. Bridges