LIMITS OF NEGATIVE GROUP DELAY PHENOMENON IN LINEAR CAUSAL MEDIA

Asymptotic limits of Negative Group Delay (NGD) in linear causal media satisfying Kramers-Kronig relations are investigated. Even though there is no limit on the NGD-bandwidth product of a linear medium, it is shown that the out-of-band to center frequency amplitude ratio, or out-of-band gain, increases with the NGD-bandwidth product, and is proportional to the amplitude of undesired transients when waveforms with deflned \turn on/ofi" times propagate in the media. The optimal dispersion characteristic exhibiting NGD, which maximizes the NGD-bandwidth product as a function of the out-of-band gain, is obtained through Kramers- Kronig relations. It is shown that the NGD-bandwidth product has an upper asymptotic limit proportional to the square root of the logarithm of the maximum out-of-band gain. The derived NGD- bandwidth upper asymptotic limit of the optimally engineered causal dispersion characteristic is validated with two examples of physical media, a Lorentzian dielectric medium, and an artiflcially fabricated loaded transmission line medium.

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