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Progress In Electromagnetics Research
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LIMITS OF NEGATIVE GROUP DELAY PHENOMENON IN LINEAR CAUSAL MEDIA

By M. Kandic and G. E. Bridges

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Abstract:
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 defined "turn on/off" times propagate in the media. The optimal causal dispersion characteristic exhibiting NGD is obtained through Kramers-Kronig relations, which maximizes the NGD-bandwidth product as a function of the out-of-band gain. 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 artificially fabricated loaded transmission line medium.

Citation:
M. Kandic and G. E. Bridges, "Limits of Negative Group Delay Phenomenon in Linear Causal Media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013.
doi:10.2528/PIER12082915
http://www.jpier.org/PIER/pier.php?paper=12082915

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