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Limits of Negative Group Delay Phenomenon in Linear Causal Media

By Miodrag Kandic and Greg E. Bridges
Progress In Electromagnetics Research, Vol. 134, 227-246, 2013


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.


Miodrag Kandic and Greg E. Bridges, "Limits of Negative Group Delay Phenomenon in Linear Causal Media," Progress In Electromagnetics Research, Vol. 134, 227-246, 2013.


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