Kramers-Kronig, Bode, and the meaning of zero

Details Kramers-Kronig, Bode, and the meaning of zero Kramers-Kronig, Bode, and the meaning of zero

2011-06-30

arxiv.org/abs/1107.0071v1

Physics

Classical Physics

8 pages; American Journal of Physics, to appear

Scientific paper

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.

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