Kramers–Kronig, Bode, and the meaning of zero

  title={Kramers–Kronig, Bode, and the meaning of zero},
  author={J. Bechhoefer},
  journal={American Journal of Physics},
  • J. Bechhoefer
  • Published 2011
  • Physics
  • American Journal of Physics
  • The implications of causality are captured by the Kramers–Kronig relations between the real and imaginary parts of a linear response function. In 1937, Bode derived a similar relation between the magnitude (response gain) and the phase. Although the Kramers–Kronig relations are an equality, the Bode’s relation is effectively an inequality. This difference is explained using elementary examples and is traced back to delays in the flow of information within the system formed by the physical… CONTINUE READING
    51 Citations

    Figures from this paper

    Generalization of Kramers-Krönig relations for evaluation of causality in power-law media
    Perfect Dispersive Medium for Real-Time Signal Processing
    • 8
    Phase Limitations of Zames–Falb Multipliers
    • 9
    • PDF
    S-parameters quality estimation in physical units
    • 1