KRAMERS-KRONIG TRANSFORMATION OF CONSTANT PHASE IMPEDANCES

The question of whether constant phase impedances [Z(ω) = a/(jω)α] obey the Kramers-Kronig relations has been examined analytically and numerically. We show that these impedances do transform correctly provided that -∣⋜ α ⋜∣. This range of a values covers all minimum phase passive electrical elements (R, C, L), semi-infinite diffusion (α = 0.5), pore diffusion (α = 0.25), RC transmission lines (O ⋜ α ⋜ 1), R-L transmission lines (−1 < α < O), and R-C-L transmission lines (−1 ⋜ α ⋜ 1). © 1990, The Electrochemical Society, Inc. All rights reserved.