Comparison of Extrapolation Methods for Truncated Cable Response Transfer Functions Used in De-Embedding Time-Domain Measurements

Abstract

This letter presents a comparison of three extrapolation methods used to reconstruct the missing parts of truncated cable response transfer functions (TFs) used to de-embed measured transient electromagnetic signals. In the first method (M1), the magnitude of the known TF at the extreme frequencies is kept constant for all the unknown frequencies. The second method (M2) uses a linear extrapolation of the magnitude of the known TF at the highest frequency and a decade earlier. The third method (M3) uses the known portions of the TF to extract its minimum phase function, using the discrete Hilbert transform integrals. The performance of the three methods is analyzed for different rise times of the incident field and with practical signal-to-noise ratio (SNR) at the oscilloscope input. For noise-free signals, M1 and M2 outperform M3 for almost all the considered rise times. On the other hand, the three methods produce errors within the same order of magnitude for noised signals. Given the complexity and computational time required to implement M3, it is suggested that M1 or M2 are used in practical applications.