A numerical study of dielectric measurements using single-reflection time-domain reflectometry

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Abstract
A computational analysis of single-reflection time-domain reflectometry using synthetic waveforms is used to study the effects of incorrect time alignment, waveform truncation and added noise, as a function of frequency, upon calculated permittivity values. Large errors in both the real ( epsilon ') and imaginary ( epsilon ") parts of the permittivity resulted from time misalignments of only 2 ps, from truncating waveforms to less than three relaxation times, and with signal-to-noise ratios of less than 20 dB. The calculated value of relaxation frequency was particularly sensitive to waveform truncation. An automatic alignment algorithm, presented as an appendix, was accurate to within one sample period (1 ps) in the few cases tested. The commonly used technique of determining permittivity from sample length and delay time is examined. Significant errors occur when the returned TDR pulse has strong spectral components near the material relaxation frequency.