Influence of coaxial cable resistance on impedance measurements at low frequency and guidelines for phase determination of ac electrical signals

Abstract

We present an experimental study on ac measurements at low frequencies (below 1 MHz) when the coaxial cables used for the measurement are resistive, as in cryogenic conditions. More precisely, we are interested in admittance or impedance measurements and the accurate determination of the phase. Our experiments were completed using an auto-balancing bridge impedance analyzer and various standard coaxial cables, as well as their serial combinations. We characterize the experimental setup, and then, we analyze and measure the phase shift introduced in impedance measurements by lead resistance. Using basic equations for electrical signal propagation in coaxial cables, we calculate phase shift in the whole frequency range and explain our data in the low frequency limit of our model. We propose a quantitative criterion to determine whether the experimental context is appropriate. If not, we show that by using an original calibration procedure, the imaginary part can be accurately recovered, avoiding artifacts. The calibration procedure can be applied to any ac voltage or current measurement, whatever the detection technique is, with known accuracy.