Effects of Stray Capacitance to Ground in Bipolar Material Impedance Measurements Based on Direct-Contact Electrodes

Abstract

Bipolar material impedance measurements are easier to implement than tetrapolar measurements but are more affected by electrode impedance. This effect can be reduced by measuring at a high-enough frequency albeit with the risk of deviations due to stray capacitances. High frequency measurements intended to reduce the influence of material conductivity when its permittivity is of interest also suffer from the effects of parasitic capacitances. In this paper, the effect of stray capacitance to ground in bipolar material impedance measurements implemented with direct-contact electrodes has been analyzed to identify the relevant parameters that determine the best frequency range to measure the conductivity or permittivity of the material when impedance analyzers based on an auto-balancing bridge are used. Stray capacitance to ground yields inductive effects proportional to it and also resistive and capacitive effects. If the ratio between this stray capacitance and the capacitance of the material under test is high enough, the modulus of the measured impedance can display a peak at relatively low frequency (about 100 kHz) and its phase angle can become positive. The consequences are that the best estimate of the conductivity of the material is that obtained from the modulus of the impedance at about midrange between the characteristic frequency of electrodes and that of the material, whereas the permittivity cannot be estimated from the impedance modulus measured at high frequency unless the sample capacitance is much larger than its capacitance to ground and propagation effects are negligible.

A fast method to estimate body capacitance to ground at mid frequencies

“…Figure 1 shows the equivalent circuit when impedance Z b is measured by connecting it between terminals H and L. The instrument applies a voltage to terminal H and measures the current at node L, which is held at 0 V (virtual ground) by a feedback loop. This current measurement method is analogous to a transimpedance amplifier based on an ideal op amp [11,13]. The impedance at a given frequency is calculated by dividing the vector voltage (phasor) VHG measured between H and ground by the vector current (phasor) IL measured at that frequency.…”

“…Moreover, the "air" capacitance Chl between electrodes and the capacitance Cg from the material to ground affect the measurement results [13]. Chl mostly depends on interelectrode distance and can be minimized by placing a small grounded electric shield between the electrodes [11].…”

“…Cg, however, cannot be easily minimized because it is a distributed capacitance, hence it will depend on the volume of the material and its distance to ground. Furthermore, Cg increases when a grounded electric shield is placed between electrodes to reduce Chl [13].…”

Effects of stray capacitance to ground in three electrode monopolar needle bioimpedance measurements

“…If Z i = (jωC i ) -1 is capacitive, the error term Z i /Z g = C g /C i , this is a frequencyindependent error and affects the impedance in the overall measurement range [4]. When the ratio C g /C i << 1, there is not effect in the measured impedance [5].…”

“…But, in both cases, the dependence on the frequency is more complex. If the Z k has a form similar to Z i , then the equivalent circuit of the measured impedance could contain parallel resonant RLC circuits [5].…”