Capacitive Impedance Measurement: Dual-frequency Approach

Abstract

The most widely used technique for measuring capacitive impedances (or complex electrical permittivity) is to apply a frequency signal to the sensor and measure the amplitude and phase of the output signal. The technique, although efficient, involves high-speed circuits for phase measurement, especially when the medium under test has high conductivity. This paper presents a sensor to measure complex electrical permittivity based on an alternative approach to amplitude and phase measurement: The application of two distinct frequencies using a current-to-voltage converter circuit based in a transimpedance amplifier, and an 8-bit microcontroller. Since there is no need for phase measurement and the applied frequency is lower compared to the standard method, the circuit presents less complexity and cost than the traditional technique. The main advance presented in this work is the use of mathematical modeling of the frequency response of the circuit to make it possible for measuring the dielectric constant using a lower frequency than the higher cut-off frequency of the system, even when the medium under test has high conductivity (tested up to 1220 μS/cm). The proposed system caused a maximum error of 0.6% for the measurement of electrical conductivity and 2% for the relative dielectric constant, considering measurement ranges from 0 to 1220 μS/cm and from 1 to 80, respectively.