A Harmonic Error Cancellation Method for Accurate Clock-Based Electrochemical Impedance Spectroscopy

Electrochemical impedance spectroscopy (EIS) is a widely used method to characterize the biological materials. In traditional methods for EIS, a sinusoidal current is used to excite the material under test and the measured voltage across that material is demodulated by a linear multiplication with quadrature sinusoidal signals. From the resulting demodulated output, the impedance (magnitude and phase) can be calculated. Although this sine-wave-based impedance measurement method can produce accurate impedance measurements, it requires bulky components and suffers from poor power efficiency due to sinusoidal waveform generation and linear multiplication. Alternatively, a method using square-wave signal, which is simply a clock, for both excitation and demodulation can be much more area and power efficient, but inherently suffers from substantial errors in the result due to significant harmonics in square waves. In this paper, we propose a technique to cancel out the errors caused by such harmonics of the square-wave-based excitation and demodulation. The proposed technique, based on the fact that the magnitude ratio of all the harmonics of a square wave are known, cancels out harmonic errors by subtracting or adding the square-wave-based measured results at higher harmonic frequencies as a simple post-processing calculation. Simulations on specific and also generic impedance models demonstrate the applicability of this technique to various impedance models. Experimental results using a discrete circuit model show that this technique can provide a precise measurement of the impedance with 1% magnitude error and $< $0.5° phase error considering just five terms. In addition, measurements with a biological tissue show an average magnitude and phase error of 0.7% and $< \text{0.5}^{\circ }$, respectively, using the proposed error cancellation. Because this method replaces sinusoidal signal generation and linear multiplication with clock generation and simple switching, it has great potential to be integrated in a wearable and implantable health monitoring device at low area and power consumption.