# A Phase Error Correction System for Bioimpedance Measurement Circuits
## 1 Introduction  
Bioelectrical impedance or bioimpedance sensing, a versatile sensing method widely employed in diverse biomedical applications, plays a pivotal role in detecting pathologies, monitoring physiological processes, and assessing tissue dynamics. It has been applied to a range of critical areas, such as evaluating skin hydration [1], differentiating between healthy and cancerous tissue [2], evaluating heart and lung function [3], and detecting tissue ischemia. Additionally, it facilitates comprehensive analyses of body composition, imaging of various anatomical regions, and monitoring wound healing [4]. Moreover, bioimpedance also serves as a valuable tool for assessing muscle health in neuromuscular diseases [5]. Bioimpedance measurement systems feature an output stage applying an AC voltage or current to biological tissue and an input stage measuring the resulting current or voltage, thus allowing impedance to be calculated. Although the output stage is often designed to be voltage-generating due to simpler associated circuit architectures, current output stages are considered safer in terms of minimising the risk of tissue damage and compliance with medical safety standards [6, 7]. When it comes to the measurement stage, various architectures can be employed, with synchronous demodulation (SD), magnitude and phase (MP), or synchronous sampling (SS) circuits commonly employed in true tetrapolar configurations. Meanwhile, bridge and oscillation-based feedback topologies are the most prevalent in bipolar or pseudo-tetrapolarconfigurations [7; 8; 9]. Among these, SD architecture is the most widely employed, especially for multifrequency tetrapolar measurements, featuring four electrodes to overcome electrode contact impedance-related errors. It uses both an in-phase (I) and quadrature (Q) signal for demodulation, generated with a 0\({}^{\circ}\) and 90\({}^{\circ}\) phase shift relative to the applied signal, enabling the extraction of the real and imaginary components of impedance, respectively. SD systems can measure very weak signals without supplementary bandpass filters owing to their lock-in amplifier mechanism [6; 10]. Research on improving SD-based systems predominantly focuses on minimising systematic errors that affect the measured impedance magnitude, including bandwidth limitations and issues related to output current amplitude degradation at frequencies higher than 100 kHz [6; 10]. Minimal research and attention have been devoted to rectifying inaccuracies in SD phase detection stemming from nonidealities on the signal generation side, causing the voltage-controlled current source to introduce phase shifts, altering the synchronization of the injected current with the in-phase (I), and quadrature (Q) demodulation signals. Although less detrimental than the current injection due to I,Q phase errors, further phase shifts can be introduced by preamplification stages on the monitoring side of the system. The injected signal, I,Q phase errors, result in frequency-dependent measurement degradation, which reduce the suitability of conventional SD systems for bioimpedance-sensing applications where precise phase detection is critical for accurate disease diagnosis, including assessment of cell integrity, cancer detection and characterisation, and myography [2; 11]. To the best of the authors' knowledge, most previous studies towards improving the phase accuracy of measurements in SD systems focused on ASIC realizations. When it comes to commercial realizations, Texas Instruments (TI) (Dallas, TX, USA) offers AFE4300, a specialised integrated bioimpedance circuit based on SD topology primarily designed for body composition analysis and weight scale applications. However, it has constraints regarding load and bandwidth. It can handle maximum reactive and resistive loads of 700 \(\Omega\) and 22 \(\Omega\), respectively, and its bandwidth is limited to \(\leq\)80 kHz [12; 13].