Asynchronous Quadrature-Phase Undersampling Technique for Wide-Frequency Impedance Measurement

An impedance measurement (IM) technique based on asynchronous quadrature-phase undersampling is proposed to support a wide frequency range (FR) while achieving a high throughput with reduced hardware overhead. In the proposed method, a reference resistor is placed in series with the target impedance, and a sinusoidal current is injected into these. The two sinusoids from the target impedance and the reference resistor are amplified by instrumentation amplifiers (IAs) and directly sampled by an analog-to-digital converter (ADC). The magnitude and phase of each sinusoid can be calculated in the digital domain through only four samples with quadrature-phase differences. In the conventional digital demodulation design, the delay of IAs and the limited sampling frequency of the ADC, $f_{S}$ , restrict the maximum FR. To address this challenge, we proposed an asynchronous sampling and processing method that can measure the magnitudes and phases of sinusoids regardless of IA’s delay. Furthermore, to extend the FR beyond $f_{S}/2$ , the proposed technique employs undersampling when the frequency of the injected signal is higher than $f_{S}/2$ . As a result of these techniques, a wide FR from 10 Hz to 4.01 MHz is achieved with magnitude and phase errors of less than 0.8% and 0.8°, respectively, through an ADC of a maximum $f_{S}$ of 40 kSps only. The implemented prototype shows a hardware-efficient IM design, requiring only two IAs, a microcontroller unit (MCU) with an embedded ADC, and a reference resistor. A high throughput of $f_{S}/8 \approx ~5$ kSps can be achieved through an ADC in a time-interleaving manner.