Low-Gm tunable CMOS transconductors for simultaneous multi-sine bioimpedance spectroscopy

Bioimpedance spectroscopy allows determining the characteristics of a medium through its electrical response. In dynamic events, the approach based on sequential bioimpedance analyses at different frequencies is not appropriate due to its duration. Simultaneous multi-sine spectroscopy is a suitable alternative to obtain the bioimpedance spectrum in a fast way. The practical implementation of this technique requires the design of programmable filters, which include tunable transconductors, for the separation of the different frequency components of the response signal. Two circuit techniques to design a transconductor with tunable transconductance ($G_m$), are proposed. The originality of the solution relies on the subtraction of the $G_m$ of two voltage-to-current sections, thus leading not only to a wide tuning range of the effective $G_m$ but also to a low value of this circuit parameter. The transconductors were designed and fabricated in 180 nm CMOS technology to operate with 1.8 V. Measurements on 9 samples of the silicon prototypes show that mismatch prevents achieving the very low $G_m$ obtained in simulations, even though the deviations are within the variation ranges determined by a Montecarlo analysis. The SF and DP solutions display mean values for the maximum/minimum $G_m$ of 10.29 $\mu$A/V/149.5 nA/V and 10.1 $\mu$A/V/302.8 nA/V, respectively, which represent transconductance tuning ratios of 68.8$\times$ and 33.4$\times$, also respectively. Other remarkable feature of this proposal is that the second-order transconductor-capacitor ($G_m$-C) bandpass filters (BPFs), designed for signals separation, incorporate multiple-output versions of the proposed transconductors, thus leading to a reduction of area occupation and power consumption. The BPFs were designed to have nominal values of the gain at the centre frequency and of the quality factor of 0 dB and 2.83, respectively, whereas the centre frequency can be programmed over approximately one decade.