**1. Introduction**

The electrical bioimpedance technique allows for characterizing indirectly the properties of a biological media in a noninvasive way [1]. An AC excitation signal is applied to the impedance under test, *ZBIO*, and the corresponding response is acquired by means of an instrumentation amplifier [2], conditioned and processed. This technique is being widely used nowadays to assist in the diagnosis of different diseases extended among the population as well as for monitoring physiological variables [3,4]. Frequently, the response of the sample is required to be repeated at different frequencies in order to obtain a more complete information, which is known as bioimpedance spectroscopy. The typical frequency range, known as dispersion range, varies from several hundreds of Hz to a few MHz. The frequency analysis can be carried out sequentially, by modifying the frequency of the excitation signal. Nevertheless, when the bioimpedance of the media varies rapidly, a multi-frequency analysis is required in order to obtain all the responses at the same

**Citation:** Carrillo, J.M.; de la Cruz-Blas, C.A. 0.6-V 1.65-μW Second-Order *Gm*-*C* Bandpass Filter for Multi-Frequency Bioimpedance Analysis Based on a Bootstrapped Bulk-Driven Voltage Buffer. *J. Low Power Electron. Appl.* **2022**, *12*, 62. https://doi.org/10.3390/ jlpea12040062

Academic Editor: Orazio Aiello

Received: 31 October 2022 Accepted: 28 November 2022 Published: 30 November 2022

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time. In this case, as illustrated in Figure 1, different AC excitation signals are generated and simultaneously applied to the impedance, being subsequently separated with the help of bandpass filter (BPF) sections, being the *Gm*-*C* a flexible and suitable approach for monolithic integration [5–15]. The resulting solution is susceptible of being incorporated in an Internet of Things (IoT) platform [16]. Nevertheless, different specifications must be met for this purpose, which can be especially stringent in terms of total power consumption when the overall application is intended to be incorporated into a wearable device.

**Figure 1.** Block diagram of a multi-frequency bioimpedance system.

The bulk-driven technique is well-suited for low-voltage CMOS analog design, as it allows for operation with very low supply voltages and overcomes the non-zero threshold voltage constraint [10,17–25]. Indeed, in a bulk-driven transistor, the DC voltage required to switch the device on and the signal to be processed are decoupled and applied, respectively, to the gate and bulk terminal, which allows for providing and extending the input voltage range with respect to the conventional gate-driven device. Nevertheless, one of the main drawbacks of such technique is the reduction of the effective transconductance, due to the lower value of the bulk transconductance, *gmb*, as compared to the gate transconductance, *gm*. As a consequence, an increase of input-referenced magnitudes, such as the offset voltage or the noise, takes place. Different techniques have been proposed to electronically enhance the effective transconductance of a bulk-driven transistor, consequently increasing area and power consumption [26,27].

In this contribution, the application of a bootstrapping effect to a bulk-driven MOS transistor to increase its intrinsic voltage gain is proposed. The technique has been used to design a low-voltage voltage buffer, in which the noise contribution is reduced and the linearity is increased. The voltage buffer has been incorporated in the implementation of a linearized transconductor, which, in turn, is the basic building block of a second-order *Gm*-*C* BPF aimed to signal separation in a multi-frequency bioimpedance measurement system. All the circuits have been designed in 180 nm CMOS technology to operate with a 0.6-V single supply. The rest of the manuscript has been organized as follows: In Section 2, the voltage buffer is described and analyzed, whereas simulated results are used to confirm its principle of operation. The design of the linearized transconductor is detailed in Section 3 and the implementation of the filter is presented in Section 4. Simulated results are provided in Section 5 and conclusions are drawn in Section 6.

## **2. Boostrapped Bulk-Driven Voltage Follower**
