#
0.6-V 1.65-μW Second-Order G_{m}-C Bandpass Filter for Multi-Frequency Bioimpedance Analysis Based on a Bootstrapped Bulk-Driven Voltage Buffer

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## Abstract

**:**

## 1. Introduction

## 2. Boostrapped Bulk-Driven Voltage Follower

#### 2.1. Bulk Driven Buffer: Simulation and Analytical Results

#### 2.2. Analytical and Simulated Results

## 3. Proposed Linearized Transconductor

## 4. Second-Order ${\mathit{G}}_{\mathit{m}}$-C Bandpass Filter

## 5. Simulated Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Bulk-driven FVF cell: (

**a**) conventional approach; (

**b**) proposed bootstrapped version; and (

**c**) small–signal circuit (${g}_{m,MD}=0$ for the bootstrapped case).

**Figure 6.**Noise comparison. The input power spectral density is represented in dB on the y-axis to illustrate more clearly the tendencies.

Conventional | Bootstrapped | |
---|---|---|

Gain | $\frac{{g}_{mb,MD}}{{g}_{m,MD}+{g}_{mb,MD}}$ | ≈1 |

${R}_{out}$ | $\frac{1}{{g}_{m,MF}\xb7({g}_{m,MD}+{g}_{mb,MD})\xb7({r}_{o,MD}\Vert {r}_{o,MS})}$ | $\frac{1}{{g}_{m,MF}\xb7{g}_{mb,MD}\xb7({r}_{o,MD}\Vert {r}_{o,MS})}$ |

${R}_{D,MD}$ | $\frac{1}{{g}_{m,MF}}$ | $\frac{1}{{g}_{m,MF}}$ |

${R}_{S,MD}$ | $\frac{1}{{g}_{m,MD}+{g}_{mb,MD}}$ | $\frac{1}{{g}_{mb,MD}}$ |

Open loop gain | ${g}_{mb,MD}\xb7{r}_{o,MD}$ | ${g}_{mb,MD}\xb7{r}_{o,MD}$ |

Loop gain | $({g}_{m,MD}+{g}_{mb,MD})\xb7{r}_{o,MD}$ | ${g}_{mb,MD}\xb7{r}_{o,MD}$ |

**Table 2.**Aspect ratios ($\mathsf{\mu}$m/$\mathsf{\mu}$m) for the main transistors of the transconductor in Figure 7.

Device | W/L | Device | W/L |
---|---|---|---|

MD1, MD2 | 20/1 | M1, M2, M3, M4 | 1/1 |

MF1, MF2 | 1/1 | M1C, M2C | 30/0.5 |

MS1, MS2 | 4/1 | M3C, M4C | 10/0.5 |

MG1, MG2 | 0.24/0.34 | MR1, MR2 | 1/0.5 |

**Table 3.**Simulated performance of the linearized transconductor and comparison with other similar solutions previously reported.

Parameter | [17] ALOG’12 | [18] ALOG’14 | [22] Access’21 | [24] TCAS-II’22 | This Work |
---|---|---|---|---|---|

Technology ($\mathsf{\mu}$m) | 0.35 | 0.13 | 0.18 | 0.13 | 0.18 |

Results | Measured | Measured | Simulated | Measured | Simulated |

${V}_{DD}$ (V) | 0.8 | 0.25 | 0.5 | 0.3 | 0.6 |

Power (nW) | 40 | 10 | 0.278–535 | 708 | 361.2 |

${G}_{m}$ (nA/V) | 66 | 22 | 0.34–383 | 4070 | 248.3–1024.9 |

Open-loop gain (dB) | 61 | NA | 31.2 | 15 | 54.2 |

BW (kHz) | 0.195 | NA | 2.67×10${}^{-3}$ | 6 | 99.5 |

SR${}^{+}$/SR${}^{-}$ (V/ms) | 0.12 | 94600 | NA | NA | 3.15/1.56 |

THD (dB) | −48.2 @ 600 mV${}_{pp}$ | −45.5 @ 100 mV${}_{pp}$ | −46.0 @ 480 mV${}_{pp}$ | −54.4 @ 100 mV${}_{pp}$ | −52.6 @ 200 mV${}_{pp}$ |

$Fo{M}_{T}$ (kHz·pF/nW) | 12.2 | NA | 19.2-11.5 | 84.7 | 27.5 |

**Table 4.**Simulated performance of the proposed ${G}_{m}$-C filter and comparison with similar BPF solutions.

Parameter | [7] TBCAS’07 | [9] TCAS-II’12 | [10] ${}^{*}$ MEJ’15 | [14] ICECS’20 | [15] ${}^{*}$ ICECS’21 | [23]${}^{*}$ Access’21 | This Work ${}^{*}$ |
---|---|---|---|---|---|---|---|

Technology ($\mathsf{\mu}$m) | 0.35 | 0.35 | 0.05 | 0.13 | 0.18 | 0.18 | 0.18 |

${V}_{DD}$ (V) | 1 | 3.3 | 0.4 | 1.2 | 0.8 | 0.5 | 0.6 |

Power ($\mathsf{\mu}$W) | 44.3 | 75.4 | 31.8 | 256.0 | 24.0 | 0.06 | 1.65 |

Filter order | 6 | 2 | 2 | 8 | 2 | 3 | 2 |

${f}_{0}$ (kHz) | 0.67 | 20 | 10 | 100 | 72.7 | 0.25 | 19.1 |

${f}_{0}^{min}-{f}_{0}^{max}$ (Hz) | ∼100–20 k | 20–20 k | 1–30 k | 2–100 k | 72.7 k | 250 | 6.5–37.5 k |

Q | N.A | 3 | 1 | 4.8/5.2 | 5 | N.A. | 5.9 |

${v}_{IN,max}$ (m${V}_{pp}$) | 40 | 245 ${}^{\u2021}$ | 178 ${}^{\u2020}$ | 140 ${}^{\u2021}$ | 800 | N.A. | 110 ${}^{\u2020}$ |

In-band noise ($\mathsf{\mu}$V) | 70.8 | 58.7 | 53.0 | 100 | 266.6 | 240.0 | 190.5 |

DR (dB) | 49.0 | 63.5 | 68.4 | 49.0 | 60.5 | 60.4 | 47.4 |

$Fo{M}_{BPF}\times {10}^{-13}$ (SI) | 3.4 | 979.6 | 93.1 | 64.0 | 21.9 | 0.377 | 5.5 |

^{†}@ −40 dB THD,

^{‡}@ 1-dB compression point.

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**MDPI and ACS Style**

Carrillo, J.M.; de la Cruz-Blas, C.A.
0.6-V 1.65-μW Second-Order *G _{m}-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

**AMA Style**

Carrillo JM, de la Cruz-Blas CA.
0.6-V 1.65-μW Second-Order *G _{m}-C* Bandpass Filter for Multi-Frequency Bioimpedance Analysis Based on a Bootstrapped Bulk-Driven Voltage Buffer.

*Journal of Low Power Electronics and Applications*. 2022; 12(4):62. https://doi.org/10.3390/jlpea12040062

**Chicago/Turabian Style**

Carrillo, Juan M., and Carlos A. de la Cruz-Blas.
2022. "0.6-V 1.65-μW Second-Order *G _{m}-C* Bandpass Filter for Multi-Frequency Bioimpedance Analysis Based on a Bootstrapped Bulk-Driven Voltage Buffer"

*Journal of Low Power Electronics and Applications*12, no. 4: 62. https://doi.org/10.3390/jlpea12040062