# A Tree-Based Architecture for High-Performance Ultra-Low-Voltage Amplifiers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Topology

#### 2.1. Stage${}_{1}$

#### 2.2. Stage${}_{2}$

#### 2.3. Stage${}_{3}$

#### 2.4. Architectural Considerations

## 3. Circuit Analysis

#### 3.1. Differential Gain

#### 3.2. Common Mode Gain

#### 3.3. Large-Signal Performances

#### 3.4. Noise Analysis

## 4. Amplifier Design and Simulation Results

#### 4.1. Sizing

#### 4.2. Circuit Simulations

#### 4.3. Robustness to Mismatch and PVT Variations

#### 4.4. Discussion and Comparison with the Literature

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Body-to-Gate (B2G) Interface

## Appendix B. Body-to-Body (B2B) Mirror

## References

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**Figure 12.**Histogram of the common mode rejection ratio (CMRR) of the proposed OTA for 200 Monte Carlo mismatch iterations.

**Figure 13.**Histogram of the power supply rejection ratio (PSRR) of the proposed OTA for 200 Monte Carlo mismatch iterations.

Transistor | Stage | Width [$\mathsf{\mu}$m] | Length [$\mathsf{\mu}$m] | I${}_{\mathbf{bias}}$ [nA] |
---|---|---|---|---|

M${}_{1A}$, M${}_{1B}$ | 1 | 4.465 | 1.000 | 4 |

M${}_{2A}$, M${}_{2B}$, M${}_{9A}$, M${}_{9B}$ | 1 | 0.375 | 3.000 | 4 |

M${}_{3A}$, M${}_{3B}$, M${}_{10}$ | 2 | 4.465 | 1.000 | 4 |

M${}_{4A}$, M${}_{4B}$ | 2 | 0.375 | 3.000 | 4 |

M${}_{5A}$, M${}_{5B}$, M${}_{8A}$, M${}_{8B}$ | 3 | 13.390 | 1.000 | 19.67 |

M${}_{6A}$, M${}_{6B}$, M${}_{7A}$, M${}_{7B}$ | 3 | 1.125 | 3.000 | 19.67 |

Mean | StdDev | Min | Max | |
---|---|---|---|---|

P${}_{D}$ (nW) | 20.85 | 1.44 | 16.6 | 24.34 |

Idiss (nA) | 69.50 | 4.80 | 55.33 | 81.13 |

Offset (mV) | 3.84 | 15.46 | −30 | 50 |

SR${}_{p}$ (V/ms) | 18.54 | 0.30 | 17.84 | 19.42 |

SR${}_{m}$ (V/ms) | 11.63 | 0.34 | 10.82 | 12.52 |

Gain (1 Hz) (dB) | 51.48 | 1.22 | 49.59 | 56.49 |

CMRR (dB) | 42.11 | 10.44 | 27.84 | 98.85 |

PSRR (dB) | 56.13 | 2.12 | 48.05 | 56.39 |

Mphi (deg) | 53.08 | 6.27 | 38.25 | 74.98 |

GBW (kHz) | 32.72 | 8.42 | 11.54 | 49.33 |

THD (%) | 0.74 | 0.57 | 0.51 | 2.61 |

Temp (°C) | 0.00 | 16.67 | 27.00 | 43.33 | 50.00 | 70.00 |
---|---|---|---|---|---|---|

P${}_{D}$ (nW) | 21.48 | 21.93 | 21.89 | 20.40 | 20.54 | 21.35 |

I${}_{D}$ (nW) | 71.59 | 73.10 | 72.98 | 68.00 | 68.46 | 71.18 |

SR${}_{p}$ (V/ms) | 11.44 | 15.66 | 18.61 | 23.55 | 25.60 | 31.76 |

SR${}_{m}$ (V/ms) | 10.11 | 10.99 | 11.51 | 12.47 | 12.84 | 13.65 |

Gain (1Hz) (dB) | 58.65 | 57.61 | 52 | 50.07 | 48.87 | 46.72 |

CMRR (dB) | 64.45 | 57.56 | 44.96 | 34.31 | 32.03 | 26.66 |

Mphi (deg) | 48.63 | 46.26 | 52.40 | 54.54 | 52.86 | 48.88 |

GBW (kHz) | 32.85 | 39.45 | 35.16 | 30.80 | 32.16 | 37.95 |

Noise ${}^{\u2021}$ ($\mathsf{\mu}\mathrm{V}$/$\sqrt{\mathrm{Hz}}$) | 0.60 | 0.85 | 1.60 | 3.42 | 3.91 | 4.85 |

THD (%) | 0.45 | 0.51 | 0.67 | 0.72 | 0.84 | 1.23 |

^{‡}Computed at 1 kHz.

V${}_{\mathbf{DD}}$ (mV) | 270.0 | 285.0 | 300.0 | 315.0 | 330.0 |
---|---|---|---|---|---|

P${}_{D}$ (nW) | 21.710 | 21.980 | 21.890 | 20.500 | 20.240 |

Idiss (nA) | 72.370 | 73.270 | 72.980 | 68.350 | 67.460 |

SR${}_{p}$ (V/ms) | 8.532 | 12.750 | 18.610 | 26.500 | 36.790 |

SR${}_{m}$ (V/ms) | 7.147 | 9.161 | 11.510 | 14.230 | 17.210 |

Gain (1 Hz) (dB) | 54.34 | 53.22 | 52.93 | 52.84 | 53.07 |

CMRR (dB) | 60.340 | 53.720 | 44.960 | 38.740 | 35.450 |

Mphi (deg) | 47.530 | 50.230 | 52.920 | 53.550 | 49.570 |

GBW (kHz) | 34.830 | 35.230 | 35.160 | 33.470 | 36.980 |

Noise ${}^{\u2021}$ ($\mathsf{\mu}\mathrm{V}$/$\sqrt{\mathrm{Hz}}$) | 0.869 | 1.011 | 1.595 | 2.485 | 3.161 |

THD (%) | 0.50 | 0.37 | 0.29 | 0.23 | 0.19 |

^{‡}Computed at 1 kHz.

Corner | TYP | FF | SS | SF | FS |
---|---|---|---|---|---|

P${}_{D}$ (nW) | 21.89 | 20.32 | 21.68 | 21.98 | 26.60 |

Idiss (nA) | 72.97 | 67.73 | 72.27 | 73.27 | 88.67 |

SR${}_{p}$ (V/ms) | 18.61 | 27.32 | 12.18 | 28.77 | 11.63 |

SR${}_{m}$ (V/ms) | 11.51 | 15.47 | 8.62 | 9.00 | 14.43 |

Gain (1 Hz)(dB) | 52.92 | 50.41 | 57.90 | 55.72 | 49.93 |

CMRR (dB) | 44.96 | 33.72 | 63.31 | 53.26 | 35.5 |

PSRR (dB) | 56.40 | 48.26 | 73.31 | 64.93 | 47.52 |

Mphi (deg) | 52.40 | 51.37 | 48.59 | 42 | 58.59 |

GBW (kHz) | 35.16 | 34.43 | 37.19 | 49.626 | 27.55 |

Noise ${}^{\u2021}$ ($\mathsf{\mu}\mathrm{V}$/$\sqrt{\mathrm{Hz}}$) | 1.60 | 3.03 | 3.03 | 3.21 | 5.16 |

THD (%) | 0.67 | 0.25 | 0.43 | 0.95 | 0.46 |

^{‡}Computed at 1 kHz.

This Work * | [42] * | [45] ${}^{\u2020}$ | [40] * | [39] * | [25] * | [37] ${}^{\u2020}$ | [50] ${}^{\u2020}$ | [23] ${}^{\u2020}$ | [36] * | [51] ${}^{\u2020}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|

Year | 2021 | 2021 | 2021 | 2021 | 2021 | 2020 | 2020 | 2019 | 2019 | 2018 | 2018 |

Technology ($\mathsf{\mu}$m) | 0.13 | 0.13 | 0.18 | 0.13 | 0.13 | 0.18 | 0.18 | 0.18 | 0.13 | 0.065 | 0.18 |

${V}_{DD}$ (V) | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |

${V}_{DD}/{V}_{TH}$ | 0.86 | 0.86 | 0.6 | 0.86 | 0.86 | 0.6 | 0.6 | 0.6 | 0.86 | - | 0.6 |

$D{C}_{gain}$ (dB) | 52.92 | 38.07 | 30 | 40.80 | 64.6 | 39 | 98.1 | 64.7 | 49.8 | 60 | 65.8 |

${C}_{L}$ (pF) | 50 | 50 | 150 | 40 | 50 | 10 | 30 | 30 | 2 | 5 | 20 |

GBW (kHz) | 35.16 | 24.14 | 0.25 | 18.65 | 3.58 | 0.9 | 3.1 | 2.96 | 9100 | 70 | 2.78 |

$m\phi $ (deg) | 52.40 | 60.15 | 90 | 51.93 | 53.76 | 90 | 54 | 52 | 76 | 53 | 61 |

$S{R}_{+}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{V}}{\mathrm{ms}}\right]$ | 18.61 | 20.02 | - | 10.83 | 1.7 | - | 14 | 1.9 | - | 25 | 6.44 |

$S{R}_{-}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{V}}{\mathrm{ms}}\right]$ | 11.51 | 8.44 | - | 32.37 | 0.15 | - | 4.2 | 6.4 | - | 25 | 7.8 |

$S{R}_{avg}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{V}}{\mathrm{ms}}\right]$ | 15.06 | 14.23 | 0.085 | 21.60 | 0.93 | - | 9.1 | 4.15 | 3.8 | 25 | 7.12 |

THD (%) | 0.673 | 1.635 | 2 | 1.4 | 0.84 | 1 | 0.49 | 1 | - | - | 1 |

% of input swing | 90 | 80 | 90 | 80 | 100 | 23 | 83.33 | 85 | - | - | 93.33 |

CMRR (dB) | 42.11 ${}^{\u2021}$ | 54.88 | 41 | 67.49 | 61 | 30 | 60 | 110 | - | 126 | 72 |

PSRR (dB) | 56.13 ${}^{\u2021}$ | 51.05 | 30 | 45 | 26/28 ${}^{\star}$ | 33 | 61 | 56 | - | 90/91 ${}^{\star}$ | 62 |

spot-noise $\left[\frac{\mathsf{\mu}\mathrm{V}}{\sqrt{\mathrm{Hz}}}\right]$ | 1.60 | 3.16 | - | 2.12 | 2.69 | 0.81 | 1.8 | 1.6 | 0.035 | 2.82 | 1.85 |

@freq (Hz) | 1000 | 1000 | - | 1000 | 100 | 1000 | - | - | 100,000 | 1000 | 36 |

Power (nW) | 21.89 | 59.88 | 2.4 | 73 | 11.4 | 0.6 | 13 | 12.6 | 1800 | 51 | 15.4 |

Mode | BD | BD | DIGITAL | BD | BD | GD | BD | BD | GD | BD | BD |

$FO{M}_{S}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{MHz}\xb7\mathrm{pF}}{\mathrm{mW}}\right]$ | 80.29 k | 20.16 k | 15.89 k | 10.20 k | 15.72 k | 15.00 k | 7.15 k | 7.05 k | 10.11 k | 6.86 k | 3.61 k |

$FO{M}_{L}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{V}\xb7\mathrm{pF}}{\mathsf{\mu}\mathrm{s}\xb7\mathrm{mW}}\right]$ | 34.40 k | 11.88 k | 5.40 k | 11.82 k | 4.08 k | - | 21.00 k | 9.88 k | 4.67 k | 2.45 k | 9.25 k |

$FO{M}_{{L}_{WC}}\phantom{\rule{0.277778em}{0ex}}\left[\frac{\mathrm{V}\xb7\mathrm{pF}}{\mathsf{\mu}\mathrm{s}\xb7\mathrm{mW}}\right]$ | 26.30 k | 7.04 k | - | 5.93 k | 4.52 k | - | 6.30 k | 4.52 k | - | 2.45 k | 8.36 k |

Area $\left[{\mathrm{mm}}^{2}\right]$ | 0.0052 ${}^{\u2605}$ | 0.0027 | 0.000982 | 0.0036 | 0.0036 | 0.00047 | 0.0098 | 0.0085 | - | 0.003 | 0.0082 |

^{†}Measured;

^{‡}Monte Carlo mean-value;

^{⋆}PSRR

_{+}/PSRR_ [dB];

^{★}area estimated accounting for the minimum distances due to deep N-Wells for body connections.

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**MDPI and ACS Style**

Centurelli, F.; Della Sala, R.; Monsurrò, P.; Scotti, G.; Trifiletti, A.
A Tree-Based Architecture for High-Performance Ultra-Low-Voltage Amplifiers. *J. Low Power Electron. Appl.* **2022**, *12*, 12.
https://doi.org/10.3390/jlpea12010012

**AMA Style**

Centurelli F, Della Sala R, Monsurrò P, Scotti G, Trifiletti A.
A Tree-Based Architecture for High-Performance Ultra-Low-Voltage Amplifiers. *Journal of Low Power Electronics and Applications*. 2022; 12(1):12.
https://doi.org/10.3390/jlpea12010012

**Chicago/Turabian Style**

Centurelli, Francesco, Riccardo Della Sala, Pietro Monsurrò, Giuseppe Scotti, and Alessandro Trifiletti.
2022. "A Tree-Based Architecture for High-Performance Ultra-Low-Voltage Amplifiers" *Journal of Low Power Electronics and Applications* 12, no. 1: 12.
https://doi.org/10.3390/jlpea12010012