# A 1 V 92 dB SNDR 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Asynchronous Delta-Sigma Modulator

## 3. Transistor Level Realization

#### 3.1. Active-RC Integrator

#### 3.2. Class AB Fully Differential Operational Amplifier

#### 3.3. Comparator with Hysteresis

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ADC | Analog-to-digital converter |

ADSM | Asynchronous delta-sigma modulator |

$CBR$ | Carrier-to-bandwidth ratio |

CIFB | Cascade of integrators with distributed feedback |

CTDSM | Continuous-time delta-sigma modulator |

$DR$ | Dynamic Range |

DTDSM | Discrete-time delta-sigma modulator |

$FOM$ | Figure-of-merit |

MASH | Multi-stage noise shaping |

$SNDR$ | Signal-to-noise and distortion ratio |

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**Figure 5.**MATLAB model simulation results: (

**a**) timing diagram and (

**b**) frequency spectrum of the ADSM for ${V}_{IN}$ = 0 V.

**Figure 10.**Post-layout simulation results: (

**a**) timing diagram and (

**b**) frequency spectrum of the ADSM for ${V}_{IN}$ = 0 V.

**Figure 11.**PSDof the ADSM for the sinusoidal input signal with an amplitude of (

**a**) ${V}_{IN}$ = 100 mV and (

**b**) ${V}_{IN}$ = 500 mV.

DTDSM | CTDSM | ADSM |
---|---|---|

+ Synchronous system | + Synchronous system | + Immunity to clock jitter |

+ High resolution | + Implicit antialiasing filter | + Implicit antialiasing filter |

+ Highly linear SC integrator | + Higher sampling frequency | + Simple circuit |

+ Accurately defined integrator | + Relaxed operational amplifier | + Relaxed OpAmp |

gains and transfer function | speed requirements | speed requirements |

+ Low sensitivity to clock jitter | + Higher conversion speed | + Higher conversion speed |

and excess loop delay | + Low power | + Low power |

+ Low sensitivity to DAC settling time | + Do not require a clock | |

- Low conversion speed | - Sensitivity to clock jitter | - Complex decoding scheme |

- Required pre-antialiasing filter | - Excess loop delay | - Lack of noise shaping |

- Required non-overlapping | - Lower resolution | - Lower resolution |

clock generator |

Parameter | Condition | Value |
---|---|---|

Hysteresis | $\left(\right)open="|"\; close="|">{V}_{TH}$ | 90 mV |

Time delay | ${C}_{L}=3\mathrm{pF}$ | 50 ns |

Slew-rate | ${C}_{L}=3\mathrm{pF}$ | 42 V/$\mathsf{\mu}$s |

Power consumption | duty cycle = 50% | 5 $\mathsf{\mu}$W |

Input capacitance | 0.4 pF | |

${I}_{BIAS}$ | 2.5 $\mathsf{\mu}$A |

Parameter | Condition | Value |
---|---|---|

Hysteresis | $\left(\right)open="|"\; close="|">{V}_{TH}$ | 90 mV |

Time delay | ${C}_{L}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{pF}$ | 50 ns |

Slew-rate | ${C}_{L}=3\phantom{\rule{0.166667em}{0ex}}\mathrm{pF}$ | 42 V/$\mathsf{\mu}$s |

Power consumption | duty cycle = 50% | 5 $\mathsf{\mu}$W |

Input capacitance | 0.4 pF | |

${I}_{BIAS}$ | 2.5 $\mathsf{\mu}$A |

Parameter | This Work | [24] 2015 | [25] 2016 | [26] 2018 | [27] 2012 |
---|---|---|---|---|---|

Technology | 180 nm | 130 nm | 65 nm | 65 nm | 130 nm |

Topology | ADSM | DTDSM | CTDSM | DTDSM | DTDSM |

Order | 2 | 3 | 3 | 3 (2-1 MASH) | 3 |

Quantizer | 1 bit | 1 bit | 5 bit | 1 bit | 1 bit |

Supply voltage | 1 V | 0.4 V | 1 V | 1 V | 0.25 V |

Modulator frequency | 848 kHz | 3.2 MHz | 6.4 MHz | 5 MHz | 1.4 MHz |

Bandwidth | 10 kHz | 20 kHz | 25 kHz | 25 kHz | 10 kHz |

Peak $SNDR$ | 92 dB | 76.1 dB | 95.2 dB | 94.6 dB | 61 dB |

Dynamic range | 112 dB | 82 dB | 103 dB | 98.5 dB | ≅ 58 dB |

Power consumption | 290 $\mathsf{\mu}$W | 63 $\mathsf{\mu}$W | 800 $\mathsf{\mu}$W | 175 $\mathsf{\mu}$W | 7.5 $\mathsf{\mu}$W |

Area | 0.54 mm${}^{2}$ | 0.33 mm${}^{2}$ | 0.256 mm${}^{2}$ | 0.384 mm${}^{2}$ | 0.3375 mm${}^{2}$ |

$FO{M}_{1}$ | 0.45 pJ/step | 0.31 pJ/step | 0.34 pJ/step | 0.079 pJ/step | 0.41 pJ/step |

$FO{M}_{2}$ | 187 dB | 167 dB | 177.9 dB | 176.2 dB | - |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kledrowetz, V.; Fujcik, L.; Prokop, R.; Háze, J.
A 1 V 92 dB *SNDR* 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing. *Sensors* **2020**, *20*, 4137.
https://doi.org/10.3390/s20154137

**AMA Style**

Kledrowetz V, Fujcik L, Prokop R, Háze J.
A 1 V 92 dB *SNDR* 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing. *Sensors*. 2020; 20(15):4137.
https://doi.org/10.3390/s20154137

**Chicago/Turabian Style**

Kledrowetz, Vilém, Lukáš Fujcik, Roman Prokop, and Jiří Háze.
2020. "A 1 V 92 dB *SNDR* 10 kHz Bandwidth Second-Order Asynchronous Delta-Sigma Modulator for Biomedical Signal Processing" *Sensors* 20, no. 15: 4137.
https://doi.org/10.3390/s20154137