# Study on the Voltage Reference Noise at Sub-Millihertz Frequencies for Developing an Ultra-Stable Temperature Measurement Subsystem

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## Abstract

**:**

## 1. Introduction

## 2. TMS’s Composition and Noise Budget

- Voltage reference

- NTC thermistor

- Amplifier

- Filter

- A/D converter

## 3. Voltage Reference Noise Measurement System: Methods, Fabrication, and Evaluation

#### 3.1. Measurement Methods

#### 3.1.1. Dual-Channel Measurement Eliminates Noise Floor

#### 3.1.2. Chopper Suppresses $1/f$ Noise

#### 3.1.3. Two-Stage Amplification Improves Gain

#### 3.1.4. Insulation Suppresses Temperature Fluctuation

#### 3.2. Circuit Design

#### 3.2.1. Dual-Channel Chopper

#### 3.2.2. Two-Stage Amplification

#### 3.3. Thermal Insulation

#### 3.4. System Setup and Performance Assessment

## 4. Voltage References Selection

## 5. Results of Voltage Reference Noise

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Temperature spectral density of insulation box. The blue curve shows the exterior ambient temperature, and the cyan and red curves show the simulated and experimental results of the interior temperature of the insulation box, respectively.

Noise Source | Budget ($\mathsf{\mu}\mathbf{K}/{\mathbf{Hz}}^{\mathbf{1}/\mathbf{2}}$) | Requirements (0.1 mHz–1 Hz) |
---|---|---|

Voltage reference | $0.57$ | ${N}_{\mathrm{V}}/{V}_{0}\le 2.8\times {10}^{-5}\phantom{\rule{0.166667em}{0ex}}/{\mathrm{Hz}}^{1/2}$ |

Thermistor | $0.57$ | ${N}_{{R}_{T}}/{R}_{0}\le 2.3\times {10}^{-8}\phantom{\rule{0.166667em}{0ex}}/{\mathrm{Hz}}^{1/2}$ |

Amplifier | $0.57$ | ${N}_{\mathrm{e}}\le 8\phantom{\rule{0.166667em}{0ex}}\mathrm{nV}/{\mathrm{Hz}}^{1/2},$ |

${N}_{\mathrm{i}}\le 1.1\phantom{\rule{0.166667em}{0ex}}\mathrm{pA}/{\mathrm{Hz}}^{1/2}.$ | ||

Others | $0.16$ | − |

Total | $1.0$ | − |

**Table 2.**DC voltage range setting and noise multiplier of the multimeter 3458A [20].

Range | ${\mathit{k}}_{\mathit{n},\mathit{R}}$ |
---|---|

$0.1\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ | 0.2 (0.07) |

$1\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ | 0.2 |

$10\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ | 1 |

$100\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ | 20 |

$1000\phantom{\rule{0.166667em}{0ex}}\mathrm{V}$ | 100 |

Layer | Material | Conductivity [$\mathbf{W}/(\mathbf{m}\xb7\mathbf{K})$] | Specific Heat [$\mathbf{J}/(\mathbf{kg}\xb7\mathbf{K})$] | Density [$\mathbf{kg}/{\mathbf{m}}^{3}$] | Thickness [$\mathbf{cm}$] |
---|---|---|---|---|---|

Outer | Polyurethane foam | 0.02 | 1000 | 46 | 20 |

Middle | Ceramic fiber cotton | 0.08 | 1000 | 300 | 5 |

Inner | Aluminum | 900 | 237 | 2700 | 0.5 |

Order | Model | Manufacturer | Type | Noise in 0.1–10 Hz ($\mathsf{\mu}{\mathbf{V}}_{\mathbf{p}-\mathbf{p}}$) | Temperature Coefficient ($\mathbf{ppm}/\mathbf{K}$) |
---|---|---|---|---|---|

1 | ADR441BRZ | Analog Devices | XFET | 1.2 | 1 |

2 | ADR4525CRZ | Analog Devices | Bandgap | 1.25 | 1 |

3 | LTC6655BHMS8 | Analog Devices | Bandgap | 0.625 | 2 |

4 | MAX6126A25 | Maxim Integrated | Proprietary | 1.45 | 1 |

5 | MAX6226ALA25 | Maxim Integrated | Proprietary | 1.45 | 1 |

6 | MAX6325CPA | Maxim Integrated | Buried zenner | 1.5 | 0.5 |

7 | MAX6071BAUT25 | Maxim Integrated | Bandgap | 4.8 | 1.5 |

8 | ADR291WF | Analog Devices | XFET | 8 | 5 |

9 | REF03GS | Analog Devices | Bandgap | 6 | 10 |

10 | REF192GR | Analog Devices | Bandgap | 25 | 10 |

11 | LT1034B | Analog Devices | Bandgap | 6 | 10 |

12 | LT1461B | Analog Devices | Bandgap | 20 | 3 |

13 | MAX6025A | Maxim Integrated | Bandgap | 50 | 6 |

14 | MAX6033B | Maxim Integrated | Bandgap | 16 | 1.5 |

15 | MAX6125E | Maxim Integrated | − | 15 | 15 |

16 | MAX6192A | Maxim Integrated | Bandgap | 60 | 2 |

17 | REF3225A | Texas Instruments | Bandgap | 33 | 4 |

18 | REF3425I | Texas Instruments | Bandgap | 12.5 | 2.5 |

19 | REF4132A | Texas Instruments | Bandgap | 37.5 | 12 |

20 | REF6025I | Texas Instruments | Bandgap | 7.5 | 5 |

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**MDPI and ACS Style**

Gu, L.; Chen, H.; Liu, P.; Wen, M.; Ling, C.; Sun, Z.; Ding, Y.
Study on the Voltage Reference Noise at Sub-Millihertz Frequencies for Developing an Ultra-Stable Temperature Measurement Subsystem. *Sensors* **2023**, *23*, 4611.
https://doi.org/10.3390/s23104611

**AMA Style**

Gu L, Chen H, Liu P, Wen M, Ling C, Sun Z, Ding Y.
Study on the Voltage Reference Noise at Sub-Millihertz Frequencies for Developing an Ultra-Stable Temperature Measurement Subsystem. *Sensors*. 2023; 23(10):4611.
https://doi.org/10.3390/s23104611

**Chicago/Turabian Style**

Gu, Lingyun, Houyuan Chen, Peng Liu, Mingxuan Wen, Chen Ling, Zening Sun, and Yanwei Ding.
2023. "Study on the Voltage Reference Noise at Sub-Millihertz Frequencies for Developing an Ultra-Stable Temperature Measurement Subsystem" *Sensors* 23, no. 10: 4611.
https://doi.org/10.3390/s23104611