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A Low Power Energy-Efficient Precision CMOS Temperature Sensor ^{†}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{BE}offers advantageous temperature characteristics. Lee et al. [6] proposed a BJT-based temperature sensor that achieved an inaccuracy of ±1 °C from −55 °C to 125 °C. Aita et al. [7] presented a BJT-based temperature sensor that achieved an inaccuracy of ±0.25 °C from −70 °C to 130 °C using dynamic element matching (DEM).

## 2. Sensor Operating Principles and Error Budgeting

_{b}bias a pair of PNPs (Q

_{LB}and Q

_{RB}).

_{BE}of the PNPs (V

_{BELB}and V

_{BERB}) are complementary to the absolute temperature (CTAT), whereas the difference between the two values of V

_{BE}, denoted as ∆V

_{BE_PB}, is proportional to the absolute temperature (PTAT). For a BJT, these voltages can be given by

_{C}and I

_{S}are the collector and saturation currents of the BJT. An opamp forces ∆V

_{BE_PB}across a resistance of R

_{b}to generate a PTAT bias current I

_{b}= ∆V

_{BE_PB}/R

_{b}. The PTAT current is mirrored to the bipolar core, and two current branches with a ratio of 1:p are directed to two PNPs (Q

_{L}and Q

_{R}) to generate two additional V

_{BE}(V

_{BEL}and V

_{BER}) and ∆V

_{BE_BC}values.

_{C}(Q

_{LB}and Q

_{RB}) is not the same as a current branch. Using a β-compensating resistance of R

_{β}= R

_{b}/5 in the pre-bias circuit suppresses the effect of β on V

_{BE}[12].

_{BE}with respect to a reference voltage V

_{REF}= V

_{BEL}+ α·∆V

_{BE_BC}, where α is a constant [9]. This provides the parameter μ

_{PTAT}= α·∆V

_{BE_BC}/V

_{REF}, which varies linearly from ~0.3 to ~0.7 over the temperature range considered [12]. Alternatively, as shown in Figure 2b, a zoom ADC is employed for this purpose to reduce the power consumption, die area, and required conversion time [8,13].

_{BEL}/∆V

_{BE_BC}, which varies nonlinearly from ~28 to ~8 over the temperature range considered [8]. In this case, the parameter μ

_{PTAT}can be determined in the digital back-end according to the relationship μ

_{PTAT}= X/(α + X), where α is a calibration parameter. The discretized output D

_{out}based on the parameter μ

_{PTAT}can then be converted to units of °C by a linear fit as follows [8]:

_{out}to error in V

_{BEL}and ∆V

_{BE_BC}can be respectively expressed by

_{PTAT}≈ T/A has been employed in the final forms. For example, supposing that V

_{REF}= 1.2 V, A = 600, and α = 14, a 0.1 °C temperature error is approximately equal to a 0.3 mV error in V

_{BEL}at +126.85 °C or a 0.02 mV error in ∆V

_{BE_BC}at −73.15 °C. Therefore, the accuracy of the sensor is limited by the error in V

_{BEL}and ∆V

_{BE_BC}.

_{BE_BC}is a current ratio mismatch ∆p between the two current branches in the bipolar core. The absolute error in ∆V

_{BE_BC}can then be given as follows:

_{L}, whereas the other current sources are directed to Q

_{R}. This averaging process cancels the first-order error in ∆V

_{BE_BC}whereas the second-order error remains, which is given as follows [12]:

_{b}and V

_{BEL}. The absolute error in V

_{BEL}can then be given as follows:

_{BEL}corresponds to a temperature error of at most 65 mK.

## 3. Temperature Sensor Front-End Circuit

_{b}= p = 5, the proposed circuit is illustrated in Figure 3.

_{LB}, current sources 2–6 are directed to Q

_{RB}, current source 7 is directed to Q

_{L}, and current sources 8–12 are directed to Q

_{R}.

_{LB}, current sources 3–7 are directed to Q

_{RB}, current source 8 is directed to Q

_{L}, and current sources 9–12 and current source 1 are directed to Q

_{R}.

## 4. Zoom Analog-to-Digital Converter

## 5. Calibration

_{BE}and ∆V

_{BE}, which are fed to the zoom ADC. The output of the zoom ADC in the normal operating mode is the ratio X

_{N}= V

_{BE}/∆V

_{BE}. However, the ADC can be configured to output X

_{c}= V

_{ext}/∆V

_{BE}when the temperature sensor chip is placed in the calibration mode. A PT-100 thermistor, which was calibrated to an error of less than 1 mK and placed in good thermal contact with the temperature sensor, was used to obtain the reference temperature T

_{chip}[17].

_{ext}, and obtain ∆V

_{BE}as follows:

_{BE}and T

_{chip}according to Equation (2).

_{out}from each testing point, respectively. The average value X

_{AVG}at each testing point can be calculated from the values of X obtained at each testing point. Then, the calibration parameters A, B, and α can be calculated according to Equation (3).

_{D}can be calculated using η, Equations (2) and (9).

_{ideal}can be calculated using T

_{D}, A, B, and α according to Equation (3). In addition, we can obtain the actual output X

_{D}from the chip.

_{ideal}, and X

_{D}as follows:

^{’}= X + X

_{ideal}− X

_{D}, A, B, C, and E are calibration parameters that are calculated in Step 1. In this paper, the voltage calibration employed single-point calibration, and the value T

_{D}was set to 37 °C.

## 6. Experimental Results and Discussion

## 7. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Zaliasl, S.; Salvia, J.C.; Hill, G.C.; Chen, L.; Joo, K.; Palwai, R.; Arumugam, N.; Phadke, M.; Mukherjee, S.; Lee, H.C.; et al. A 3 ppm 1.5 × 0.8 mm
^{2}1.0 μA 32.768 kHz MEMS-based oscillator. IEEE J. Solid-State Circuits**2015**, 50, 291–302. [Google Scholar] [CrossRef] - Maderbacher, G.; Marsili, S.; Motz, M.; Jackum, T.; Thielmann, J.; Hassander, H.; Gruber, H.; Hus, F.; Sandner, C. A digitally assisted single-point-calibration CMOS bandgap voltage reference with a 3σ inaccuracy of ±0.08% for fuel-gauge applications. In Proceedings of the 2015 International IEEE ISSCC, San Francisco, CA, USA, 22–26 February 2015; pp. 1–3. [Google Scholar]
- Wu, C.K.; Chan, W.S.; Lin, T.H. A 80 kS/s 36 μW resistor-based temperature sensor using BGR-free SAR ADC with a unevenly-weighted resistor string in 0.18 μm CMOS. In Proceedings of the 2011 Symposium on VLSI Circuits (VLSIC), Honolulu, HI, USA, 15–17 June 2011; pp. 222–223. [Google Scholar]
- Chen, P.; Chen, C.-C.; Tsai, C.-C.; Lu, W.-F. A time-to-digital-converter-based CMOS smart temperature sensor. IEEE J. Solid-State Circuits
**2005**, 40, 1642–1648. [Google Scholar] [CrossRef] - Testi, N.; Yang, X. A 0.2 nJ/sample 0.01 mm
^{2}ring oscillator based temperature sensor for on-chip thermal management. In Proceedings of the IEEE International Symposium on Quality Electronic Design, Santa Clara, CA, USA, 4–6 March 2013; pp. 696–702. [Google Scholar] - Lee, H.-Y.; Hsu, C.-M.; Luo, C.-H. CMOS thermal sensing system with simplified circuits and high accuracy for biomedical application. In Proceedings of the 2006 IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21–24 May 2006; pp. 4367–4370. [Google Scholar]
- Aita, A.L.; Pertijs, M.A.P.; Makinwa, K.A.A.; Huijsing, J.H. A CMOS smart temperature sensor with a batch-calibrated inaccuracy of ±0.25 °C (3σ) from −70°C to 130 °C. In Proceedings of the 2009 IEEE International Solid-State Circuits Conference—Digest of Technical Papers, San Francisco, CA, USA, 8–12 February 2009; pp. 342–343. [Google Scholar]
- Souri, K.; Chae, Y.; Makinwa, K.A.A. A CMOS temperature sensor with a voltage-calibrated inaccuracy of ±0.15 °C (3σ) from −55 °C to 125 °C. IEEE J. Solid-State Circuits
**2013**, 48, 292–301. [Google Scholar] [CrossRef] - Pertijs, M.A.P.; Makinwa, K.A.A.; Huijsing, J.H. A CMOS smart temperature sensor with a 3σ inaccuracy of ±0.1 °C from −55 °C to 125 °C. IEEE J. Solid-State Circuits
**2005**, 40, 2805–2815. [Google Scholar] [CrossRef] - Pertijs, M.A.P.; Niederkorn, A.; Ma, X.; Bakker, A.; Huijsing, J.H. A CMOS smart temperature sensor with a 3σ inaccuracy of ±0.5 °C from −50 °C to 120 °C. IEEE J. Solid-State Circuits
**2005**, 40, 454–461. [Google Scholar] [CrossRef] - Souri, K.; Kashmiri, M.; Makinwa, K. A CMOS temperature sensor with an energy-efficient zoom ADC and an Inaccuracy of ±0.25 °C (3σ) from −40 °C to 125 °C. In Proceedings of the IEEE International Solid-State Circuits Conference, San Francisco, CA, USA, 7–11 February 2010; pp. 310–311. [Google Scholar]
- Pertijs, M.A.P.; Huijsing, J. Precision Temperature Sensors in CMOS Technology; Springer: Dordrecht, The Netherlands, 2006. [Google Scholar]
- Souri, K.; Makinwa, K.A.A. A 0.12 mm
^{2}7.4 μW micropower temperature sensor with an inaccuracy of ±0.2 °C (3σ) from −30 °C to 125 °C. IEEE J. Solid-State Circuits**2011**, 46, 1693–1700. [Google Scholar] [CrossRef] - Hastings, A. The Art of Analog Layout; Prentice Hall: Upper Saddle River, NJ, USA, 2006. [Google Scholar]
- Klaassen, K.B. Digitally controlled absolute voltage division. IEEE Trans. Instrum. Meas.
**1975**, 24, 106–112. [Google Scholar] [CrossRef] - Van De Plassche, R.J. Dynamic element matching for high-accuracy monolithic D/A converters. IEEE J. Solid-State Circuits
**1976**, 11, 795–800. [Google Scholar] [CrossRef] - Yousefzadeh, B.; Shalmany, S.H.; Makinwa, K.A.A. A BJT-Based Temperature-to-Digital Converter with ±60 mK (3σ) Inaccuracy From −55 °C to +125 °C in 0.16-μm CMOS. IEEE J. Solid-State Circuits
**2017**, 52, 1044–1052. [Google Scholar] [CrossRef] - Heidary, A.; Wang, G.; Makinwa, K.; Meijer, G. 12.8 A BJT-based CMOS temperature sensor with a 3.6pJ·K2-resolution FoM. In Proceedings of the 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC), San Francisco, CA, USA, 9–13 February 2014; pp. 224–225. [Google Scholar]

**Figure 1.**Conventional bipolar junction transistor (BJT) based temperature sensor front-end circuit.

**Figure 2.**Operating principles of analog-to-digital converters (ADCs): (

**a**) sigma-delta ADC; (

**b**) zoom ADC.

**Figure 4.**Maximum temperature errors simulations with different dynamic element matching (DEM) schemes.

**Figure 5.**Structure of the zoom ADC. (Note: SAR: successive approximation; LSB: least significant bit; MSB: most significant bit; DAC: digital-to-analog converter).

**Figure 7.**Chip micrograph. (Note: OTA: operational transconductance amplifier; C-DAC: capacitive digital-to-analog converter; COMP: comparator).

**Figure 8.**Simulation results of the front-end circuit: (

**a**) first-order fitting; (

**b**) third-order fitting.

Item | [8] | [9] | [17] | [18] | This Work |
---|---|---|---|---|---|

Year | 2013 | 2005 | 2017 | 2014 | 2018 |

Process (μm) | 0.16 | 0.7 | 0.16 | 0.7 | 0.18 |

Area (mm^{2}) | 0.08 | 4.5 | 0.16 | 0.8 | 0.5 |

V_{DD} (V) | 1.5–2 | 2.5–5.5 | 1.5–2 | 2.9–5.5 | 1.8 |

Supply Current (μA) | 3.4 | 75 | 4.6 | 55 | 6.1 |

Temperature Range (°C) | −55 to +125 | −55 to +125 | −55 to +125 | −45 to +130 | 0 to +100 |

Resolution (°C) T_{conv} (ms) | 0.02 (5.3) | 0.01 (100) | 0.015 (5) | 0.003 (2.2) | 0.01 (3.4) |

Inaccuracy (°C) | ±0.15 | ±0.1 | ±0.06 | ±0.15 | ±0.2 |

FOM * (pJ°C^{2}) | 11 | 1875 | 7.8 | 3.2 | 3.8 |

Rel.InAcc. ** (%) | 0.17 | 0.11 | 0.07 | 0.17 | 0.4 |

_{conv}) × (Resolution)

^{2}. ** Rel.InAcc = (2 × Inaccuracy/Range) × 100%.

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**MDPI and ACS Style**

Wei, R.; Bao, X.
A Low Power Energy-Efficient Precision CMOS Temperature Sensor ^{†}. *Micromachines* **2018**, *9*, 257.
https://doi.org/10.3390/mi9060257

**AMA Style**

Wei R, Bao X.
A Low Power Energy-Efficient Precision CMOS Temperature Sensor ^{†}. *Micromachines*. 2018; 9(6):257.
https://doi.org/10.3390/mi9060257

**Chicago/Turabian Style**

Wei, Rongshan, and Xiaotian Bao.
2018. "A Low Power Energy-Efficient Precision CMOS Temperature Sensor ^{†}" *Micromachines* 9, no. 6: 257.
https://doi.org/10.3390/mi9060257