# A CMOS Readout Circuit for Resistive Transducers Based on Algorithmic Resistance and Power Measurement

Abstract: This paper reports a readout circuit capable of accurately measuring not only the resistance of a resistive transducer, but also the power dissipated in it, which is a critical parameter in thermal flow sensors or thermal-conductivity sensors. A front-end circuit, integrated in a standard CMOS technology, sets the voltage drop across the transducer, and senses the resulting current via an on-chip reference resistor. The voltages across the transducer and the reference resistor are digitized by a time-multiplexed high-resolution analog-to-digital converter (ADC) and post-processed to calculate resistance and power dissipation. To obtain accurate resistance and power readings, a voltage reference and a temperature-compensated reference resistor are required. An accurate voltage reference is constructed algorithmically, without relying on precision analog signal processing, by using the ADC to successively digitize the base–emitter voltages of an on-chip bipolar transistor biased at several different current levels, and then combining the results to obtain the equivalent of a precision curvature-corrected bandgap reference with a temperature coefficient of 18 ppm/°C, which is close to the state-of-the-art. We show that the same ADC readings can be used to determine die temperature, with an absolute inaccuracy of ±0.25 °C (5 samples, min–max) after a 1-point trim. This information is used to compensate for the temperature dependence of the on-chip polysilicon reference resistor, effectively providing a temperature-compensated resistance reference. With this approach, the resistance and power dissipation of a 100 $\Omega $ transducer have been measured with an inaccuracy of less than $\pm 0.55~\Omega $ and ±0.8%, respectively, from −40 °C to 125 °C.

## Summary (3 min read)

### Introduction

- Most integrated readout circuits for resistive transducers only measure resistance, without measuring or stabilizing power dissipation [1, 2, 5, 6].
- As a result, the previously-reported constant power circuits, based on translinear loops or other feedback loops, still rely on the accuracy of external voltage and current (or resistance) references.
- Using precision circuit design techniques as well as appropriate calibration and correction schemes, bandgap references can achieve high accuracy over a wide temperature range with low chip-to-chip variations [12-15].

### A. Algorithmic resistance and power measurement

- Measuring resistance and/or power involves both voltage and current measurements.
- For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
- > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 3.
- These results depend on the ADC’s reference voltage Vref and on accurate knowledge of the value of Rref.
- As detailed below, to eliminate the dependence on Vref, the authors algorithmically construct an accurate bandgap voltage reference, by digitizing several base-emitter voltages.

### C. Algorithmic temperature measurement

- Expressions (3) and (11) still depend on Rref, which will generally be subject to process tolerances and temperature drift: Copyright (c) 2017 IEEE.
- For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
- To compensate for the resistor’s temperature drift, information about the die temperature T is needed.
- Fortunately, this can readily be obtained from the PTAT voltage given by (6): (13) where the relation (9) between Vref and Vbg is again used to obtain an expression independent of Vref.
- The result only depends on the current ratio p, the bandgap scale factors a1,2, the bandgap voltage Vbg and physical constants k and q.

### D. Compensation for BJT non-idealities

- As mentioned, expression (5) for the base-emitter voltage ignores various non-idealities of the BJT [15].
- Second, the transistor’s finite current gain causes the collector current to deviate from the bias current, which is applied to the transistor’s emitter.
- Leakage current and series resistance lead to errors in the bandgap reference and the temperature measurement that cannot be corrected based on a single-temperature calibration [14].
- The conventional approach to dealing with this is to choose the current level and transistor size such that these errors are sufficiently small.
- The authors algorithmic approach offers the unique possibility to correct for leakage and series resistance by combining more than two base-emitter voltages digitally.

### III. CIRCUIT IMPLEMENTATION

- The block diagram of the readout circuit is shown in Fig.
- For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
- Since the algorithmic readout relies on the accuracy of the ADC, the non-idealities of the ADC must be taken into account when selecting or designing the ADC.
- Similarly, CMRR also plays an important role due to the different common-mode voltage levels to be measured.

### A. Circuit Implementation of the Transducer Front-End

- The transducer front-end circuit for resistance and power measurements is shown in Fig.
- The voltage-to-current converter includes a chopped operational transconductance amplifier (OTA) in a feedback loop.
- The voltage across the transducer is thus stabilized to Vbias.
- The added cascode transistor M0b decreases the drain-source voltage of the main transistor M0a, effectively reducing this leakage current.

### B. Circuit Implementation of the BJT Front-End

- The BJT front-end circuit shown in Fig. 8 generates the base-emitter voltages needed for the construction of the voltage reference and temperature sensor.
- The OTA used in the BJT front-end is the same as the one used in the transducer front-end (as shown in Fig. 7).
- The amplifier needs to have low offset and high open-loop gain to minimize errors in the bias current [25].
- This is achieved by applying dynamic element matching (DEM) in the current mirror in Fig.
- Thus, the mismatch of the current sources is modulated by the DEM clock, and the resulting average current is close to p times the average unit current.

### IV. EXPERIMENTAL RESULTS AND DISCUSSION

- A chip photograph and a plot of the chip layout with the main circuit blocks are shown in Fig. 10.
- The chip (DUT), mounted on a PCB (PCB1), is placed inside a climate chamber (Vötch VTM 7004) to perform measurements at temperatures ranging from -40°C to 125°C.
- This is improved to about 24 ppm/°C after compensation for series resistance and leakage using the method described in Section II-D. After compensation for the systematic quadratic curvature, the temperature coefficient is further improved to 18 ppm/°C (Fig. 13(b)).

### B. Temperature Measurement

- Fig. 14 shows the error in the temperature measured using the method described in Section II-C, relative to the reference temperature sensor, for 5 samples of the chip.
- By applying the algorithmic approach described by (13) and (14), a leakage-free PTAT voltage Vbe,ideal can be obtained, which can then be converted to temperature by linear scaling.
- These errors are relatively large compared to the state of the art [25], which can be attributed to the large initial errors due to the leakage currents in the multiplexer switches, which can be reduced in a re-design by reducing the transistor sizes.
- Nevertheless, the accuracy currently obtained is sufficient to Copyright (c) 2017 IEEE.

### C. Resistance Measurement

- As described in II-A, the resistance of the transducer is measured relative to an on-chip reference resistor Rref in series with the transducer (Fig. 6).
- The error in the measurement of the precision resistor then reduces significantly, as shown in Fig. 15(b).
- Second, the temperature coefficient Rref is determined by a two-point batch correction (at 27C and 100C) in the calibration result of Fig. 15(a).
- > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 9.

### D. Power Measurement

- The power consumption of the transducer was measured using the method described in Section II, eq. (11).
- As described above, the accuracy of the on-chip reference resistance can be further improved by a room-temperature individual trim and a two-point batch calibration (27°C and 100°C) to find Rref0 and Rref.
- This reduces the errors in the power dissipation measurement to ±0.8% as shown in Fig. 17(c).

### V. CONCLUSIONS

- The authors have reported a readout architecture for resistive transducers, which is capable of accurately measuring their resistance and power dissipation.
- The key idea behind the readout architecture is to avoid analog signal processing as much as possible, by first digitizing the analog signals and then combining the results in the digital domain.
- This algorithmic approach greatly improves the flexibility of the signal processing and facilitates the removal of errors such as leakage current, series resistance, and systematic nonlinearity in the digital domain.
- In addition, the accuracy of the analog reference voltage of the ADC in this system does not impact the measurement accuracy, as this reference voltage is replaced by the constructed bandgap reference voltage in further data processing.
- Experimental results have shown that the resistance and power dissipation of a Pt100 resistor can be measured with an inaccuracy of ±0.55 Ω and less than ±0.8% respectively over the military temperature range of -40°C and 125°C, showing the effectiveness of the applied techniques.

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##### References

^{1}, Zoran Corporation

^{2}, Microchip Technology

^{3}, ON Semiconductor

^{4}, Analog Devices

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### "A CMOS Readout Circuit for Resistiv..." refers background or methods in this paper

...in which n is the BJT’s non-ideality factor, k is Boltzmann’s constant, q is the electron charge, T is absolute temperature, and IS is the BJT’s saturation current (IS I1,2) [24]....

[...]

...First of all, the non-linear temperature dependence of IS will lead to a (slightly) non-linear temperature dependence of Vbe, which leads to a small non-linear temperature dependence of the bandgap reference voltage, also referred to as curvature [24]....

[...]

...2: 1,21,2 lnbe S InkTV q I (5) in which n is the BJT’s non-ideality factor, k is Boltzmann’s constant, q is the electron charge, T is absolute temperature, and IS is the BJT’s saturation current (IS I1,2) [24]....

[...]

...A PTAT bias generation circuit is used to provide a well-defined bias current that is an integer multiple p of a unit bias current of nominally 6 μA [24]....

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### "A CMOS Readout Circuit for Resistiv..." refers background in this paper

...The difference of the two base-emitter voltages is a PTAT voltage that depends, to first order, only on the current ratio p = I1 / I2: 1 2 lnbe be be kTV V V p q (6) In a conventional bandgap reference, a temperature-independent reference voltage is obtained by adding a scaled Vbe to Vbe: 1 1 1 2 2bg be be be beV V V a V a V , (7) where a1 = 1 + , a2 = – , and the optimal coefficient is subject to tolerances on the BJT’s saturation current and the bias current, and can be found based on a single-temperature calibration [15]....

[...]

...As mentioned, expression (5) for the base-emitter voltage ignores various non-idealities of the BJT [15]....

[...]

...It operates algorithmically, by successively digitizing the voltage drop across the transducer (Vload), the voltage drop across an on-chip reference resistor carrying the same current (Vref), and the base-emitter voltages of a single BJT (Vbe) biased at different current levels, and then processing the results in the digital domain....

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...The BJT front-end circuit shown in Fig....

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...The OTA used in the BJT front-end is the same as the one used in the transducer front-end (as shown in Fig....

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### "A CMOS Readout Circuit for Resistiv..." refers methods in this paper

...ADCs implemented in standard CMOS technology have been reported [27], which can readily be co-integrated to realize...

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...For future on-chip integration, the ADC presented in [27] can be adopted for its low INL (±6 ppm), low input-referred noise (0....

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