[IEEE 2008 3rd International Conference on Sensing Technology (ICST 2008) - Taipei, Taiwan...

An Inherently Linear Transducer using Thermistor Practical Approach

Valter C Rosa, Lígia Souza Palma, Amauri Oliveira, Tiago Rodrigues Torres Department of Electrical Engineering, Federal University of Bahia, Salvador, Bahia, Brazil

[email protected], [email protected], [email protected], [email protected]

Abstract In this article we describe a feedback circuit, with thermoresistive sensor, based on thermal sigma-delta modulator. This circuit uses a one-bit first order sigma-delta modulator in which considerable part of conversion functions is performed by the sensor. This transducer circuit is able to perform digital measurement of physical quantities that interacts with the sensor: temperature, thermal radiation and fluid velocity. In this paper, this circuit was used to measure environment temperature. In this circuit, digital output voltage is linearly dependent on the environment temperature. We show the equations that support circuit behaviour, simulation results and experimental results. In addition, we present the thermal radiation architecture version in which digital output is intrinsically linear to the thermal radiation measure.

Keywords: thermistor, sigma-delta modulator, pulse density modulation, temperature, thermal radiation

1 Introduction Negative feedback system configurations with thermoresistive sensor using the power balance principle have been employed in measurement of thermal radiation, H [1], fluid velocity, U [2], and temperature, Ta [3]. In the most used method, called constant temperature, the sensor is heated by Joule effect to a chosen temperature and the thermal radiation (or fluid velocity, or temperature) variation is compensated by a change in electrical heating due to the negative feedback employed. Thus the sensor is kept at an almost constant temperature.

We studied some configurations to implement a measurement system with a sensor heated to a constant temperature. The most usual is the configuration that uses a Wheatstone bridge with the sensor in one of its branches [4]. In that configuration, the relation between the output signal and input physical quantity is not linear.

Another attractive possibility is the use of sigma–delta configurations [5], in which the sensor is a part of the feedback loop. One-bit sigma–delta modulation is already a feedback configuration in which output signal is an oversampled version of the analogue input signal [6]. Sigma–delta modulator has been employed in signal processing to convert an analogue quantity to a digital quantity using simple analogue circuitry. Sigma–delta converters are recognized to be robust and high performance A/D converters.

This work presents a temperature circuit meter composed of a one-bit sigma–delta modulator in which some of its blocks functions are performed by the thermoresistive sensor itself. This architecture was presented with simulation results in [7] for thermal radiation measurement. Here we present, circuit simulation results and experimental results for environment temperature measurement. We will also

show the thermal radiation circuit version in which digital output is also intrinsically linear with the thermal radiation measure.

2 Temperature Meter

2.1 Circuit Topology The circuit in figure 1 is a sigma-delta modulator. The sum and integration functions were replaced by a negative temperature coefficient sensor (NTC sensor) which operated at constant temperature .

Figure 1: Proposed circuit topology.

In this circuit, is the sensor voltage when it is operating at reference temperature . The PDM signal at flip-flop output is an oversampled digital version of CMP signal at comparator output, and NTC is the voltage between sensor terminals. PDM signal is level ‘’1’’ when sensor temperature is greater than and level “0” when sensor temperature is less than . This signal is used to estimate environment temperature after filtering. It also feeds the digital to analogue current converter (DAC) at modulator feedback path to maintain sensor temperature

978-1-4244-2177-0/08/$25.00 © 2008 IEEE

3rd International Conference on Sensing Technology, Nov. 30 – Dec. 3, 2008, Tainan, Taiwan

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constant. When PDM signal is level “1”, the sensor needs to be cooled. So a slight current pulse with amplitude , period and width is generated at sensor terminal by the DAC and the sensor is cooled by dissipation. When PDM signal is level “0”, the sensor needs to be heated. So a pulse current with amplitude , period and width

is generated at sensor terminal by the DAC and the sensor is heated by Joule effect.

The environment temperature variation is obtained by sensor resistance variation, which is proportional to the voltage at sensor terminals. If the medium peak voltage at sensor terminals is maintained constant at

value (figure 1), the medium sensor resistance is maintained constant at / . Consequently, sensor temperature is also maintained constant.

2.2 Circuit Analysis The circuit from figure 1 is able to maintain sensor temperature constant and to provide a pulse density modulated power to the sensor. In steady state, the electric power provided to the sensor is given by [7]: 1

In which, Ta is the environment temperature and is the sensor thermal conductance.

When the ambient temperature was equal to the power provided to the sensor is (figure 2): 2

When the ambient temperature was equal to the power provided to the sensor is: 3

In which and are the environment temperature limits to be measured.

Figure 2: Electric power provided to the sensor versus environment temperature in steady state.

The maximum power provided to the sensor is given by: 4

The minimum power provided to the sensor is given by:

1 5

In which ⁄ and is the oversampling period.

From equations (2), (3) and (5): ∆ 6 ∆ 1 7

In which, ∆

The voltage in sensor terminals is given by: 8

From equations (4), (7) e (8): ∆ 1 9 ∆ 1 / 10

and are dependent on sensor characteristics, environment temperature range, sensor operation point ( , ) and the relation between ⁄ .

2.3 Linearity In this analysis we considered 0. In this case, equations (6), (7), (9) and (10) can be written as: 11 ∆ 12 13 / 14

The electrical power provided to the sensor is a pulse density modulated signal that can be written by: 15

In which is the normalized medium power signal in the sensor and can be written as: 1 16

In which, is the normalized medium value of the signal PDM at modulator output.

Substituting equations (12), (16), (1) and (11) in equation (15):

∆ 17

The equation (17) shows that the PDM medium signal at modulator output has an intrinsic linear relationship with the environment temperature from to .

It can be proved that if 0, equation (17) is also valid.

2.4 Verification Circuit The proposed circuit was implemented using discrete components and the NTC sensor. The same circuit


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was simulated in a circuit simulator using the same conditions of the implemented circuit. Figure 3 shows the DAC circuit, a constant current generator that can drive transistor T1 current to the output (sensor terminal) or to ground depending on the input signal.

Figure 3: Digital to analogue current converter.

Some simulated results can be observed in figures 4 and 5. Figure 4 shows transient and stead state of the signals: CMP (comparator output), NTC (sensor voltage) and PDM (modulator output digital voltage) (figure 1).

Figure 4: Transient and stead state CMP, NTC and

PDM signals (figure 1).

During 5 sec, PDM signal remains in zero voltage commanding the sensor to initial heating. When the sensor reaches Ts0, PDM signal alternates to maintain sensor temperature at the constant value Ts0.

Figure 5 shows a zoom in figure 4 from 9.05 sec to 9.10 sec. CMP signal shows the progressive sensor cooling during each sample time while PDM signal is kept at level “1”. When PDM signal is level “0” CMP signal shows the continuous sensor heating.

Figure 6 shows the linearity between circuit simulation results and experimental results. Linearity between environment temperature and medium PDM signal was 100% in simulated circuit results and 99.93% in experimental circuit results.

An analogue Butterworth filter with 60 dB/decade of attenuation in rejection frequency band and cut-off frequency of 1 Hz was used to obtain medium value

of PDM signal due to implementation and test facilities. In the final implementation we will use a digital filter.

Figure 5: Stead state CMP, NTC and PDM signals.

Figure 6: Analogue filter output voltage versus

environment temperature.

Test conditions:

NTC sensor characteristics:

A = 0.01366 Ω B = 3334 K

= 10.73 mJ/K = 0.841 mW/K Environment temperature range: = 0.0 oC = 68.6 oC

Sensor stead state operation point: = 83.4 oC = 163.3 Ω Oversampling frequency: Fs = 755 Hz Relation ⁄ = 21,5%

= 3,38 V = 20,69 mA

The medium value of PDM signal at filter output was measured with a 6 ½ digits voltmeter and 0.0035% basic DC accuracy.

The experimental tests were done with the NTC sensor near the sensor element of a 4 ½ digits thermometer with 0.01 oC of accuracy together in a

OUTPUT

+V

-

+3

2

6

74 OP1

T1

R1

P2R3

T2

INPUT

R2

R4

T

Time (s)0.00 2.50 5.00 7.50 10.00

CMP

-8.00

8.00

NTC

0.00

10.00

PDM

0.00

4.00

y = 0,1213x - 0,2617R² = 0,9993 (REAL)

y = 0,0967x + 0,3235R² = 1,0000 (SIMULATED)

3

4

5

6

7

8

9

35.00 45.00 55.00 65.00

Ana

logu

e fi

lter o

utpu

t (V

)

Temperature (⁰C)

T

Time (s)9.05 9.06 9.07 9.08 9.09 9.10

CLK

0.00

5.00

CMP

0.00

3.00

NTC

0.00

4.00

PDM

0.00

4.00


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laboratory heater. The heater was kept at constant temperature by a controller.

2.5 Proposed Circuit using a Microcontroller

We needed to use the verification circuit to validate the power approach proposed in this paper, however most of the circuit must be implemented in a microcontroller as can be seen in figure 7.

Figure 7: Proposed circuit with a microcontroller.

Equations (8) and (9) show that the electrical power provided to the sensor by the DAC depends on environment temperature range (∆ ).

In figure 7 DAC circuit was kept out of the microcontroller to be possible to measure any environment temperature range allowed by the sensor. This feature must require power that the microcontroller is not able to supply. However, if it was not an application demand, as in thermal radiation or fluid velocity measurements, the DAC could be brought inside a microcontroller with specials analogue characteristics.

3 Thermal Radiation Measurement The idea to measure thermal radiation is to use the circuit of figure 7 in a differential format with two sensors. One sensor will be able to measure thermal radiation and surrounding temperature, the other sensor will be protected from thermal radiation and will measure surrounding temperature. This architecture is shown in figure 8.

Sensor behavioural, under thermal radiation and surrounding temperature must be modelled by [1]: 20

In which . is the absorb thermal radiation coefficient, S is the sensor surface area and H is the thermal radiation.

In this analysis we considered 0. In this case, as the sensor must operate at constant temperature and the electrical power provided to the sensor in this

circuit is pulse density modulated, the electric power can be written by: ∆ 21 0 ∆ 22

Figure 8: Proposed circuit for thermal radiation

measurement.

Suppose that we submit both sensors to the same surrounding temperatures to operate in the same temperature range, and protect them from forced thermal conduction (remember that sensor B is protected from thermal radiation) the equation (17) can be used in equation (21): ∆ ∆ 23

The thermal radiation can be measured by: ∆ 24

Using equation (16): ∆ 25

Equation (25) shows that thermal radiation to be measured is intrinsically linear with the difference of the medium of the two PDM signals at modulator output. As PDM and PDMs signals are at the same oversampling frequency, thermal radiation can be expressed also by: ∆ 26

Equation (26) shows that there is no need to filter the two PDM signals but only the difference between them using one filtering routine.

Equation (22) shows that the maximal thermal radiation that can be measured happens when


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0 and that it is dependent of surrounding temperature and the worst case happens when surrounding temperature is equal to Ta(max). 27

4 Conclusions We presented a circuit architecture based on sigma-delta modulation applied to environment temperature and thermal radiation measurements. This circuit architecture can be extended to fluid velocity measurement. The thermal sigma-delta transducer circuit for environment temperature application measurement was implemented to validate this architecture. The linear relationship between environment temperature and the average signal value at the thermal sigma-delta output was demonstrated, equation (17). The methodology for sensor reference voltage and sensor reference current calculations was developed for any temperature range supported by the sensor. The thermal sigma-delta architecture topology applied to thermal radiation measurement was theoretically developed. The experimental results show the intrinsic linearity between variable to be measured and circuit response. Thus they are in accordance with the simulation results and the developed theory in the case of surround temperature measurement. This architecture, based on sigma-delta modulation, has the advantage of transforming the physical greatness directly to digital form, without the need to pass it through intermediate voltage or current value. In addition, the analogue part of this architecture is easy to implement in an integrated circuit because it is reduced to the sensor polarization circuit and a comparator circuit. Another advantage is the linear relationship between the measure variable and the estimated greatness for the thermal radiation and temperature meter cases. The disadvantage of this architecture is that the resolution is poor, given that it is based on a first order sigma-delta architecture [8]. To obtain better resolution it is necessary to use a high oversampling rate or thermal sigma-delta architecture of higher order. The improvement suggestions are: a) the implementation of a thermal sigma-delta digital circuit part to be applied to temperature measurement in a microcontroller for new verification; b) the proposed thermal sigma-delta architecture circuit implementation for thermal radiation application; c) a study on thermal sigma-delta architecture of higher order in order to improve resolution; d) a study about

others sensors to improve frequency response and d) to implement thermal sigma-delta architecture using integrated mixed circuit technology.

5 References [1] A. Oliveira, G. S. Deep, A. M. N. Lima, R. C. S.

Freire, “A Feedback I2-controlled Constant Temperature Solar Radiation Meter”, Proc. IEEE-IMTC, vol. 2, pp. 1062-1066 (1998).

[2] H. Fujita, T. Ohhashi, M. Asakura, M. Yamada, K. Watanabe,”A thermistor Anemometer for Low-Flow-Rate Measurements”, IEEE Trans. Instrum. Measurement, 44 (3), pp. 779-782 (1998).

[3] L. S. Palma, A. Oliveira, A. S. Costa, A. Q. Andrade Jr., C. V. R. Almeida, M. E. P.V. Zurita, R. C. S. Freire, “Implementation of a Feedback I2-controlled Constant Temperature Environment Temperature Meter”, Sensors 3 (10), pp 498-503 (2003).

[4] P. C. Lobo, “An electrically Compensated Radiometer”, Solar Energy, 36 (3) pp.207-216 (1985).

[5] K. A. A. Makinwa, J. H. Huijsing, “Constant power Operation of a Two-dimensional Flow Sensor using Thermal Sigma-Delta Modulation Techniques”, Proc. IEEE-IMTC, pp. 1577–1580 (2001).

[6] P. M. Aziz, H. V. Sorensen, J. V. D .Spiegel, ”An Overview of Sigma-Delta Converters”, IEEE Signal Processing Magazine, pp. 61-81 (1996).

[7] A. Oliveira, L. S. Palma, A. S. Costa, R. C. S. Freire, A. C. C. Lima, “A Constant Temperature Operation Thermoresistive Sigma-Delta Solar Radiometer”, Measurement, (34) pp 267-273 (2006).

[8] L.S. Palma, A. Oliveira, R. C. S. Freire, A. B. Fontes, “Sigma-Delta Modulator: with Themoresistive Sensor Frequency Response”, Proc. IEEE-IMTC, pp. 776-780, (2006).


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