A flow sensor for liquids based on a single temperature sensor operated in pulsed mode

A flow sensor for liquids based on a single temperature sensor operated in pulsed mode

Sensors and Actuators A 110 (2004) 269–275 A flow sensor for liquids based on a single temperature sensor operated in pulsed mode P. Bruschi a,∗ , D...

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Sensors and Actuators A 110 (2004) 269–275

A flow sensor for liquids based on a single temperature sensor operated in pulsed mode P. Bruschi a,∗ , D. Navarrini a , M. Piotto b b

a Dipartimento di Ingegneria dell’Informazione, Università di Pisa,Via Diotisalvi 2, 56122 Pisa, Italy Istituto di Elettronica, di Ingegneria dell’Informazione e delle Telecomunicazioni, CNR, Via Diotisalvi 2, 56122 Pisa, Italy

Received 20 September 2002; received in revised form 16 August 2003; accepted 10 October 2003

Abstract An anemometric flow sensor for liquids based on a single temperature sensor is presented. The sensor is based on a probe composed by a silicon chip glued to a copper cylinder acting as thermal feed-through. A precise temperature sensor and a resistive heater are integrated on the chip surface. The sensor is operated in pulsed mode to eliminate the interference of the fluid temperature, switching either the heater power or the probe temperature. The results of water flow tests in the range (1–30) l/h are presented. The problem of reducing the duration of the measurement cycle has been addressed with theoretical and experimental arguments. © 2003 Elsevier B.V. All rights reserved. Keywords: Flow sensor; Integrated circuit; Anemometer; Liquid flow

1. Introduction Many industrial and laboratory applications require the detection or precise measurements of liquid flows. Commercially available sensors, mostly constituted by turbines equipped of an optical or magnetic pick-up, are generally very expensive devices, especially if reasonable precision and reliability are requested. Cost considerations often lead to renounce the benefits of including one or more flow sensors in liquid circulation systems. Other factors that limit the extensive use of flow sensors for liquids are the difficulty of matching low flow measurement ranges (order of several l/h) with low insertion loss, the compatibility with corrosive or unfiltered liquids and the possibility to plug the sensors directly on the conducts. Such requirements are typical of the automotive, biomedical and environmental monitoring fields where the cost is also a crucial factor. Integrated hot-wire flow sensors [1,2], widely studied in the last decade, represent a promising solution, especially for the possibility to exploit large scale fabrication technologies to keep production costs to a minimum. However, most of the proposed sensors for liquids are based on making the fluid to flow inside micro channels etched on the chip surface

Corresponding author. Tel.: +39-050-568511; fax: +39-050-568522. E-mail address: [email protected] (P. Bruschi). 0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.10.045

and are therefore suitable only for microfluidic applications where the fluid is also completely free of solid impurities [3,4]. Only a few works [5] deal with integrated sensors applicable to the mentioned flow-rate range. Hot-wire anemometers for flow sensing can be operated fixing either (i) the total power dissipation (constant power anemometry (CPA)) [6] or (ii) the sensor temperature (constant temperature anemometry (CTA)) [7]: in both cases, the classical hot-wire scheme requires a reference temperature sensor to take into account the effect of the fluid temperature. Recent works [8,9] demonstrated that flow measurements can be performed with single temperature sensor anemometers by means of a proper pulsed heater driving. The use of a single temperature sensor avoids mismatching problems and, at the same time, considerably simplifies the mechanical and thermal design of the package. CPA and CTA methods can be extended to work with pulsed heater driving. In the case of CPA, the heater power is switched between two fixed values and the resulting temperature variation is measured. In the case of CTA, the switching is applied to the sensor temperature and the required power difference is measured. In both cases the sensor output is related to (t) the flow rate Q through the overall thermal resistance, RS , between the heated element and the fluid, given by the relationship: 1 (t) RS (Q)


P1 − P2 T1 − T 2



P. Bruschi et al. / Sensors and Actuators A 110 (2004) 269–275

where P1 − P2 and T1 − T2 are the heating power and the temperature variations, respectively. Note that here and in the rest of the paper, we have indicated the thermal resistance with the apex (t) to distinguish it from the electrical resistance. Using a pulsed driving method with typical hot-wire sensing elements can be problematic either in the case of CPA or CTA since the heater acts also as the temperature sensor and the required changes in heating power (i.e. in the applied current) result also in sensitivity changes [10]. Designing an integrated thermal flow sensor for liquids poses the problem of avoiding direct contact between the fluid and the chip bonding pads, while preserving a sufficient thermal contact. A possible solution is that of placing the sensor on the outer pipe walls, relying on the conductivity of the latter for the required heat exchange. This approach has been applied to the fabrication of a wind sensor [11] where a ceramic membrane separates the fluid from the active integrated circuit. The solution presented in this work consists in a measuring probe composed by a silicon chip glued on top of a metal finger that provides an improved thermal contact with the fluid. The chip includes a heater and a separate precise temperature sensor. The calculation of the difference P1 − P2 is facilitated by the use of a pulse width modulation (PWM) power driver which feeds the heater with an average power proportional to a control voltage Vth . The probe is operated in pulsed CTA mode by means of a closed loop circuit, optimized for reducing the acquisition time.

2. Description of the sensor The flow sensor presented here is based on a 1.5 mm × 1.5 mm integrated circuit, fabricated in the BCD3S STMicroelectronics process, consisting of a proportional to absolute temperature (PTAT) temperature sensor [8,12] and a resistive heater. The measuring probe is obtained soldering the chip on top of a copper cylinder which, in turn, is sealed to a printed circuit board (PCB). The diameter of the cylinder is 2 mm and its length is 6 mm. The probe is fitted directly to the pipe wall and the metallic cylinder is put in contact with the fluid through a small aperture of the pipe itself, as shown in Fig. 1, thus providing the thermal exchange between the liquid and the chip. Such a structure

bonding wires PCB

sensing chip pipe walls

flow metallic cylinder Fig. 1. Sketched structure of the probe used in the flow meter.

presents the very attractive feature of avoiding direct contact of the chip with the fluid to be measured, so it can be made compatible with reactive liquids by simply coating the copper cylinder with a thin protecting layer (e.g. PTFE). The schematic diagram of the temperature sensor and the layout of the chip are shown in Figs. 2 and 3, respectively. The temperature sensor can be easily recognised in the middle of the layout, surrounded by the four polysilicon resistors to assure uniform heating. The resistors were externally connected in parallel, so the total heater resistance resulted to be 100 . The output voltage provided by the temperature sensor is proportional to the absolute temperature with a sensitivity of 3.3 mV/K. The temperature control circuit used to stabilise the chip temperature to an external set point is shown in Fig. 4. The heater is driven by a PWM power signal with a frequency of 5 kHz, far further the thermal band limit of the probe. The filter FC(s) has a unity dc gain. In steady state conditions, the average power P dissipated by the heater is tied to the signal Vth , according to the relationship: P=

Vmax 2 Vth Rheat V0


where Rheat is the heater resistance, Vmax is the maximum value of the PWM voltage and V0 is the triangular wave peak-to-peak amplitude. A programmable arbitrary waveform generator (HP 33210A) is utilised to switch the set point voltage Vs between two fixed values, corresponding to the temperatures T1 and T2 of Eq. (1). Each set point is maintained for a period tm after which the signal Vth is acquired by means of a digital multimeter (HP3478A). Indicating with Vth1 and Vth2 the Vth values corresponding to the set point temperatures T1 and T2 , the difference Vth2 − Vth1 is related to the total thermal resistance of the probe, i.e. to the flow rate Q, by the following equation, obtained by combining Eqs. (1) and (2): Rheat V0 (T2 − T1 ) Vth2 − Vth1 = (3) Vmax 2 R(t) (Q) S

In practice it is possible to calculate the difference Vth between the threshold voltages at each transition of the set up voltage Vs . Clearly, if the temperature of the fluid is constant, the Vth values acquired at two consecutive transitions are opposite. The output produced by the flow meter is the average of the absolute values of the Vth calculated at the two latest transitions. This, as it can be easily shown, cancels the interference of the fluid temperature drift at the first order. At this stage a personal computer is used to operate the required operations and to control the multimeter and waveform generator by means of an IEEE 488 cable. A stand-alone version of the system is currently being developed. A key parameter for the performance of the system is the settling time of the Vth signal after a Vs step, since this coincides with the minimum duration of the measurement cycle. In order to estimate the settling time and optimize the control circuit, the probe has been modeled by means of the

P. Bruschi et al. / Sensors and Actuators A 110 (2004) 269–275







Q10 Q15

Q9 Q12


R5 Q6



R4 Q16



Q3 Q5

C1 Q17 Q18

R3 Q1





Fig. 2. Schematic diagram of the temperature sensor.

Fig. 3. Layout of the chip, including the temperature sensor and the polysilicon heater.


P. Bruschi et al. / Sensors and Actuators A 110 (2004) 269–275

Triangular wave generator (f=5 kHz)

PWM voltage source OP-AMP

Comparator filter FC(s) PROBE Vth

HP3478A 3,400 V





Multimeter Differential Amplifier

Fig. 4. Block diagram of the system used to operate the probe in CTA mode.

simple equivalent electrical network shown in Fig. 5, where (t) with RSC we have indicated the thermal resistance between (t) the chip and the copper cylinder and with RCF the resistance between the copper cylinder and the fluid. Clearly only the latter is flow dependent. The equivalence between electrical and thermal quantities is the same as in [13]. The capacitors CC and CS represent the heat capacitance of the chip and the cylinder respectively. TF, TC, TS and P are the fluid temperature, the cylinder temperature, the sensor temperature and heater power, respectively. The overall thermal resistance, (t) RS measured in steady state configuration is given by the sum: (t)





It can be easily shown that the time constant introduced by the capacitor CS is by far shorter than the dominant time constant due to CC . For this reason we have neglected CS in the following discussion. On the other hand, the resistor (t) RSC plays an important role in limiting the performance of the system in closed loop configuration (CTA) and cannot be neglected. With this simplification the response of the sensor temperature TS to the heater power in the Laplace domain is given by the transfer function: TS (t) 1 + sτ0 FS (s) = (5) = RS P 1 + sτP (t)



where τP = CC RCF , τ0 = CC RP , and RP are the parallel (t) (t) of RSC and RCF . In CPA operation mode, the transient time (t ) (t ) TS RSC TC RCF T





Fig. 5. Electrical equivalent circuit used to model the thermal behaviour of the probe. The temperature and heat flow are represented by the voltage and current respectively.

depends on the time constant of the pole, namely ιP . As will be shown in the next section, the measured ιP values are of the order of 1 s, leading to settling times, i.e. acquisition times, of several seconds. In CTA operation mode, using the scheme of Fig. 4, the transient is the response of Vth to a Vs step. By simple analytical arguments it can be shown that, if a simple proportional controller is used (FC(s) = 1) and the loop gain tends to infinity, the pole and zero swap. As a result the signals evolves according to the time constant ι0 , which is significantly smaller than ιP , since it is possible to make (t) (t) RSC smaller than RCF using a proper procedure to bond the chip to the cylinder. The measurement time reduction that can be achieved using a CTA approach instead of CPA is clearly of the order of the ratio ι0 /ιP , equal to: (t)

R τ0 = (t) SC (t) τP RSC + RCF

(6) (t)

The importance of RSC is now apparent since it limits the maximum acquisition frequency improvement that can (t) be brought by the CTA approach. Note that if RSC was zero the closed loop time constant would become equal to τP / (1 + βA), where βA is the finite loop gain, and could be made arbitrarily short. In order to reduce the settling time, a first possi(t) ble approach is that of reducing RSC by improving the (t) chip-cylinder connection. Unfortunately RSC includes also contributions of the distributed resistance inside the cylinder body which cannot be modified. A second possibility, which has been studied in this work, is that of canceling the zero (t) introduced by RSC . To accomplish this, a simple first order low pass circuit has been used for the block FC (s) in Fig. 4. A perfect cancellation of the zero cannot be achieved since (t) the frequency of the zero depends on the flow through RCF . The pole of the low pass circuit should therefore be chosen empirically to provide the best performance improvements over the whole flow range of interest.

P. Bruschi et al. / Sensors and Actuators A 110 (2004) 269–275 ∆Vth [V]







2.5 20 2.0 15

Settling time [s]




CPA (open loop) CTA (closed loop)



1.5 10

0 0















Q [l/h]

Q [l/h] Fig. 6. Output signal Vth and corresponding thermal resistance obtained in CTA mode with a set up temperature difference of 1.5 ◦ C.

Fig. 7. Settling time for CTA (open circles) and CPA (solid triangles) configuration.

3. Results and discussion

that changing the latter cause only a scaling of the sensor response. This was not obvious since the cylinder temperature was expected to affect the thermal resistance through the temperature dependence of the water viscosity. A second series of experiments was aimed to evaluate the settling time of the signal Vth , which, as stated in the previous section, gives the lower limit of measurement time of the sensor. The 2% settling times measured in CTA and CPA operating mode are compared in Fig. 7 as a function of the flow rate. CPA measurements have been performed by simply applying a step to the heating power of the probe and recording the output voltage of the temperature sensor; in CTA mode, the scheme of Fig. 4 is used applying the step to the set up voltage Vs and recording the signal Vth . A simple proportional controller (FC (s) = 1) is used in these experiments. The results of Fig. 7 prove that the CTA method allows a significant reduction of the settling time, particularly noticeable at low flow-rates. This effect is described by Eq. (6), considering that at the lowest flow rates the overall thermal resistance (see Fig. 6) is much larger that the con(t) stant term RSC . A satisfactorily quantitative agreement can be observed. The consequences of choosing a measurement time, tm , smaller than the settling time is clearly illustrated in Fig. 8. The curve (a), acquired for tm = 1.5 s, is compared with curve (b) obtained with tm = 5 s. In both cases FC (s) = 1 A significant reduction of the total signal excursion can be observed for the faster measurement time. The response degradation occurs mainly at low flow rates, where, as shown in Fig. 7, the settling times are longer and the Vth values are sampled when the signal is still far form steady state. In order to improve the performance of the sensor, a first order RC low pass filter has been used for the transfer function FC (s). The pole of the filter has been chosen in order to match the zero introduced into the frequency response (t) of the probe by the thermal resistance RSC . As explained in the previous section, a perfect pole-zero cancellation is prevented by the flow rate dependence of the frequency of

The proposed flow sensor has been tested in a deionised water circulation system, including two commercial reference flow-meter (McMillan S110-S112) covering the overall range 1–30 l/h with a 2.5% precision. A specially built adapter has been used to fit the probe to a circular pipe of 1 cm inner diameter. All the experiments have been carried out at room temperature. A first series of measurements has been devoted to characterise the static sensor response, i.e. the dependence of the output signal Vth (averaged over the two latest set-up transitions) on the flow rate. In order to assure that Vth was sampled in steady state conditions, long measurement times tm (>10 s) have been chosen in this phase. The results for a difference T2 − T1 fixed to 1.5 ◦ C are shown in Fig. 6, where the overall thermal resistance, estimated by means of Eq. (3), is also plotted as a function of the flow rate. The convective thermal resistance was fitted by the generalised King’s law [14] that yield an acceptable approximation over an interval including both the regions of (t) free and forced convection. The resistance RS was written as: R0 (t) (t) RS = RSC + (7) 1 + (Q/Q0 )n (t)

where RSC , R0 and Q0 and n are constant parameters. The values estimated from the curve of Fig. 6 are summarised in Table 1. The same operation has been performed for different T2 − T1 values, up to 5 ◦ C, obtaining the same results, demonstrating that the thermal resistance does not significantly depend on the set up temperatures and, equivalently,

Table 1 Estimated parameters of the probe thermal model (t)


R0 (K/W)

Q0 (l/h)







P. Bruschi et al. / Sensors and Actuators A 110 (2004) 269–275

2.0 1.9 1.8 1.7 ∆Vth [V]

1.6 1.5 (a) (b) (c)

1.4 1.3 1.2 1.1








Q [l/h] Fig. 8. Comparison between the output signals obtained in various experimental conditions: (a) FC (s) = 1.5 s and tm = 5 s; (b) FC (s) = 1 and tm = 1.5 s; (c) tm = 1.5 s and FC (s) consisting in a first order low pass with a pole at 0.33 Hz.

8 6

Vth [V]

4 2 0 FC(s) =sp / (s+sp) FC(s)=1

-2 0.0








Time [s] Fig. 9. Transient behaviour of the threshold voltages Vth obtained at a flow rate of 0.6 l/h with the FC (s) = 1 (continuous line) and with a low pass inserted in the FC (s) block.

the zero. Temporary saturation effects occurring in PWM power driver at the beginning of each transition complicate the analysis of the system. Optimization of the correcting pole have been therefore carried out empirically. Curve (c) in Fig. 8 has been obtained with tm = 1.5 s and a low pass filter characterized by a pole at 0.33 Hz. By this choice the signal excursion at low flow rates has been partly recovered without affecting the response at high flow rates. The effect of the filter on the signal transient is shown in Fig. 9 for a flow rate of 0.6 l/h. The faster settling exhibited by the signal when the filter is inserted is clearly visible.

4. Conclusions A flow sensor for liquids based on the anemometric principle, designed for a very low flow range, has been described

in details. The measured high sensitivity makes the sensor suitable for leakage detection. The main advantage of the proposed solution with respect of more conventional ones consists in the absence of a reference sensor resulting in a greater mechanical simplicity of the probe. Due to the reduced section restriction introduced by the probe, small insertion losses can be expected. The fluid temperature interference has been cancelled by a pulsed version of CTA. The integration of distinct temperature sensor and heater on the same chip, instead of the common single resistive heating/sensing elements, has greatly simplified the pulsed driving strategy, maintaining at the same time the dimensions of the probe and its heat capacitance to a minimum. A significant improvement of the output settling times, resulting in a shorter measurement cycle, has been achieved with an original control loop where the zero due to the thermal resistance between the chip and the copper cylinder has been cancelled by means of a low frequency pole. Even if a perfect zero cancellation occurs only at a single flow rate value, by this simple modification a satisfactory response could be maintained for measurement times down to 1.5 s over the whole flow range of interest. To our knowledge, a single chip anemometric sensors for liquids that combines similar characteristics of: (i) sensitivity, (ii) possibility to be directly plugged into a standard pipe with low insertion losses, (iii) short acquisition time, has not yet been presented in the literature. In order to facilitate the design and parameter setting, two general purpose instruments controlled by a personal computer have been included in the present version of the flow meter. The simplicity of the required signal processing makes the system particularly suitable to be completely integrated on a single chip.

Acknowledgements We wish to thank STMicroelectronics, Division of Cornaredo (Milano, Italy), for the fabrication of the integrated circuits.

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Biographies P. Bruschi was born in Massa, Italy, in 1964. He received the laurea degree in electronic engineering from the University of Pisa, Italy, in 1989. In 1993, he joined the Department of Information Engineering as a researcher. He is currently an associate professor of the Department of Information Engineering of the University of Pisa. His main area of interest is the development of integrated silicon sensors and actuators. He is also involved in the design of analog integrated circuits and the development of process simulators. D. Navarrini was born in Piombino, Italy in 1975. He received the laurea degree in physics at the University of Pisa in 2000. He is currently a PhD student at the Department of Information Engineering of the University of Pisa. His research activity mainly concerns the design of integrated analog circuits and the development of integrated sensors. M. Piotto was born in 1970, La Spezia, Italy. He received his laurea degree in electronic engineering from the University of Pisa, Italy, in 1996 and his PhD degree in electronic, computer and telecommunication engineering in 2000. From 2000 to 2001 he worked at the Department of Information Engineering of the University of Pisa as a graduated technician. Since December 2001 he has been a researcher of the “Centro di Studio per Metodi e Dispositivi per Radiotrasmissioni—National Research Council” of Pisa. His main research interests concern micromachining, MEMS, microelectronic and nanoelectronic devices and technologies.