8
Advanced interfaces for resistive sensors
Abstract
Resistive sensors are among the most widespread devices in data acquisition systems. This is mainly due to the broad availability of sensors for different applications. Because of the simplicity of the sensing devices and the opportunity to implement simple and low-cost data readout systems, they are of considerable value when the focus is on the realization of smart sensors. In this chapter, traditional resistive sensor interface methods will be analyzed; more advanced techniques appropriate for specific applications, as well as targeting the effectiveness of the acquisition systems, will subsequently be explored. The chapter closes with discussion regarding future trends.
Keywords
Parasitic capacitive effects; Resistance-to-time conversion method; Resistive sensor interface; Weighted least mean squares linearization; Wide-range resistance measurement
8.1. Introduction
The success of resistive sensors is mainly due to their availability for many different applications: thermal and light detectors, gas presence and concentration evaluation, position measurement, and strain estimation to name just a few examples of the possible fields of application. The simplicity of the sensing devices together with the opportunity to implement simple and low-cost sensor interface circuits makes this kind of device highly appropriate for the realization of smart sensors—in which the sensing element, the signal conditioning electronics, and the data acquisition/elaboration/transmission stages form a unique unit.
The chapter is structured as follows: Section 8.2 gives a brief introduction and general information about resistive sensors; Section 8.3 details the electronic interface perspective, starting with an analysis of the traditional interface methods. In this section, calibration and linearization procedures are illustrated. Section 8.4 explores more advanced techniques that are suitable for specific applications (e.g., wide-range sensors) or for enhancing the effectiveness of the acquisition systems (e.g., coping with parasitic capacitive effects). Section 8.5 deals with industrial-related aspects. Finally, Section 8.6 presents a discussion related to future trends, and conclusions are offered.
8.2. Resistive sensors
A resistive sensor provides information in the form of the electrical resistivity of a material or electrical resistance of a device.
The electrical resistivity ρ is the opposition of a specific material to the flow of an electric current when an electrical field is applied; it depends on the properties of the material itself. The reciprocal of the resistivity is the conductivity σ. The alteration of the physical/chemical conditions of the resistive sensor, caused by the physical quantity of interest, results in variations in its resistivity. However, being a microscopic effect, the estimation of electrical resistivity is quite complicated and not achievable with tools and techniques available for the realization of smart sensors.
The electrical resistance R is the opposition of a device to the flow of an electric current when an electrical potential is applied. The reciprocal of the resistance is the conductance G. Because it is a property related to an object, made of a specific material and with a determined shape and size, the electrical resistance is a macroscopic effect and thus it is easier to estimate using different approaches.
Ohm's Law (Eq. 8.1) furnishes the relationship between the applied voltage V and the current I flowing through a device and gives the basic concept regarding resistance estimation techniques, which will be shown in the subsequent sections.
(8.1)If a device is made of a homogeneous material, the shape and the size determine the relationship between the electrical resistivity of the material and the electrical resistance of the object. For example, given a parallelepiped with cross-section A and length L (as in Fig. 8.1, where the conventional symbol of the electrical resistance is reported as well), Eq. (8.2) shows how to relate the resistance R (conductance G) to the resistivity ρ (conductivity σ).
(8.2)The measurement of the electrical resistance is therefore an indirect way of measuring the electrical resistivity. In addition, it should be noted that, even if the geometrical properties of the object (the ratio L/A in Eq. 8.2) are unknown or are not easy to compute (e.g., irregular object shape), the direct proportionality between R and ρ shown in Eq. (8.2) is still valid. This leads to a direct proportionality between resistivity variation Δρ and resistance variation ΔR.
8.2.1. Examples of resistive sensors
Examining Eq. (8.2), it should be noted that the resistance value R is the combination of a physical factor (ρ) and a geometrical factor (the ratio L/A). Resistive sensors exploit modifications in any of such parameters to convert the variation of the physical quantity of interest into a variation of resistance. The five main types of resistive sensor are discussed below; however, this selection is not exhaustive.
8.2.1.1. Resistive temperature detectors
As the name suggests, these sensors relate resistance to the environmental temperature. They are usually made of a metallic filament wrapped in a ceramic or other dielectric material. The basic working principle is based on the dependence on temperature of electron mobility in the metallic filament; thus, this kind of sensor employs the variation of the resistivity ρ. It should be pointed out that the size of the filament can also change according to temperature, but the effect of the geometrical variations on sensor resistance is negligible with respect to the resistivity variation.
When a conductive material is employed, sensor resistance usually increases with temperature (positive temperature coefficient - PTC); alternative techniques and materials, such as semiconductors, can be used as the sensing component, demonstrating the opposite effect: reduction of the sensor resistance with increasing temperature (negative temperature coefficient - NTC).
8.2.1.2. Light-dependent resistors
Also called resistive photodetectors, these sensors operate with a modification of a physical property because of interaction with light. The surface of the sensing component of the sensor is made of a material, which reacts to the light with a change in electron mobility and, as a consequence, in the material resistivity ρ. The choice of the material leads to different sensor characteristics, such as baseline value, sensitivity, activation threshold, and so on.
8.2.1.3. Resistive gas sensors
Similarly to the devices already mentioned, resistive gas sensors show a modification of material resistivity ρ caused by interaction with specific gases. The sensing component of these sensors is made of a material, which reacts chemically with the gas molecules, increasing or decreasing the concentration of free electrons and, therefore, the surface resistivity. Semiconductors such as metal oxides are the sensing material usually employed for these sensors (thus, metal oxide sensors—MOX). The large variety of available materials guarantees a wide range of devices, each of which is characterized by selectivity towards one or more specific substances (Korotcenkov and Cho, 2017). A MOX sensor is characterized by a steady-state resistance value, i.e., the baseline, which depends on several parameters, such as the method of manufacture, material, and working temperature. Baseline values of MOX sensors can therefore fall in a resistance interval of several decades. Moreover, the high sensitivity shown by MOX sensors to particular substances implies a modification of the sensor resistance value, which can also be in the order of several decades (Krško et al., 2017). This makes the interface procedures quite critical, as will be clarified in subsequent sections.
8.2.1.4. Strain gauges
A resistive film is sustained by a thin and flexible support. The entire structure is tightly attached to an object, and the deformation (tension and compression) of this object causes the deformation of the filament, in terms of length and cross section. Thus, the geometrical portion of Eq. (8.2) L/A is modified, leading to the modification of the filament resistance. If utilized in suitable structures, these sensors can be used to detect the strain of a material as well as strength, weight, pressure, and so on.
8.2.1.5. Potentiometers
Potentiometers are the most straightforward resistive sensors. They are basically realized with a bar of length L of conductive material or wrapped conductive filament and a moving slide with a contact, which touches the bar between its ends, as shown in Fig. 8.2. If the resistance of the whole bar (between the two ends) is R, the resistance Rx obtained between one terminal and the slide contact depends on the position x of the slide, with respect to the bar end, by means of the linear Eq. (8.3).
(8.3)This kind of structure can be therefore used as a linear relative position sensor. It should be noted that, if a structure with a circular bar and a radial slide is implemented, an angular position sensor can be obtained.
8.2.2. Parasitic capacitance
Ohm's Law, as given in Eq. (8.1), does not hold when the device model includes reactive (capacitive or inductive) components and time-varying voltages/currents are considered. In such cases, a generalized form of Ohm's Law, shown in Eq. (8.4), describes the relationship between voltage and current through the concept of electrical impedance Z.
(8.4)The electrical impedance Z is represented by a complex number, the real part of which is the resistance R, as previously defined, whereas the imaginary part X, called reactance, takes care of the reactive effects.
Some sensors carry measurand-related information in both resistive and reactive components of the impedance, thus interface circuits need to be able to perform a simultaneous estimation of R and X. On the other hand, if useful information resides only in the resistive component, as usually happens with resistive sensors, the reactive component is considered as a parasitic element, the effect of which should be minimized.
When dealing with resistive sensors, usually the main parasitic contribution has a capacitive nature. Unlike most of the circuit components' nonidealities, these capacitive effects cannot be compensated by a proper circuit calibration because they depend on the particular sensor and operating conditions. If not appropriately taken into account, such effects can cause errors in the resistance estimation, as will be clarified in the next sections.
One of the most common origins of capacitive parasitic effects is related to sensor manufacture. If the sensing effect is obtained by certain phenomena occurring on the surface of the sensor (e.g., with photodetectors and gas sensors), the usual way to improve sensor sensitivity is to maximize the surface effects by implementing a technique based on interdigitated electrodes, shown in Fig. 8.3. Unfortunately, this structure introduces increased parasitic capacitance Cee between the electrodes, as shown in Fig. 8.3, which becomes even more profound as the interdigitated structure is iterated (Polese et al., 2017).
Another situation in which parasitic capacitive effects appear is particular to gas sensors. Some devices for gas sensing need to operate at a much higher temperature than the surrounding environment and, for this reason, they are usually provided with an embedded filament Rh, which acts as the heater (Samà et al., 2017). The heater filament is a conductor realized on the same substrate of the sensing component Rs and separated by dielectric material that electrically isolates the two sensor components. However, the small size of the realized devices makes these two components interact with each other due to capacitive effects, as shown in Fig. 8.4.
In addition to these possible internal sources, capacitive effects can arise because of external reasons, such as the connection between the sensor and the measurement system, as shown in Fig. 8.5. In fact, the connectors and wires used to link the sensor to the electronic circuit show a distributed capacitive behavior Cc, which, from an instrumentation point of view, is seen in parallel with the sensor.
The computation of the overall capacitive parasitic effect is far from being easy and often involves a complete understanding of a sensor's characteristics, also at the microscopic level. For this reason, when parasitic capacitance needs to be taken into account, a simplified model of the sensor is usually considered, where a parasitic capacitor Cs is presented in parallel with the sensor resistance Rs, accounting for all possible capacitive parasitic effects. The simplified sensor model used in the next sections is shown in Fig. 8.6.
It should be pointed out that when Rs is very large (resembling the behavior associated with an open circuit) Cs can predominate, thus leading to significant errors in the resistance estimation. In these cases (e.g., when dealing with MOX sensors), the interface circuits must be designed to limit this occurrence.
8.3. Voltamperometric resistance estimation
The most straightforward method with which to estimate the sensor resistance value is by means of the voltamperometric approach. Basically, a known current I is injected into the sensor, the voltage Vs across the sensor is measured by means of a voltmeter. Using Ohm's Law, the unknown sensor resistance Rs is calculated. The same technique can be used by applying a known voltage V and measuring the current Is flowing through the sensor by means of an amperemeter.
8.3.1. Implementation in smart sensors
When dealing with smart sensors, the measurement process is often performed using an A/D converter; this is either embedded in the microcontroller or a separate component. Because cost and simplicity of the electronic circuits and components are always a key factor, A/D converters with a voltage input are usually employed; thus, the first measurement modality, shown in Fig. 8.7, is advisable. If the input current IA/D of the A/D is considered to be zero, then the injected current I entirely flows through the sensor (Is = I) and the sensor resistance can be estimated by:
(8.5)In this case, an excitation circuit able to inject the known current I into the sensor is needed. A simpler excitation circuit can be used to apply a known voltage V to the sensor; the second estimation method can be applied in this way, but only if a current/voltage conversion is performed—for instance, by means of a shunt resistor Rsh, as shown in Fig. 8.8. Once again, it is considered that IA/D is zero; thus, the generated current Is flows through both the shunt resistor and the sensor, generating the Vsh and Vs voltages, respectively. The voltage Vsh is measured by means of the A/D converter and, since the Rsh is known, the sensor current Is can be calculated using Ohm's Law. The sensor voltage Vs is obtained as Vs = V − Vsh and, given Vs and Is, the Rs value can be calculated using Ohm's Law. Eq. (8.6) shows the final formula for the Rs computation:
Figure 8.7 Resistance estimation with the voltamperometric method and a known current I injected to the sensor.
Figure 8.8 Resistance estimation with the voltamperometric method and a known voltage V applied to the sensor-shunt resistor series.
(8.6)It should be noted that the voltage Vs applied to the sensor is not constant but, instead, depends on the sensor resistance value, according to Ohm's Law for the circuit in Fig. 8.7, and to the voltage divider relationship in Eq. (8.7) for the circuit in Fig. 8.8.
(8.7)In most cases this is not a major issue because the variation of Rs, and thus of Vs, has a limited range and the behavior of the sensor is not significantly affected by the sensor polarization. However, especially when dealing with MOX sensors, variations in the sensor excitation voltage can cause the activation of inner phenomena; this leads to a sensor resistance drift effect (Kiselev et al., 2011; Yang et al., 2013) and, thus, to unpredictable sensor behavior and unreliable results.
An operational amplifier can be used in specific architectures to overcome this problem, as shown in Fig. 8.9. Because of the virtual ground, the voltage Vs across the sensor is always equal to the applied and known voltage V independently of the Rs value. The output voltage Vo depends on the value of the feedback resistor Rf by means of Eq. (8.8); by measuring Vo and using Eq. (8.8), the Rs value can thus be calculated.
(8.8)The resolution of the A/D converter, which is related to the number of bits N, and the desired maximum relative error εrel,max in the Vs measurement determine the resistance range that can be estimated. Given the circuit in Fig. 8.7 and considering the full scale voltage VFS of the A/D converter, the maximum resistance value Rs,max, which can be measured is given by Eq. (8.9); the minimum value Rs,min is given by Eq. (8.10).
(8.9)
(8.10)If a 1% maximum relative error in the measurement of Rs is required (i.e., εrel,max = 1%) and a 16-bit A/D converter is used, the operating range (i.e., the ratio between Rs,max and Rs,min) of the circuit in Fig. 8.7 is less than three decades. To increase the resistance range to four decades and retain the same measurement performance, a 20-bit A/D converter is needed, significantly increasing the system cost. To increase the range further to six decades, a 27-bit A/D converter would be required, thus making this approach impracticable with an affordable cost.
The typical solution to enlarge the resistance range is to adopt a multiple interval technique. Referring to the circuit in Fig. 8.7, if the excitation current I is varied, the Rs range is shifted up or down. Thus, a set of appropriate I values is chosen to create multiple Rs intervals; in each of them, the A/D converter provides the measurement with the desired resolution. The multiple intervals are designed to cover, possibly with some overlaps, the complete desired Rs range, which can be significantly wider than the single interval. A circuit adopting this approach is presented in Fig. 8.10, whereas Fig. 8.11 presents an example of coverage of a four-decade Rs range by using the circuit in Fig. 8.10 with the intervals designed to cover about one and a half decades each. The multiple interval technique can also be adopted with the circuit in Fig. 8.9, by using multiple feedback resistors, as shown in Fig. 8.12 (Malcovati et al., 2013).
In both cases, the switch SW selecting the active sensor current value or feedback resistor is driven by a control signal Ctrl, which has to be provided by the microcontroller or programmable logic device (PLD) of the smart sensor. This control must be performed by tracking the current value of the Rs and deciding which interval is the most suitable to acquire the resistive value.
Figure 8.10 The circuit in Fig. 8.7 modified to expand the measurable resistance range by using the multiple interval approach.
Figure 8.11 Example of the application of the circuit in Fig. 8.10 covering a four-decade resistance range by using three intervals each with a width of one and a half decades.
Figure 8.12 The circuit in Fig. 8.9 modified to expand the measurable resistance range by using the multiple interval approach.
The interval overlap regions are important for the calibration process. In fact, it must be guaranteed that, if the same resistance value can be measured using two or more intervals, the results are equal within the measurement uncertainty. If this cannot be guaranteed, nonlinear effects such as hysteresis and step variations of the estimated Rs can occur during the interval commutation due to resistance variation. The calibration procedure for this kind of circuit is therefore critical and may require significant resources, both in terms of time and costs. The adoption of this measurement technique for low-cost smart sensors therefore needs to be evaluated carefully.
8.3.2. Parasitic capacitance issues
Parasitic capacitive effects, due to the connection cables or the sensor itself, can in some cases contribute to the uncertainty with which Rs is estimated. Some considerations for the use of the solutions previously discussed will now be offered for a sensor model with resistance Rs in parallel with capacitance Cs.
First, it should be noted that if the sensor voltage Vs has been constant for some considerable time before the Rs measurement, as is the case with the circuit in Fig. 8.9, the parasitic capacitance Cs is not recharged and therefore it does not affect the measurement. Conversely, when using the circuit in Figs. 8.7 and 8.8, Vs varies with the Rs variation, thus the contribution of Cs to the measurement should be taken into account. In the following, some examples will be given to show the typical measurement problems encountered because of Cs.
Defining 〈Rs〉 as the estimated value of Rs obtained with the circuit in Fig. 8.7 and Eq. (8.5), a simulation of the behavior of 〈Rs〉 versus time is reported in Fig. 8.13, when a step variation of Rs (with final value Rs,f lower than the initial value Rs,i) is analyzed. The measured 〈Rs〉 follows a descending exponential line starting from Rs,i, toward Rs,f and with time constant τ = Rs,f·Cs. The final effect is that the measurement is a slowed down version of the real Rs behavior, and this effect is progressively more visible as the parasitic capacitive effect grows. In addition, it should be noted that this effect also becomes more evident with an increase in the Rs value, thus circuits operating with a wide resistance range do not offer a uniform performance.
Fig. 8.14 shows a simulation of the circuit in Fig. 8.8, where the sensor resistance has a descending exponential behavior, typical of MOX gas sensors. Also in these circumstances, the effect of Cs implies that the estimated resistance value 〈Rs〉 appears slower than the real Rs.
It should be pointed out that, for applications in which the variation of the sensor resistance is slower than the delays introduced by the parasitic capacitance, this effect could be ignored. Conversely, if the information to be extracted from the sensor is related not only to the Rs value but also to the dynamics of the Rs variation, the presence of parasitic capacitance effects could significantly alter the measurement results and must therefore be taken into account.
Fig. 8.15 shows a simulation of the circuit in Fig. 8.10, where a steady-state resistance Rs is considered and the injected current Is varies, because of a scale change, from I1 to I2, with I2 > I1. Because Rs is constant and the Is current increases in a step variation, according to Ohm's Law the Vs voltage should also increase in the same quantity and with the same behavior. However, the presence of Cs makes the sensor voltage Vs follows an exponential law with time constant τ = Rs·Cs, when reaching its new value. The effect on the estimated sensor resistance 〈Rs〉, evaluated by means of Eq. (8.5), is a glitch that corresponds with the scale change, as visible in the third graph of Fig. 8.15, the width of which is proportional to Rs and Cs. Once again, according to the specific application and to the involved Rs and Cs values, such an effect can be either insignificant or unacceptable.
Figure 8.13 Simulation of the circuit in Fig. 8.7 when the sensor resistance has a step variation and the parasitic capacitive effects are taken into account.
Figure 8.14 Simulation of the circuit in Fig. 8.8 when the sensor resistance has a descending exponential variation and the parasitic capacitive effects are taken into account.
Figure 8.15 Simulation of the circuit in Fig. 8.10 when the sensor resistance is constant, a scale exchange is applied and the parasitic capacitive effects are taken into account.
Finally, a brief analysis of the measurements using a sinusoidal sensor excitation voltage/current, instead of constant values, will be given. Using a parallel presentation Rs∥Cs of the sensor impedance Zs, Eq. (8.11) shows the expression of Zs in terms of real and imaginary part, whereas Eq. (8.12) shows the expression of Zs in terms of magnitude and phase, where ω is the angular speed of the excitation signal.
(8.11)
(8.12)The use of an impedance analyzer allows the real and imaginary part (or, similarly, the magnitude and phase) of Zs to be estimated and, therefore, both the Rs and Cs value to be calculated. In smart sensor implementations, this implies that the A/D acquisition needs to be synchronized with the sensor excitation voltage/current to evaluate the Zs phase correctly by means of the input/output signals phase shift. In the event that only the Zs magnitude is evaluated, an underestimation of Rs is obtained because it is evident from Eq. (8.12) that |Zs| < Rs for each ω value and that this error becomes progressively larger as the values of ω and Cs increase.
8.3.3. Calibration procedures
The calibration of a system involving resistive sensors does not differ from the usual procedures. When dealing with smart sensors, the presence of a processing unit such as the microcontroller or PLD allows these techniques to be implemented directly on the sensor node, thus facilitating the communication, sharing, and utilization of the sensor data. Moreover, additional circuitry and automatic routines could be implemented to perform online and periodic recalibration of the system to compensate for long-term effects such as component aging (Malcovati et al., 2013).
Basically, given a set of known Rs values Rs,cal, the corresponding calculated resistance values Rs,th (obtained by means of the theoretical circuit equations starting from the measured quantities—e.g., voltage Vs in Fig. 8.7) usually differ from Rs,cal because of circuit imperfections and component nonidealities. An experimentally designed calibration function G should be applied to the theoretical resistance values Rs,th to obtain, as the final result 〈Rs〉 of the estimation, the calibration values Rs,cal, thus compensating for the circuit errors. An example of a sophisticated calibration function G is shown in Fig. 8.16. It is not a problem to implement such a function by means of a cheap microcontroller or look-up table stored in a PLD. However, collecting a sufficient amount of calibration data to design an efficient calibration function is still a long and expensive procedure.
If the calibration procedures need to be simplified, a linearization of the calibration function is advisable. Basically, with a very small number of calibration points, the calibration function can be approximated by a single line or a set of lines.
Fig. 8.17 shows an example of a piecewise linearization applied to a set of N calibration samples Rs,cal. G is realized with multiple lines (N − 1), each of which characterized by the slope m and offset q, connecting each pair of consecutive calibration samples. The m and q parameters of each segment i (i = 1, …, N) can be easily defined from the calibration samples Rs,cal and the related calculated values Rs,th with Eqs. (8.13) and (8.14), respectively.
(8.13)
(8.14)To obtain the final result 〈Rs〉 of the measurement, the microcontroller or the PLD of the smart sensor needs to store the pairs of slope m and offset q of each line in a look-up table and apply the linear relation in Eq. (8.15) with the calculated values Rs,th, selecting the correct m–q pair according to the Rs,th itself.
(8.15)A single line can also be used to further simplify the calibration function.
Fig. 8.18 shows an example of approximation using a linear regression or least mean squares (LMS) algorithm. The single line approximating the calibration function is defined to minimize the sum of the absolute errors (εabs = Rs,cal − 〈Rs〉) of the estimated values 〈Rs〉 with respect to the related Rs,cal. Given N calibration samples Rs,cal and the related calculated values Rs,th, the m and q values can be obtained by Eqs. (8.16) and (8.17), respectively.
Figure 8.18 Example of a calibration function G obtained with a linear regression starting from a set of calibration samples Rs,cal.
(8.16)
(8.17)From a smart sensor perspective, the microcontroller or the PLD simply needs to apply the linear Eq. (8.15) with the calculated values Rs,th to obtain the final result 〈Rs〉 of the estimation.
This approach is particularly advantageous when the sensor resistance has a limited variation range; for instance, two or three decades. When the variation range becomes too large—for example, when dealing with MOX sensors—a more important parameter to be considered for the linearization of the calibration function is the relative error, rather than the absolute error. In fact, minimizing the absolute error in a wide range of resistance would penalize the samples with smaller values, leading to a considerable error compared with the resistance value itself. The relative error is defined as the absolute error of the estimation referred to the “true value” expected from the measurement; that is, εrel = εabs/Rs,cal. If the m and q of the calibration line are estimated to minimize this parameter, the overall performance of the calibration procedure, in terms of relative error, is more uniform in the range under consideration.
This linearization technique is called weighted LMS (WLMS); Eqs. (8.18) and (8.19) can be used to obtain the values of the parameters m and q:
(8.18)
(8.19)Table 8.1 shows an example of calibration on a five-decade resistive range, comparing the absolute and relative errors in case of no calibration, LMS, and WLMS linearization. Where there is no calibration, the Rs,th is the final result of the measurement, whereas in the other two cases, the final result of the estimation is 〈Rs〉, computed by means of Eq. (8.15). It should be noted how the LMS calibration tries to make uniform the absolute error in the whole range under consideration, leading to significantly high relative error values in the lower part of the range. Conversely, the WLMS approach makes the relative error as uniform as possible, accepting significantly high absolute error values in the upper part of the range.
8.4. Resistance-to-time conversion methods
The measurement techniques illustrated in this section are particularly advantageous when the resistance value needs to be estimated over a very wide range. This can be the case for a single sensor (the value of which can span a large interval), as well as of a set of sensors (each of which having a limited resistance variation but centered around different baseline values). A typical example of such a situation is represented by MOX sensors.
To assure simple and inexpensive calibration of the electronic circuits for the sensor interface, the schemes adopting multiple ranges for the estimation of resistance should be avoided. However, as previously stated, implementing a direct resistance measurement operating on a wide range and guaranteeing the desired performance over the whole interval can be either cost-inefficient or impracticable.
Table 8.1
The resistance-to-time conversion (RTC) method is based on the fact that the quantity “time” is easy to estimate, also in a wide range, with good resolution and by using relatively inexpensive components, such as microcontrollers and PLDs.
The basic element used for RTC is an integrator, shown in Fig. 8.19. Considering OA as an ideal operational amplifier, it can easily be found that Is = Ic, Vs = Vexc, and Vint = −Vc, thus yielding Eq. (8.20) describing the behavior of the circuit.
(8.20)Under the hypothesis that the sensor excitation voltage Vexc and the sensor resistance Rs are constant, the integrator output voltage Vint is a ramp, as illustrated in Fig. 8.20, the slope α of which is inversely proportional to the sensor resistance value, as shown by Eq. (8.21).
Figure 8.20 Output time diagram of the integrator in Fig. 8.19, considering an ideal operational amplifier and constant values for Vexc and Rs.
(8.21)The time Tr taken by the output ramp to span between two known voltage values V1 and V2 is inversely proportional to the slope α of Vint, thus a direct proportional relationship can be found between Tr and the sensor resistance Rs, as in Eq. (8.22).
(8.22)The measure of the time Tr is therefore the key point for the estimation of sensor resistance. To accomplish this task, the integrator circuit is utilized in different schemes, which mainly differ for the methodology adopted to extract the information Tr, to iterate the measurement and for the way the sensor is biased (i.e., constant or switched voltage). Particularly, in this latter case the problems related to the parasitic capacitance are more evident (Kiselev et al., 2011). As will be shown next, this issue can be limited by suitably designing the electronic interface.
Usually, the analog front-end provides a quasidigital signal, containing the information Tr. The measurement of Tr is accomplished with a digital system, which can be a digital counter or, in case of smart sensors, time measurement routines or blocks implemented in a microcontroller or PLD.
In the following, an overview of different RTC-based interface circuits will be presented, highlighting the main advantages and drawbacks for each of them. Unless otherwise specified, the sensor model including the parasitic capacitive effect Cs in parallel with the resistive value Rs will be used.
It should be noted that all the RTC methods are based on the use of a capacitor for the sensor current integration; because the capacitive value of common capacitors is usually not very accurate and stable, the accuracy of the measurement system can be affected as well. As will become clear in the following, the capacitive value is usually a multiplicative factor in the relationship for the sensor resistance calculation, and therefore the initial calibration/linearization procedure can significantly limit the problem. Moreover, it should be remembered that the proposed sensor interfaces are intended to be used in smart sensor systems, where a microcontroller or PLD could easily implement periodic and simple self-recalibration procedures to correct possible drifts of the circuit component values, included the integrating capacitor.
8.4.1. Oscillator-based systems
This family of circuits employs a first-order oscillator scheme to charge and discharge the capacitor of the integrator continuously, thus offering an easy way to iterate the measurement (Flammini et al., 2004). The basic circuit and its timing diagram are shown in Figs. 8.21 and 8.22, respectively. In this first analysis, the sensor is considered as a pure resistor Rs, thus neglecting possible parasitic capacitive effects. The sensor is biased with the output voltage of the comparator Comp (Vexc = Vout), thus it is an alternate voltage commutating between the power supply value ±Vcc (without loss of generality, it is supposed that rail-to-rail components are used). The capacitor Ci of the integrator is consecutively recharged, thus generating the triangle waveform at the integrator output Vint, as illustrated in Fig. 8.22. The inverting amplifier, composed of the operational amplifier OA2, R1 and R2, provides two alternative threshold values Vth+ and Vth− by inverting and amplifying the comparator output Vout. In this way, as can be seen in Fig. 8.22, first-order oscillator behavior is established.
Figure 8.22 Timing diagram of the circuit in Fig. 8.21.
The duration of the time intervals T1 and T2 depends on the circuit parameters and on the value of the sensor resistance Rs, as in Eq. (8.23).
(8.23)Using this method, for every period of Vout it is possible to derive two values of Rs by measuring the time intervals T1 and T2. It is worth noting that Eq. (8.23) has been obtained by considering an ideal case, with ideal components, symmetric power supply voltage, and homogeneous sensor behavior, with respect to the alternate excitation voltage Vexc. Partial compensation for any unwanted effects can be achieved by averaging the two half periods, by measuring the period T and calculating the sensor resistance Rs using Eq. (8.24).
(8.24)However, it should be noted that the integrator output waveform and Eqs. (8.23) and (8.24) have been obtained supposing that the resistance Rs is constant (or slowly varying) during the observation time. Thus, the design parameters of the circuit, on which the observation time depends, should take into account the dynamic behavior of the sensor resistance. Basically, to consider Rs constant during the measurement, the maximum variation of the sensor resistance during the observation time should be within the measurement uncertainty. If the hypothesis of constant Rs cannot be achieved, Eq. (8.24) provides an estimation of an average value of Rs within the observation time T.
8.4.1.1. Parasitic capacitance issues
Because the sensor excitation voltage Vexc is an alternate voltage, the presence of parasitic capacitance in parallel to Rs could lead to significant errors. As illustrated in Fig. 8.23, during the commutation of Vexc, the integrator output Vint has an instantaneous variation ΔVint, due to a charge-transfer effect involving the capacitors Ci and Cs. This voltage step is proportional to the parasitic capacitance Cs, as in Eq. (8.25).
(8.25)
Figure 8.23 Timing diagram of the circuit in Fig. 8.21 with nonnegligible sensor parasitic capacitive effects.
The main effect on the circuit output signal Vout is the shortening of the time intervals T1 and T2 (and therefore of the period T), with respect to the case in which the parasitic capacitance is neglected, as reported in Eq. (8.26).
(8.26)If T1 and T2 (or T) are measured and Eq. (8.24) is applied, the sensor resistance Rs is obtained with an underestimation error, which becomes progressively more significant as the parasitic effect Cs becomes comparable with the integration capacitor Ci.
To overcome this issue, the circuit in Fig. 8.21 can be modified by adding a second comparator, operating with a different threshold voltage at its input, as shown in Fig. 8.24 (Ferri et al., 2008). In this case, the second threshold value has been chosen to be in the middle of the integrator output range. This is the ground voltage in the event of a symmetrical power supply ±Vcc. The timing diagram of the circuit in Fig. 8.24 is reported in Fig. 8.25. A new square wave output signal (Vout2) is provided; the commutations of Vout2 occur when the integrator output crosses the second threshold value (ground voltage). During a period T of the signals, four time intervals (T1, T2, T3, and T4) can be defined, each of which is delimited by the commutations of Vout1 and Vout2.
As can be seen in Fig. 8.25, the time intervals T2 and T4 are not affected by the presence of the parasitic capacitive effects, being dependent only on the threshold voltage values and on the slope of Vint. Thus, the measurement of such time intervals allows the sensor resistance to be estimated without being influenced by the parasitic capacitive effects. Eq. (8.27) shows the relationship between T2 (T4) and Rs in an ideal situation, whereas Eq. (8.28) reports how Rs can be computed by averaging the information obtained from T2 and T4, thus partially compensating possible circuit asymmetries.
Figure 8.24 The modified oscillating circuit for the resistance-to-time conversion for nonnegligible sensor parasitic capacitive effects.
(8.27)
(8.28)It should be noted that, from the additional measurement of the time intervals T1 and T3 and by applying the relationship in Eq. (8.25), an estimation of the parasitic capacitance Cs can be obtained, as in Eq. (8.29).
(8.29)The estimation of Cs could be used for diagnostic purposes, for example, to monitor the effectiveness of long connections between the sensor and the electronic front-end. This task can be easily performed by the microcontroller or the PLD devoted to the smart sensor management, thus including the measurement of the time intervals T1, T2, T3, and T4. In particular, for the latter task, the digital device needs to acquire the two logical outputs Vout1 and Vout2. The implementation of counterroutines in microcontrollers requires dedicated ports with input capture features. However, if it is intended to use a cheap microcontroller, it is possible that this is available for one input only. In this case, the signal obtained from the exclusive OR (XOR) logic combination of Vout1 and Vout2 can be used as a single output of the analog front-end, as shown next. Moreover, to facilitate the integration of the analog front-end with the digital stage for a possible single-chip solution, the circuit in Fig. 8.24 can be designed to operate with a single-supply voltage Vcc. This is obtained by replacing all the connections to ground voltage with a reference voltage Vref placed in the middle of the Vint range; that is, Vref = Vcc/2 (De Marcellis et al., 2008). Figs. 8.26 and 8.27 show the electronic interface circuit with the two modifications in place and the related timing diagram.
Figure 8.25 Timing diagram of the circuit in Fig. 8.24.
In an ideal situation, T1 = T3, T2 = T4, and the circuit output VXOR is a square wave, the period of which is given by T = T1 + T2 = T3 + T4. Defining Ton, the time interval during which VXOR is at the logic level “high,” and Toff, the time interval during which VXOR is at the logic level “low,” it is evident that Ton = T2 = T4 and Toff = T1 = T3. The duty cycle of VXOR is then defined as D = Ton/T. From the estimation of T and D of the single output VXOR, it is possible to estimate the values of the sensor resistance Rs and the parasitic capacitance Cs by means of Eqs. (8.30) and (8.31), respectively.
Figure 8.26 The oscillating circuit with single power supply and single output signal. XOR, exclusive OR.
Figure 8.27 Timing diagram of the circuit in Fig. 8.26.
(8.30)
(8.31)It should be noted that the behavior of Voutl and Vout2 is identical as that in the previous case; therefore, Eqs. (8.28) and (8.29) can still be used, if the digital stage is able simultaneously to acquire the two output signals Vout1 and Vout2 and to measure the time intervals T1, T2, T3, and T4 appropriately. However, the use of the single output VXOR can simplify the implementation of the digital counterroutines in the microcontroller because a simple period and duty cycle measurement needs to be performed. Such measurement tools are often included as a hardware feature in most microcontrollers.
Finally, software averaging of two or more consecutive estimations of Rs and Cs could help with the partial compensation of possible circuit asymmetries.
8.4.1.2. The problem of long measuring times
It is evident from Eq. (8.23) that the time needed to perform a measurement is directly proportional to the value of the resistance to be measured. For example, a variation of seven decades in the resistance implies the need to measure time over seven decades, as well. The choice of the circuit parameters allows the designer to shift the time range of the output signal according to the characteristics of the system adopted for the time estimation. From perspective, the strictest requirement is usually the shortest time to be estimated. In fact, if suitable resolution is required in the measurement of time, the clock period of the time measurement system must be much less than the time interval to be estimated. Once the designer has set the minimum time duration, the maximum time duration depends on the resistance range to be measured. For example, if a 10 MHz clock frequency is adopted for the time measurement, a time interval of 10 μs can be estimated with a 1% resolution. If a six-decade resistance variation is considered, the maximum measurement time is about 10 s. If this measurement time is too long for a specific application, the designer can move the time interval range down either by increasing the clock frequency or by decreasing the measurement resolution.
To reduce the measurement time of large resistance values, the oscillator circuit architecture can be modified by introducing the concept of a moving threshold; that is, a threshold signal, which is not constant but moves toward the integrator ramp Vint (Depari et al., 2011). Fig. 8.28 shows how the circuit in Fig. 8.24 can be modified for this purpose. The former Vth signal is now the main threshold Vth1, and the former fixed threshold (ground voltage) of Comp2 is now the second threshold Vth2. The generation of the correct threshold signals is performed by the ThGen1 and ThGen2 blocks, which will be described next. As shown in the time diagram of Fig. 8.29, the threshold signals are designed to be ramps with different slopes (the slope of Vth2 being steeper than the slope of Vth1) but always in the opposite direction with respect to the integrator output ramp Vint. As in the previous oscillating circuits, the interception between the main threshold Vth1 and the integrator output Vint determines the circuit commutation, with the consequent change in the direction of the integrator output signal; thus, the threshold signals must change direction as well. To guarantee that the oscillator performs correctly, for every commutation of the circuit the threshold signals must start from established values (Vt and −Vt in Fig. 8.29), possibly symmetrical with respect to the ground voltage. Moreover, it has to be assured that the integrator output Vint is always included in the range between the starting points of the two thresholds Vt and −Vt, also when the commutations ΔVint due to the parasitic capacitance happen. As can be seen in the time diagram, even if the integrator output Vint has a quasiflat or even flat slope, the circuit output Vout1 (and sensor excitation Vexc) commutation is guaranteed because of the unavoidable interception of Vint with the main moving threshold Vth1. A type of output range compression is applied, which limits the maximum measurement time to Tmax as in Eq. (8.32), where |α1| is the absolute value of Vth1 slope.
Figure 8.28 Modification to the circuit in Fig. 8.24 with the introduction of the moving threshold signals.
(8.32)The ThGen circuits for the generation of suitable threshold signals can take advantage of the integrator scheme, which allows an output ramp to be generated. The slope and the direction of the output ramp can be easily determined with the integrator parameters and input voltage polarity; conversely, setting the correct starting values for the output ramp, according to the diagram in Fig. 8.29, requires a suitable circuit for the integrator reset. For this purpose, a possible solution is shown in Fig. 8.30, where the two-capacitor integrator (2CInt) is illustrated. This integrator scheme includes two integration capacitors; Cthr is dedicated to the generation of a rising threshold ramp during a semicycle (with the 2CInt input at Vexc = –Vcc, as in Fig. 8.30(a)), whereas Cthf is used for the falling ramp, during the other semicycle (with the 2CInt input at Vexc = Vcc, as in Fig. 8.30(b)). Thus, only one capacitor at a time is connected to OA; the disconnected capacitor is charged to a suitable voltage value, to guarantee the correct starting point for the OA output signal for the next semicycle. If the two capacitors are chosen with the same value Cth, the output ramp has a symmetrical slope, given by Eq. (8.33).
(8.33)The connection/disconnection of the capacitors is performed by means of a switch network, driven by a signal Ctrl, which commutates every semicycle, such as Vout1. In addition, it should be pointed out that, in every semicycle, the 2CInt input signal must have opposite polarity to the input signal Vexc of the main integrator, to generate a threshold ramp with a direction that is always opposite to Vint (see Fig. 8.29). It is clear that, once the polarity has been changed, the output signal Vout1 can be used as the 2CInt input signal. Fig. 8.31 shows the overall circuit scheme, where 2CInt1 and 2CInt2 are two distinct 2CInt blocks as in Fig. 8.30.
The switch network is the crucial part of the circuit and thus it should be designed with particular care. Commutation delays need to be as equal as possible among all switches and should be much smaller than the minimum expected time interval to be measured, not to have a significant effect on the measurement. The on-state resistance, which is in series with the integrator capacitor, causes an offset to appear on the threshold ramp Vth, the value of which depends on the current to be integrated, coming from the integrator input resistance Rth. Small values of on-state resistance are advisable to minimize this effect. The off-state resistance should be much larger than the chosen integrator input resistance Rth; in this way, currents flowing through open switches do not significantly alter the integration of the current flowing through Rth and, thus, the threshold ramp slope.
Figure 8.30 The two-capacitor integrator (2CInt) for the moving threshold generation: (a) generation of a rising ramp; (b) generation of a falling ramp.
The estimation of Rs and Cs can be obtained for every semicycle k, by measuring the time intervals T1,k and T2,k determined by the output signals Vout1 and Vout2 and applying Eqs. (8.34) and (8.35), where Vexc = Vcc and rα is defined as the ratio between the slope α1 of Vth1 and the slope α2 of Vth2 (0 < rα < 1), with α1 and α2 as in Eq. (8.33).
(8.34)
Figure 8.31 The oscillating circuit with moving threshold for the limitation of the maximum measuring time. Two-capacitor integrator (2CInt) blocks are as in Fig. 8.30.
(8.35)A more reliable estimation can be obtained by averaging the measurement related to two semicycles, thus partially compensating for possible circuit asymmetries.
It should be noted that, as in the case of constant thresholds, it is possible to design a single-supply single-output circuit, by shifting the voltage levels to positive values and by adding an XOR logic gate to combine Vout1 and Vout2, as shown in Fig. 8.32. The reference voltage should be placed in the middle of Vint range, i.e., Vref = Vcc/2; the new starting points of the threshold values should be symmetrical with Vref (in Fig. 8.32, Vt+ = Vref + Vt and Vt− = Vref − Vt). It is still possible to estimate the value of Rs and Cs in every semicycle by using Eqs. (8.34) and (8.35), with Vexc = Vcc/2. Conversely, taking advantage of having a single output, the estimation of Rs and Cs can be obtained by the measurement of the period T and the duty cycle D of VXOR and by using Eqs. (8.36) and (8.37), where Tprev is the period measured in the previous cycle.
(8.36)
(8.37)It should be noted that Rs depends only on the duty cycle D of VXOR, as though it was a pulse width modulation (PWM) signal. This characteristic can be made use of to design simple readout electronics, by low-pass filtering the output signal VXOR and measuring the resulting voltage by means of an A/D converter. This allows the microcontroller of the smart sensor to extract the information about the D (and therefore about Rs) without the need of a time unit hardware or having to implement duty cycle measurement routines.
Figure 8.32 Timing diagram of the oscillating circuit with moving threshold with single power supply and single output signal.
Obviously, converting the information to the voltage domain leads to additional problems, such as vulnerability to interference and, thus, increased measurement uncertainty. This kind of approach should be therefore used only when low cost is more important than system performance and very cheap microcontrollers with limited computational resources need to be used.
8.4.2. Systems with constant sensor excitation voltage
Key advantages of the oscillating circuits previously described are their simplicity and the opportunity they present because of their symmetrical architecture, to compensate partially for circuit nonidealities. The main drawback is that the sensor bias voltage Vexc is an alternate signal, which is necessary to guarantee the oscillating behavior by commutating the slope of the integrator output voltage Vint. Troubles arising from the presence of parasitic capacitive effects can be reduced by using the aforementioned modified solutions; however, the problems related to the variation of the excitation voltage of MOX sensors will still be present.
By using the integrator architecture and a suitable reset circuit, it is possible to perform the Rs estimation only during one phase of the integration (e.g., during the Vint falling ramp) and to restart the measurement without the need to modify the sensor excitation voltage Vexc (Depari et al., 2006). This concept is illustrated by using the circuit in Fig. 8.33, the timing diagram of which is presented in Fig. 8.34. Starting from the basic integrator circuit, a reset switch SW, driven by the control signal Ctrl, is placed in parallel to the integrator capacitance Ci. When activated (closed), SW forces the integrator output Vint to the initial value Vi close to the ground voltage (component nonidealities make Vi differ from the ideal value—i.e., ground voltage). In the example in Fig. 8.33, Vexc is a positive and constant voltage and thus, under the hypothesis of constant Rs, Vint, behaves as a falling ramp when SW is open. A negative threshold voltage Vth and a comparator Comp are used to generate a pulsed signal Vout. The time Tr taken by the Vint to intercept Vth is related to Rs by means of Eq. (8.38).
Figure 8.33 The basic circuit for the resistance-to-time conversion implementation with constant sensor excitation voltage.
(8.38)
Figure 8.34 Timing diagram of the circuit in Fig. 8.33.
The Controller stage in Fig. 8.33 is devoted to generate the switch control signal Ctrl. This can be realized with a simple monostable circuit, triggered by the comparator output signal Vout, as well as directly implemented in the microcontroller or PLD of the smart sensor. The time duration Tres of the reset phase should be chosen to guarantee a complete reset of the integrator. As previously stated, component nonidealities, especially those related to the operational amplifier OA and the switch SW, cause the initial value Vi not to be zero; even if Eq. (8.38) considers this effect, the evaluation of Vi is not easy and it can be affected by several uncertainty factors, such as temperature. The work in Depari et al. (2006) proposes that a feedback circuit be applied in parallel to SW and controlled by Controller, to reduce the less than ideal reset of the integrator; thus, it is possible to consider Vi ≈ 0 V. The comparator output Vout is a narrow-pulsed signal; in fact, as soon as it commutates to the high level, the Controller stage issues the reset command, making the integrator output Vint increase rapidly and, thus, Vout to commutate to the low level once more. From the measurement of the period T of Vout or Ctrl, it is possible to estimate the time Tr (by subtracting Tres) and to calculate the Rs value from Eq. (8.38).
A different approach to solve the problem related to Vi is to use two threshold values (Vth1 and Vth2, with |Vth2| < |Vth1|) and to consider the Vint ramp behavior only between such thresholds. Figs. 8.35 and 8.36 show the circuit schematic and the timing diagram related to this solution. As in the previous case, the Ctrl signal is issued by the Controller block when triggered by the comparator output signal related to the main threshold voltage (Vth1). The time interval Tr is defined as the time taken by Vint to span between the two thresholds; it can be obtained by subtracting the time interval T2 from T1 (times between the release of the reset and the interception of Vint with the threshold values Vth1 and Vth2, respectively, see Fig. 8.36), as well as by estimating the high-level time of the comparator output Comp2. The relationship between the sensor resistance Rs and Tr is obtained from Eq. (8.38), where Vth is now Vth1 and Vth2 replaces Vi, as in Eq. (8.39).
(8.39)
Figure 8.36 Timing diagram of the circuit in Fig. 8.35.
Note that the initial voltage Vi of the integrator output no longer affects the estimation of Rs. This is obtained because now the integrator output ramp is evaluated between two known voltages (Vth1 and Vth2); this solution, therefore, can avoid the use of the feedback circuit in parallel with SW, thus keeping the circuit topology quite simple. However, whereas in the previous case a simple period estimation procedure was needed, in this case a slightly more complex time measurement unit or routine needs to be implemented.
8.4.2.1. Long measuring time problem
It is evident from Eqs. (8.38) and (8.39) that the ramp time Tr is proportional to the value of the resistance Rs to be estimated, as happens with the oscillator-based circuit of Fig. 8.21. The same considerations regarding the choice of the circuit parameters to adapt the output signal timings to the sensor resistance range and the characteristics of the time estimation unit can be applied. As stated previously, when a wide range of resistances needs to be estimated, a long measurement time usually occurs in the upper part of the resistive range; this could be a problem for particular sensor applications. The moving threshold approach can be adopted also for constant sensor excitation voltage circuits, thus leading to the reduction of the measurement time (Depari et al., 2014).
Considering the basic circuit in Fig. 8.33, the moving behavior of the threshold Vth can be achieved with a second integrator, driven by a suitable input voltage to obtain an opposite output slope, with respect to Vint. A sketch of a circuit implementing such a technique and the related timing diagram are shown in Figs. 8.37 and 8.38, respectively, without loosing generality, an architecture operating with a single-supply voltage Vcc is shown.
Figure 8.37 The circuit with constant sensor excitation voltage and moving threshold approach for the limitation of the maximum measuring time.
The reference of the integrator formed with OA1 is placed at the constant voltage Vis, which should be less than the sensor excitation voltage Vexc, to obtain a falling ramp behavior of Vint, as in Fig. 8.38. Because Vis is the initial value of Vint ramp (after the reset phase ends and the switch SWs is opened), Vis needs to be less than the power supply voltage Vcc. It should be noticed that the actual bias voltage Vs of the sensor is the difference between Vexc and Vis.
Figure 8.38 Timing diagram of the circuit in Fig. 8.37.
To obtain a rising ramp behavior of the threshold voltage Vth, the input of the integrator formed with OA2 is connected to ground voltage and its reference is placed at the constant voltage Vit, with Vit > 0. Because Vit is the initial value of Vth (after the reset phase ends and the switch SWt is opened) and considering that the aim is that Vth crosses Vint, it is evident from Fig. 8.38 that Vit should be less than Vis.
In a smart sensor implementation, simplicity is a key factor and thus a limitation of the voltage sources is advisable. For example, a practical solution for the considered circuit is the use of the power supply Vcc as the excitation voltage Vexc, whereas Vis and Vit can be simply obtained by using voltage dividers applied to Vcc, i.e., Vis = Ks·Vcc, and Vit = Kt·Vcc, with 0 < Ks, Kt < 1. The correct circuit operation is guaranteed with 0 < Kt < Ks < 1 and the resulting sensor bias voltage Vs is as in Eq. (8.40).
(8.40)According to Fig. 8.38, at the end of the reset phase, during which switches SWs and SWt are closed and Vint and Vth are forced at their initial values Vis and Vit, the ramp behavior of Vint and Vth starts. After the time Tr, which depends on the circuit parameters as well as on the unknown sensor resistance Rs, Vint equals Vth, determining the commutation of the output signal Vout of the comparator Comp. The Controller stage can thus issue the switch control signal Ctrl, which ends the measurement phase and allows the integrator outputs Vint and Vth to be reinitialized for a new measurement cycle. The Rs value can be reckoned from the estimation of the time Tr by means of Eq. (8.41).
(8.41)As can be seen in the time diagram of Fig. 8.38, even if the integrator output Vint has a quasiflat or even flat slope (due to large Rs values), the time Tr has an upper limit Tr,max, due to the unavoidable interception of Vint with the moving threshold Vth. In particular Tr,max can be computed as in Eq. (8.42).
(8.42)The choice of the circuit parameters and in particular of Ks and Kt should be performed considering the desired values of the sensor bias voltage Vs and the maximum ramp time Tr,max, according to Eqs. (8.40) and (8.41).
Finally, the Controller stage, devoted to generate the switch control signal Ctrl, can be realized with a simple monostable circuit, triggered by the comparator output signal Vout, as well as directly implemented in the microcontroller or PLD of the smart sensor. The time duration Tres of the reset phase should be chosen to guarantee a complete reset of the integrators. It should be also highlighted that the overall measurement time T is the sum between the ramp time Tr and the reset time Tres.
8.4.2.2. Direct ramp slope estimation
The architecture of the constant sensor excitation voltage suggests adopting an effective solution for shortening the measurement time, by implementing a direct estimation of the slope α of Vint; this goal can be achieved by acquiring a suitable number N of samples of the Vint signal with an A/D converter, as shown in Fig. 8.39 and by applying the LMS interpolation algorithm. The sample rate Fs determines the time distance Ts between samples (Ts = 1/Fs); once all the N samples are collected, the measurement process can be either ended or iterated. The resulting acquisition time can be obtained as Tacq = N·Ts. It should be noted that Tacq is independent of the Rs value and the measurement time is constant; this characteristic is important in applications in which a certain degree of synchronization between the sensor data acquisition and other operations must be achieved (Depari et al., 2012b).
As stated previously, the estimation of α is accomplished by means of the LMS algorithm; that is by applying Eq. (8.43), where Vint,i is the sample i value, and Ts,i is the time distance of the sample i from the beginning of the acquisition (t = 0 in Fig. 8.39).
(8.43)
To apply this technique, a circuit, such as that in Fig. 8.40, has to be implemented. The Time Unit block is devoted to the generation of the Trigger signal to the A/D converter, to acquire the Vint samples with the correct timings. In addition, it has to drive the reset switch SW to start and end the estimation. The converted samples Dout have to be acquired and elaborated by the microcontroller or PLD of the smart sensor, which has to be able to implement the estimation by applying Eq. (8.43) and the first part of Eq. (8.22). Note that the signal Vint varies during the sample process, thus a sample-and-hold operation needs to be performed before the conversion. Alternatively, the conversion time of the A/D converter should be as short as possible, to consider the Vint reasonably constant during the conversion itself. This can be easily achieved because, as will be shown next, the method is usually applied for large resistance values and thus slow variable Vint. Moreover, it is worth noting that, for signal reconstruction, using the calculation of α by means of Eq. (8.43), a priori knowledge of the monotonous nature of the sampled signal Vint is employed. The only constraint for the correct signal reconstruction is that the number of samples N is at least two (due to the presence of noise, a number of samples greater than 10 is advised to guarantee the method reliability). This fact allows aliasing problems to be ignored and, therefore, the usual antialiasing low-pass filter on the signal to sample can be omitted.
The operating range of this kind of solution is limited at the lower part by the saturation voltage of OA. In fact, as visible in Fig. 8.41, if α is too large (small Rs value) the integrator output Vint can reach the negative saturation voltage Vsat− before the last sample has been taken. In this case, the estimation of α by means of the LMS algorithm is not correct. The maximum value αmax and the related minimum value Rs,min of the sensor resistance are given by Eqs. (8.44) and (8.45), respectively.
(8.44)
(8.45)Conversely, the limit at the upper part of the range mainly depends on the A/D converter characteristics and, more in particular, by the effective number of bits (ENOB). In fact, when Rs is very large and, therefore, Vint almost flat (very small α value), the total variation of Vint within the acquisition time Tacq can be less than the minimum quantity detectable by the A/D converter. In addition, the noise affecting the integrator output Vint makes the LMS interpolation, obtained with samples acquired in such conditions, totally unreliable. In greater detail, considering VA/D and B as the input range and the ENOB of the A/D converter, the minimum value αmin and the related maximum value Rs,max of the sensor resistance are given by Eqs. (8.46) and (8.47), respectively.
Figure 8.41 The problem of the least mean squares interpolation in the event of reaching the saturation voltage of the operational amplifier OA.
(8.46)
(8.47)It is worth noting that, if the circuit parameters are chosen to have VA/D = |Vsat−|, then the ratio between the maximum and minimum Rs value is determined by the ENOB B, and, in particular, Rs,max = 2B·Rs,min. In a practical example, if the resistance estimation needs to be performed over four decades, an A/D converter with B = 14 bits should be used; however, if the range needs to be expanded to six decades, then B = 20 bits, causing a significant increase in the cost of the A/D converter.
Because of the similarity of the scheme in Figs. 8.35 and 8.40, an expansion of the operating range of the front-end can be obtained by combining both the RTC and LMS approaches and suitably designing the circuit parameters to dedicate an estimation method to a specific Rs subrange (Depari et al., 2012a). The resulting circuit is shown in Fig. 8.42. The block Digital incorporates the functions of the previous stages Controller of Fig. 8.35 and Time Unit of Fig. 8.40; moreover, a decision about which method is able to furnish a correct estimation for a particular Rs value must be performed by this block. Because of the complexity of the operations to be handled by Digital, it is advisable that such a block is implemented directly in the microcontroller or PLD of the smart sensor. In this way, Digital can be also devoted to the measurement of the time interval Tr (for RTC estimation, see Fig. 8.36) and the acquisition of the Vint samples (for an LMS estimation, see Fig. 8.39).
The basic idea for the Rs range expansion is that the RTC method can be used as long as it provides a correct estimation within the desired measurement time. If the threshold value Vth1 cannot be reached by Vint, because Rs is too large (see Fig. 8.36), then the LMS approach is applied. Analogously, the LMS estimation can be used as long as the ramp Vint does not reach the OA saturation voltage; if this happens, because of Rs is too small (see Fig. 8.41), then the RTC approach is applied. Summarizing, the RTC approach is suitable for use in the lower part of the measurement range, whereas the LMS technique can be applied when Rs is in the upper part. A partial overlap of the two methods in the midrange can be useful for circuit calibration. Fig. 8.43 illustrates the Rs range partition previously discussed. The overall minimum resistance Rs,min, which can be estimated is determined by the RTC method (Rs,min-RTC) and, as previously described, it depends on the desired resolution of the time measurement. Conversely, the maximum resistance Rs,max, which can be estimated is determined by the LMS method (Rs,max-LMS) and, as detailed in this section, it mainly depends on the ENOB of the A/D converter. To guarantee a continuity in the two subranges, the circuit parameters must be chosen to have the lower limit of the LMS approach (Rs,max-LMS) less than the upper limit of the RTC method (Rs,max-RTC). Fig. 8.44 reports the time diagram of the two working modes. If the time T1 (time needed by Vint to intercept the threshold voltage Vth1) is longer than the acquisition time Tacq, only the LMS method can be applied. If Vint crosses the voltage threshold before Tacq expires, then the RTC approach is appropriate. In the case of the RTC approach, if Vint does not reach the saturation voltage Vsat−, the LMS method is valid as well, yielding the aforementioned overlap region. The overall measurement time Tmeas is given by the sum of the acquisition time Tacq and the reset time Tres and it is constant, independent of the Rs value. Usually, the time Tres is chosen to be much less than Tacq; therefore, Tmeas ≈ Tacq. A practical implementation of this method is detailed in Depari et al. (20l2a).
Figure 8.43 Sensor resistance range partition in the event of using the circuit in Fig. 8.42, uniting the resistance-to-time conversion (RTC) and the least mean squares (LMS) approaches.
Figure 8.44 The time diagram of the circuit in Fig. 8.42 with two different situations: small Rs (resistance-to-time conversion method applied) and large Rs (least mean squares method applied).
8.4.2.3. Parasitic capacitance estimation
The main advantage of the constant sensor bias voltage approach is that the parasitic capacitance of the sensor is not excited and therefore does not influence the Rs estimation. As stated before, the parasitic capacitance can arise from the sensor itself, but it can also include effects due to long connections between the sensor and the front-end. In particular, the monitoring of the parasitic capacitive effects, described by the parasitic capacitor Cs in parallel with Rs, could help the smart sensor with diagnostic operations, such as the control of sensor connection integrity.
The estimation of Cs can be obtained only if the sensor excitation voltage is varied; in the circuit that combines the RTC and LMS approaches (Fig. 8.40), this can be easily obtained by commutating the sensor excitation voltage to ground voltage during the integrator reset phase (Depari et al., 2012a). In Fig. 8.45, the circuit of Fig. 8.42 has been modified for this purpose. The sensor excitation voltage Vs can be either the constant voltage Vexc or ground voltage, chosen by means of the switch SW2. The SW2 control signal Ctrl2 is suitably driven by the Digital block. As stated before, Vs needs to be driven to ground voltage during the reset phase or otherwise to Vexc. The same control signal Ctrl1 as for the reset switch SW1 (the former Ctrl and SW in Fig. 8.42, respectively) could therefore be used as Ctrl2. On the other hand, if the capacitive effect estimation does not need to be performed during every measurement cycle but, instead, at intervals, the choice of splitting the two switch control lines affords higher system flexibility.
Figure 8.45 Modification of the circuit in Fig. 8.42 for the estimation of the parasitic capacitive effects.
The time diagram of the circuit in Fig. 8.45 around the reset phase is shown in Fig. 8.46. During the reset phase, the commutation of Vs from Vexc to ground voltage does not affect Vint because Vint is driven to Vi, (close to ground voltage) by the reset switch SW1. When the reset phase ends, the switch SW1 is opened and simultaneously the switch SW2 is driven to connect the sensor to Vexc. The sudden variation of the sensor bias voltage creates the charge-transfer effect across Cs and Ci, which can be seen in Fig. 8.46 with a step variation ΔVint of the integrator output, the value of which is given by:
Figure 8.46 Time diagram of the circuit in Fig. 8.45 highlighting the parasitic capacitance estimation procedure.
(8.48)To evaluate ΔVint, two additional samples (sample i and z) of Vi can be taken—before a time Ti, and after a time Tz with respect to the end of the reset phase. The sample i is used to estimate the Vi voltage, which is the starting value of the Vint ramp or of the ΔVint step in the event that parasitic capacitance is present. Even if, as in Fig. 8.46, Vint is considered constant within the reset phase, the nonidealities of components can cause Vint to vary; for instance, to demonstrate an exponential behavior toward Vi. For this reason, the time Ti needs to be as close as possible to the end of the reset phase. On the other hand, sample z accounts for the final value of the ΔVint step. In Fig. 8.46, ΔVint is considered to be an instantaneous voltage variation; component nonidealities—in particular, the finite slew rate of the OA—imply that the ΔVint variation has a finite duration. The time Tz therefore needs to be appropriately far from the end of the reset phase, to guarantee the completion of the charge-transfer effect.
Note that if the voltage step ΔVint is small enough either not to intercept the threshold voltage Vth2 (see Fig. 8.44) or not to cause Vint to reach the saturation voltage of OA (see Fig. 8.41), then either the RTC or LMS method can be used to estimate the Vint slope α.
The final value Vf of Vint after the voltage step ΔVint has occurred can be extrapolated by using the Vint value Vz obtained with the sample z and α; the ΔVint can be therefore obtained by Eq. (8.49):
(8.49)8.5. Industrial-related aspects
The interface solutions that have been presented can be used for a broad range of applications. However, they are particularly advantageous when dealing with wide-range devices, such as chemical sensors for gas detection. In industrial environment, applications are generally related to the monitoring of environmental quality or product quality; for example, in the detection of food degradation.
In the case of environmental quality monitoring, usually the main requirements are the compactness of the sensor system and the low cost. In fact, these systems are usually placed in different areas of the site to be monitored, to guarantee a complete coverage of the places of interest. Moreover, constraints related to sensor system location could require battery-operated devices, thus low-power consumption becomes a necessity.
Oscillator-based approaches with constant threshold voltages are ideal for this purpose, due to the simple architecture, which helps in keeping the overall system cost low and makes it possible to implement as an integrated circuit, assuring compactness of the system (Ferri et al., 2009). Moreover, as can be seen in Eqs. (8.27) and (8.28), the circuit parameters appear as multiplicative factors in the sensor estimation relationship; thus, simple calibration procedures are suitable to compensate for circuit nonidealities. Realization of the sensor interface together with a microcontroller or PLD makes it possible to implement data filtering, preprocessing, and simple procedures of self-recalibration—thus assuring compensation for instability or aging effects of the circuit components.
Regarding power consumption, best practice is the utilization of the sensors in a pulsed (sleep mode) regime; that is, keeping the sensor system off for a long time and activating it only when taking a measurement. In this case, the sensor readout time plays an important role because it determines the activation time of the system and, therefore, the power requirement. Short measuring time interfaces, such as the approaches with variable threshold voltages, are better choices for this kind of application. However, it should be mentioned that the price to be paid in this case is not only in the more complex system architecture but also in a more difficult calibration procedure. In fact, as can be seen from Eqs. (8.34) and (8.41), the relationships to apply are more complex and a simple calibration/linearization procedure is not suitable for compensating all the circuit nonidealities.
It is worth noting that, in many applications, systems for environmental quality monitoring do not need to be precisely accurate because they simply have to generate alerts in case the quantity under consideration exceeds a certain threshold level. This level can be suitably lowered to allow for system inaccuracy, still guaranteeing an adequate level of safety, even if false alarms could be generated. In this case, a trade-off between the cost (included the calibration) and the system performance can usually be achieved, with the cost being the greater consideration.
The reverse is relevant for the realization of systems for food quality monitoring: the primary aspect to consider is the system performance; the measurements need to be precise to guarantee the effectiveness of the elaboration algorithms applied for the detection of the substances of interest. In these systems, also called artificial olfactory systems (AOS), the compactness and the cost are therefore secondary aspects (EOS AROMA catalog, available at SACMI website, http://www.sacmi.it/default.aspx?ln=en-US). Also, in these applications the measuring time plays a significant role because advanced elaboration techniques need to work with the dynamic response of the sensors rather than with a steady-state response. A high-sampling rate also allows sensor signal oversampling to be performed, thus allowing the microcontroller or PLD of the smart sensor the opportunity to employ more effective data filtering. In addition, it is worth noting that a short measuring time is also beneficial for speeding up the system calibration and the process of collecting data for the training of the AOS. Therefore, even if more complex than the oscillator-based systems, solutions such as that presented in Fig. 8.42 seem to be more suitable for this purpose.
8.6. Conclusion and future trends
The rapid progress in microelectronics and the consequent drop in the cost of electronic components are a key factor for the improvement of sensor systems in general. The availability of low-cost microcontrollers and PLDs with relatively high computational resources allows designers to implement more complex data acquisition solutions. Regarding smart sensor realization, the most suitable and effective calibration, estimation, and data elaboration techniques for a specific sensor/application can be therefore chosen and utilized without increasing the overall system cost to an appreciable degree.
Concerning resistive sensors, technical innovations to improve the effectiveness of such devices are continuously in progress. Physical effects, which are the basis of the working principle of resistive sensors, are nowadays well known and consolidated, and the current improvement of the devices mainly concerns innovative technological solutions. In particular, the research on new materials and their application in the sensing field seems to be the key point for the development of new resistive sensors. The increase of sensitivity towards the physical quantity of interest is a common objective for each kind of sensor.
An exception to this innovation trend of resistive sensors is related to position detection systems realized with potentiometers. At least for linear position detection, magnetostrictive sensors represent a good alternative to potentiometers because of the contactless characteristic of the moving slide, which guarantees better performance in terms of life span, even if at a higher cost (Deng et al., 2014).
Regarding new materials for resistive gas sensors, issues related to the improvement of sensor selectivity to a specific target substance or group of substances is one of the main concerns (Zhu et al., 2011). To this end, particular sensor operating modes, in terms of pulsed thermal excitation and multivariate data analysis, are also being explored and they are proving to be quite satisfactory (Bicelli et al., 2009; Ponzoni et al., 2012; Yin et al., 2016).
Another key point for the improvement of resistive gas sensors is the choice of materials and operating techniques that can show good sensitivity when operating at low temperatures, ideally at the temperature of the environment (Sharma et al., 2011). This aspect is particularly important when power consumption is the main concern (e.g., as with battery-operated smart sensors) because the power required by the sensor heating operation is definitely the greatest draw on power, unlike that needed for sensor excitation and data readout/elaboration. Finally, innovative technologies in the field of nanostructures, such as nanotubes and nanowires, are under examination for the realization of sensors with improved sensitivity and reduced power consumption because of optimization of the sensor sensitive area and the optimization of sensor size (Gupta Chatterjee et al., 2015; Woo et al., 2016).
To be suitable for the new sensor requirements, electronic interfaces usually tend to follow the evolution of sensors. For example, for pulse-operated sensors, solutions with a short measuring time and synchronized thermal excitation management have been proposed (Depari et al., 2012b). Realization of the electronic sensor interface as an integrated circuit is also a key point (Ferri et al., 2009) as this is in keeping with the present trend for sensor miniaturization (Dong et al., 2016). Advantages that can be obtained with interface integration, besides the reduction in system size, can also be found in improved circuit reliability and stability and reduced power consumption.
Because of the progressively higher computational resources available in inexpensive devices, all modern sensor interfaces include a microcontroller or PLD. They are not only used for the proper management of interfaces but also provide advanced functionalities such as the opportunity to apply sensor compensation, data filtering and elaboration, and so on, thus delivering the concept of the smart sensor. Lately, particular effort has been put into facilitating data exchange of smart sensors with existing infrastructures, by using typical ICT technologies, such as USB and Bluetooth, also in the recent low-power version (Bluetooth Low Energy - BLE), to realize networks of sensors (Depari et al., 2007; Kumar et al., 2011; Hortelano et al., 2017). Even if still at the research stage, the trend in smart sensors for industrial applications is also directed to the implementation of sensor networks, using the modern and promising communication technologies of the industrial world, such as real-time Ethernet (RTE) and WirelessHART (Vitturi and Tramarin, 2015; Ferrari et al., 2013).
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