Resistance Compensation Technique Assignment PDF

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sensorsArticleLead-Wire-Resistance Compensation TechniqueUsing a Single Zener Diode for Two-Wire ResistanceTemperature Detectors (RTDs)Wei Li1, Shusheng Xiong2,* and Xiaojun Zhou11School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China;11725081@zju.edu.cn (W.L.); me_zhouxj@zju.edu.cn (X.Z.)2College of Energy Engineering, Zhejiang University, Hangzhou 310027, China*Correspondence:xiongss@zju.edu.cnReceived:13 April 2020; Accepted:9 May 2020; Published:11 May 2020Abstract:In remote measurement systems,the lead wire resistance of the resistance sensor willproduce a large measurement error.In order to ensure the accuracy of remote measurement, a novellead-wire-resistance compensation technique is proposed, which is suitable for a two-wire resistancetemperature detector.By connecting a zener diode in parallel with the resistance temperaturedetector (RTD) and an interface circuit specially designed for it, the lead-wire-resistance value canbe accurately measured by virtue of the constant voltage characteristic of the zener diode whenreverse breakdown occurs, and compensation can thereby be made when calculating the resistanceof RTD. Through simulation verification and practical circuit testing, when the sensor resistance isin 848–2120scope and the lead wire resistance is less than 50, the proposed technology canensure the measuring error of the sensor resistance within±1and the temperature measurementerror within±0.3C for RTDs performing 1000at 0C. Therefore, this method is able to accuratelycompensate the measurement error caused by the lead wire resistance in two-wire RTDsand is suitablefor most applications.Keywords:RTD; zener diode; temperature measurement; lead wire1.IntroductionHigh-precision temperature measurement provides basic data for product development andindustrial automation applications to improve product quality and ensure production safety.Due toits excellent linearity, measurement repeatability and stability [1], a resistance temperature detector(RTD) is widely used therein.However, for remote measurements, the electrical resistances of longconnecting lead wires between the RTD and the control room instrument produce an appreciable errorin measurement.This unwanted error varies not only with the length of the lead wires but also withambient temperature variations where the lead wires layout [2].Therefore, methods to reduce oreliminate measurement errors caused by lead wire resistance have been studied in many literatures.Currently,the aforementioned problem is addressed by adding lead wires.For example,in Reference [3,4] three-wire and four-wire techniques were used separately.However,the costof one additional lead wire in a three-wire RTD and of two additional lead wires in a four-wire RTD willbe extremely high and with extra difficulty of wiring, especially in industries where a large number ofprocess points are to be monitored from a control room located at a remote place [5], such as chemical,thermal power, electric plant and other industries.In the bridge-based measuring system, lead wireresistance also exerts an adverse effect on measurements.Authors in Reference [6,7] presented amethod to eliminate lead wire resistance for quarter- and half-bridge interface circuit respectively,Sensors2020,20, 2742; doi:10.3390/s20092742www.mdpi.com/journal/sensors
Sensors2020,20, 27422 of 11which employed several operational amplifiers (OPAMPs) and made use of their high input impedance.This method was able to eliminate the unfavorable effect on the measurement caused by lead wires,but it cannot obtain the specific lead-wire-resistance values, in addition, its interface circuits and powercircuits were complicated due to the OPAMPs.Similar methods using OPAMPs were also publishedin Reference [810].All of these bridge-based interface circuits used a three- or four-wire method,except for Reference [6].Therefore, researches have been carried out on the compensation method of two-wire sensors.In Reference [11], a compensation resistor is selected having the same value and of the same materialof the lead resistances combined with three operational amplifiers and a constant current source tocompensate the lead wires error.Although the circuit of this method is simple, the compensationresistance must be adjusted manually if the lead wire length is changed due to reconstruction.In addition, the compensation effect due to temperature drift of the lead wire resistance remains to bevalidated.The authors of [5] proposed a novel lead-wire-resistance compensation technique using atwo-wire RTD. This technique employed two diodes, one of which was in series with the RTD andthe other was in parallel with the series circuit composed of the RTD and the first diode.A currentsource, four analogy switches and four sample-holding circuit were used in its interface circuit, and anoperational amplifier is used to output the voltage with respect to the RTD resistance.In principle,this technique completely eliminated the measurement error caused by the lead wire resistance and itstemperature drift, but its measurement accuracy depended on the consistency of the forward voltagedrop of the two diodes.Therefore, in order to achieve a high precision measurement, it is indispensableto measure and pair the diodes in advance.Besides, this technique cannot obtain the true value ofthe lead wire resistance.This method was also seen in other references, and some improvementshad been made in the interface circuit.In the Reference [12], three single-pole double-throw (SPDT)analog switches are used to realize the lead-wire-resistance compensation, which was independentof the voltage reference.The authors of [13,14] used a voltage-to-current converter to provide thecurrent and reduced the number of SPDT analog switches to two.A Chinese patent invented amethod that employed the transient characteristics of resistor–capacitor (RC) circuit to measure thelead wire resistance and compensate measurement error of the thermal resistance.In this method,the measurement precision is not affected by the characteristics of the additional capacitor, and thelead-wire-resistance value could be obtained in real time, which avoided the negative influence of thetemperature drift of the lead wire resistance.According to the patent, the update rate is less than 5 Hz,and it is not suitable for the applications where temperature changes need to be tested dynamically.In References [15,16], the interface circuits for four-wire resistive sensor were designed by the similarmethod of multiple charge and discharge to a capacitor,and the update rate reported was 25 Hz.The authors in References [17,18] combined the method for two-wire sensors reported in Reference [5]and also proposed the method using a capacitor, and the their minimum complete measurement cyclerequired 5.3 ms.These methods have the same problem of limited update rate.The aim of this paper is to solve the problem of lead-wire-resistance compensation for two-wireRTDs based on as simple interface circuit as possible, on the premises that the measurement accuracyand the update rate are acceptable.So that, a new technique for compensating the lead-wire-resistancemeasurement error of two-wire RTD is proposed,which can also resist the negative influence ofthe temperature drift of the lead wire resistance on the compensation circuit.This technique onlyadds one zener diode on the sensor side,and the lead wire resistance and RTD resistance can beaccurately measured through time sharing based on the stability of the reverse breakdown voltageand the minuteness of reverse leakage current.A simple implementation and its validation of theinterface circuit will be described later in this paper, which only requires one SPDT analog switch anda pair of reference power sources, and OPAMPs are not required.Compared to the current methods,the proposed technique not only uses fewer components, only one zener diode, for two-wire RTDs,but also can detect and diagnose the failures of the lead wires by measuring the lead wire resistance inreal time.
Sensors2020,20, 27423 of 112.Materials and Methods2.1.PrincipleCombined with the engineering application scenarios of remote measurement, the circuit schematicof the technique proposed in this paper is shown in Figure1which is composed of four regions.Rtrepresents an RTD, and Region A is the region of the object to be measured.The area B where thezener diode is located should be as close to the RTD as possible, and the ambient temperature in this areashould not change significantly due to the change of the temperature in Region A. The RTD in Region Aand zener diode in Region B are connected by two wires.As their length is very limited, the resistanceof these wires is negligible.Region C represents the layout path of the lead wires.In the remotemeasurement system, the path is quite long.Its specific length depends on the practical engineeringconditions and is often changed due to engineering changes and other reasons.The resistancesRw1and Rw2represent the lead wire resistance,and it is generally believed thatRw1=Rw2=Rw.Region D represents the remote-control room or equipment room, where the interface circuit is located.The other elements in Figure1will be described combined with the measurement procedures in thenext paragraph.Sensors2020,20, x3 of 112. Materials and Methods2.1. PrincipleCombined with the engineering application scenarios of remote measurement, the circuitschematic of the technique proposed in this paper is shown in Figure 1 which is composed of fourregions. Rtrepresents an RTD, and Region A is the region of the object to be measured. The area Bwhere the zener diode is located should be as close to the RTD as possible, and the ambienttemperature in this area should not change significantly due to the change of the temperature inRegion A. The RTD in Region A and zener diode in Region B are connected by two wires. As theirlength is very limited, the resistance of these wires is negligible. Region C represents the layout pathof the lead wires. In the remote measurement system, the path is quite long. Its specific lengthdepends on the practical engineering conditions and is often changed due to engineering changesand other reasons. The resistances Rw1and Rw2represent the lead wire resistance, and it is generallybelieved that Rw1= Rw2= Rw. Region D represents the remote-control room or equipment room, wherethe interface circuit is located. The other elements in Figure 1 will be described combined with themeasurement procedures in the next paragraph.Figure 1.Circuit schematic for the lead-wire-resistance compensation technique.In the proposed technique, a complete measurement procedure of RTD resistance consists ofthree steps:1.Measurement of lead wire resistance.Switch SW in Region D of Figure 1 is switched to Position 1. Constant current source (CCS)provides current Icthrough lead wire resistors Rw1and Rw2, giving rise to the reverse breakdown ofthe zener diode and establishing a stable voltage Udacross it. Since the resistance of zener diode afterreverse breakdown is very small, most of the current goes through the diode. Although the currentflowing through Rtis relatively small, the negative influence of RTD's self-heating effect on thetemperature measurement must be considered. The voltage at Position 3 marked as U3is measured.Then the lead wire resistance Rwcan be calculated by substituting U3into Equation (1).U3= 2 IcRw+ Ud(1)Record the values for U3and Rw, which will be used in the following steps.2.Measurement of working current.SW is switched to Position 2. RTD is supplied by constant voltage source (CVS) with a voltageof Uc, which is not more than Ud. At this time, the zener diode works in the reverse cut-off mode, andthe equivalent resistance is very large. The current passing through it marked as Idis in microamperesrange [19], whose specific value should be obtained by measurement in advance. In this step, thevoltage at Position 3 is marked as U3, which is measured and satisfies Equation (2).U3'= 2 I · Rw+I-IdRt(2)The I in Equation (2) represents the output current of the CVS. At the same time, the voltagemeasured at Position 2 is represented by U2. Thus, I can be obtained from Equation (3). Save thevalues of U2and U3for Step 3:RtUdRw1231SWCCS+CVSRw2ABCDUcIcRs-U3U2I-+-+Figure 1.Circuit schematic for the lead-wire-resistance compensation technique.In the proposed technique,a complete measurement procedure of RTD resistance consists ofthree steps:1.Measurement of lead wire resistance.Switch SW in Region D of Figure1is switched to Position 1.Constant current source (CCS)provides current Icthrough lead wire resistors Rw1and Rw2, giving rise to the reverse breakdownof the zener diode and establishing a stable voltage Udacross it.Since the resistance of zener diodeafter reverse breakdown is very small, most of the current goes through the diode.Although thecurrent flowing through Rtis relatively small, the negative influence of RTD’s self-heating effect on thetemperature measurement must be considered.The voltage at Position 3 marked as U3is measured.Then the lead wire resistance Rwcan be calculated by substituting U3into Equation (1).U3=2Ic·Rw+Ud(1)Record the values for U3and Rw, which will be used in the following steps.2.Measurement of working current.SW is switched to Position 2.RTD is supplied by constant voltage source (CVS) with a voltage ofUc, which is not more than Ud.At this time, the zener diode works in the reverse cut-offmode, and theequivalent resistance is very large.The current passing through it marked as Idis in microamperesrange [19], whose specific value should be obtained by measurement in advance.In this step, the voltageat Position 3 is marked as U3, which is measured and satisfies Equation (2).U30=2I·Rw+(IId)Rt(2)
Sensors2020,20, 27424 of 11The I in Equation (2) represents the output current of the CVS. At the same time, the voltagemeasured at Position 2 is represented by U2.Thus, I can be obtained from Equation (3).Save thevalues of U2and U3for Step 3:I=(UcU2)/Rs(3)where Rsrepresents a calibration resistor.3.Calculation of RTD resistance.By substituting Equations (1) and (3) into Equation (2), the resistance of RTD can be obtained,as shown in Equation (4).Rt=Ic·Rs·U30+(UCU2)(UdU3)Ic(UcU2Id·Rs)(4)Equation (4) shows that it is a simple algebraic equation, which can be solved in a microcontroller toobtain RTD resistance.Then the RTD resistance can be converted to the temperature simply by look-uptable method or directly computation of the polynomial.From Equation (4), it can be seen that the factors affecting the measurement accuracy of RTDresistance are as follows:Stability of Udand IdStability of Ucand IcMeasurement accuracy of U2, U3and U3Accuracy and Stability of RsThe first one is the key and most difficult factor to implementing the proposed technique.Other factors can be met by conventional technical means, such as using high-precision analog todigital sampling, low temperature drift power source and sampling resistance.Compared with the I-V curve of normal diode,the I-V curve of zener diode has a narrowerbreakdown voltage range and a larger curve slope.Therefore, the change of the reverse breakdownvoltage of Udwith its operating current is very small.At present, for high-precision zener diodes,the nominal error of the reverse breakdown voltage can reach 0.05%, and the device consistency is veryhigh.Besides, the reverse leakage current of the zener diode can be kept relatively stable in the reversecutoffregion.These characteristics of zener diode make it possible to calibrate the system.In orderto obtain higher measurement accuracy, it is necessary to calibrate the values of reverse breakdownvoltage and reverse leakage current of zener diode in each measurement circuit and store them in thenonvolatile memory.Based on this principle, the update rate depends on the response time of zener diode under thestep voltage input (200μs), the single switching time of the analog switch (18 ns), the two analog todigital sampling times and the calculation time of the micro controller.The values in brackets aboveare from the device datasheet used in the circuit prototype in Section2.3.The conversion time ofconventional 16-bit analog to digital chips is 2μs, and the calculation time of Equation (4) for 32-bitmicrocontroller with 72 MHz should not exceed 30μs.Therefore, the total time for one measurementshould be within 250μs.In other words, the update rate in this paper can reach 4 KHz.2.2.SimulationThe circuit modelas shown in Figure1was established in the circuit simulation softwareMultisim 14.The model simulates the resistance changes of RTD and lead wires through adjustableresistor.In this paper, RTD with the nominal value of 1000at 0C was focused on, and the range form38.67C to+299.86C was selected as the research range.The range of its resistance is848–2120accordingly [20].Providing a maximum of 50of single lead wire, the distance is about 553 m when ashielded tin-plated copper conductor with nominal cross section of 0.2 mm2was selected, which can
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