Non-contact measurement of dc voltages using nonlinear elements This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2012 Meas. Sci. Technol. 23 045001 (http://iopscience.iop.org/0957-0233/23/4/045001) Download details: IP Address: 137.195.17.130 The article was downloaded on 28/02/2012 at 11:20 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience
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Non-contact measurement of dc voltages using nonlinear elements
This article has been downloaded from IOPscience. Please scroll down to see the full text article.
2012 Meas. Sci. Technol. 23 045001
(http://iopscience.iop.org/0957-0233/23/4/045001)
Download details:
IP Address: 137.195.17.130
The article was downloaded on 28/02/2012 at 11:20
Please note that terms and conditions apply.
View the table of contents for this issue, or go to the journal homepage for more
Home Search Collections Journals About Contact us My IOPscience
Received 19 August 2011, in final form 8 January 2012Published 27 February 2012Online at stacks.iop.org/MST/23/045001
AbstractIn this work, it is shown that dc voltages may be measured via a capacitive interface, providedthat the capacitance between the measurement system and the dc voltage source beingmeasured is nonlinearized. This nonlinearization is achieved by the addition of a nonlinearcapacitor in series with the coupling capacitance. Two types of nonlinear capacitor areused—multilayer ceramics and varicap diodes. Currently available multilayer ceramics have alarger value than desired but prove the concept, while the small capacitance of the varicapdiode allows measurement on real wires. Results show that over a low voltage range (−8 V to+8 V), the voltage on a conductor can be measured if the coupling capacitance between sourceand electrode is larger than 20 pF, which equates to an electrode length of 5 cm when wirecompliant with MIL-W-81044-22 is used. Detection is performed by momentarily applying avoltage at a node within the measurement system, then measuring the time it takes for thisvoltage to decay to a threshold level—the capacitive nonlinearity causes this time delay to bedependent upon the dc input voltage whose value is being measured.
(Some figures may appear in colour only in the online journal)
1. Introduction
The aim of this work was to measure dc voltage on a wire,through a coupling capacitance of 10–100 pF formed bythe wire’s insulation layer; such non-contact measurement isdesirable in many situations, allowing measurements to bemade without physical access to the conductors. Measuring acvoltages is relatively straightforward—an electrode in closeproximity to the insulated conductor causes a capacitanceto be formed between the electrode and the conductor beingmonitored, through which an alternating current will flow thatis in proportion to the peak to peak ac voltage. However,to measure dc voltages in a similar situation requires morethought.
The device presented here was conceived as an aid tomonitoring aircraft wiring, where failures have been seen inolder aircraft [1]. A variety of research projects have soughtto find these faults; this work aimed to detect voltage on aconductor, to be used in conjunction with a current sensor toyield impedance and power measurements. Since ac and dc
systems are found onboard, a dc voltage sensor was requiredto make the complete system truly useful; additionally, thisdevice can also be used in any situation where non-contactdc voltage measurement is desirable, not necessarily in thecontext of aircraft wiring.
Other non-contact methods exist, most of them basedon the principle of a variable capacitance. Their operationis governed by the fundamental equation:
i = CdV
dt+ V
dC
dt. (1)
If capacitance between wire and nearby electrode is time-varying (nonzero dC/dt), ac current flows with an amplitudeproportional to the dc potential difference between the two.The Kelvin probe [2] was the first demonstration of this, wherea vibrating electrode above the conductor gave continuallyvarying capacitance and a current waveform predicted byequation (1). More recently, microsystems manufacturingtechniques have given rise to a new generation of MEMSelectrometers based on this principle [3–5]; when used to
measure charge, resolutions at room temperature approachingone electron charge have been claimed [4]. However, afundamental problem with these systems is their need formoving parts—mechanical systems are more prone to failurethan purely electrical ones.
A small number of purely electrical systems have beenproduced, a recent example being an electronically varyingcapacitance in series with the source–electrode couplingcapacitance [6]. The key element of the electronicallyvarying capacitor [7] was a transconductor, used to injectadditional in-phase current without changing the capacitor’svoltage. The resultant change in I/V gave capacitancechange, controllable by varying the quantity of additionalcurrent. However, this method proved incapable of giving ameasureable response with coupling capacitance (Cin) valuesof <1 nF—for real electrode-around-insulation situations,Cin is typically 10–100 pF, which defines the aim stated atthe outset.
2. Physical arrangement
For the tests carried out, ground was assumed common to bothmeasurement system and voltage source being monitored, asillustrated in figure 1.
This is a realistic representation for most systems,when some arbitrary ground reference is available. However,the device could, if necessary, be made fully differentialto measure the voltage difference between two separateconductors—the only change would be an additionalcoupling capacitance in the equivalent circuit between theother side of the source and measurement ground, thecommon ground connection having been removed. Electrically
Figure 2. Charge/discharge circuit with series nonlinear capacitor.
this is simply an additional series capacitor, acting to reduce,but not eliminate, Cin.
3. Theory
The key principle is that of charge conservation on twoseries capacitors across a voltage source. Capacitor potentials,VCx and VCy, can easily be found by simple potential divisionformulae, and charge on both capacitors is equal.
A linear capacitor is one whose charge versus voltagecurve is a straight line through the origin, where thecapacitance is a constant given by the gradient of the line. In anonlinear capacitor, however, capacitance is a function ofvoltage, which may or may not show hysteresis. Nonlinearcapacitors have been known for many years, with charge anddischarge behaviour described in 1955 [8].
Effective capacitance between conductor and ameasurement node can be made nonlinear by placing avoltage-dependent capacitor in series with the linear couplingcapacitance. If the principle of charge conservation in seriescapacitors is upheld, the series combination is also nonlinearand voltage dependent. The charge/discharge circuit utilizingthis principle is shown in figure 2.
In this situation, Cin is the input coupling capacitancethrough the wire’s insulation while Cnl is the nonlinearcapacitive element placed in series as part of the measurementsystem. V1 is the instantaneous voltage at the node labelledas such in figure 2. The capacitance Cnl is a function of thepotential difference present across it, and therefore also afunction of charge. Initially the switch is closed to allow theseries combination to charge to (Vin – Vinit), before it is openedto begin discharge. The differential equation describing circuitbehaviour during discharge is
Vin = dQ
dtR + Q
Cin+ Q
Cnl. (2)
The initial value of Q during discharge is the same as thefinal value of Q from the charging phase, with Cnl being afunction of Q while R and Cin are constants. Solving yieldsQ for all time, and from this the voltages across Cin, Cnl andR can easily be found. Although a nonlinear element is used,this is still a form of R–C circuit, and as such it should be
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
expected that V1 will decay from Vinit to 0 during discharge.However, decay characteristics are different to those seen ina circuit containing only linear capacitors—decay in figure 2depends not only on Vinit but also upon the value of Vin, aswell as the nature of voltage–capacitance relationship of thenonlinear capacitor. Given that the decay characteristic is afunction of Vin (the quantity being measured), the expectationis that the capacitively coupled Vin can be deduced by analysingthe voltage V1 as its value decays from Vinit to zero.
A possible alternative of using ac excitation and directlymeasuring capacitance was not explored. Direct measurementis complicated by not having access to both ends of the seriescombination (figure 1), and while it may have been possibleto replace the switch and Vinit of figure 2 with an ac source,this too complicates matters by introducing both terms on theright-hand side of equation (2); signal processing would thenbe required to decode the resultant waveforms and digitize theresult. Using suitable comparator circuitry, the result in thepreferred charge/discharge circuit is digitized immediately.
4. Coupling capacitance
Some tests were undertaken with a polystyrene or ceramic Cin,while others used a real conductor-to-electrode capacitanceformed by wrapping an electrode around the outside of a wire’sinsulation layer. When discussing real electrodes and theirassociated coupling capacitance, the particular type of wireused was Tyco’s 440111-22-9—a stranded radiation-treatedwire used on aircraft that complies with military standard MIL-W-81044. The datasheet does not give the effective dielectricconstant, but it was found experimentally to be 2.99.
5. Modelling with varicap diode as the nonlinearelement
One of the most commonly available nonlinear capacitancedevices having a large change in capacitance with appliedvoltage is the varicap diode. By measurement it was found thatfor electrode lengths of 30–100 mm, coupling capacitanceswere in the range 12–40 pF. Ideally, the varicap’s capacitancevalue, over its full range, should be comparable or less thanthe value of Cin—this ensures that a significant portion of theinput voltage is dropped across the sensitive element. Withthis in mind the ZC830B, with its 2–10 pF range (for reversevoltages in the range 0 to 20 V), was chosen. Translatingdata points from the published capacitance versus voltagecurve to obtain a lookup table of the Cnl versus Q function,equation 2 was numerically solved using MATLAB’s ode45()function. The results of this, showing the decay characteristicsfor different input voltages with Cin = 33 pF, are shown infigure 3. For clarity, traces obtained for larger negative valuesof Vin are omitted.
The results of the modelling show that, provided reversebias is maintained (the condition for capacitance of the varicapdiode being a function of voltage), then the nature of thedecay in V1, falling from Vinit to zero, does indeed dependupon the input voltage. In general, the larger the magnitudeof the negative voltage at the input (the voltage that is being
Figure 4. Modelled times to decay to 90%, 50% and 10% thresholdlevels, varicap with Cin = 33 pF.
measured), the shorter the time required to decay to zero.Therefore, if a trip point is set at a particular value somewherebetween Vinit and zero, and the time taken for V1 to reach thetrip level is measured, then input voltage can be deduced fromthis time measurement. The curves of figure 3 are analysedin this way, with time to decay to threshold being plottedagainst input voltage in figure 4, using three arbitrary triplevels of 90% of Vinit, 50% of Vinit and 10% of Vinit.
It can be seen that for all selected trip thresholds, thedevice is more sensitive in the region where input voltage issmall and negative. A similar analysis was performed withCin shorted out and the input voltage connected directly tothe anode of the ZC830—the result is shown in figure 5. Thisrepresents the limiting case, equivalent to having infinite Cin.As expected, the response is larger in this situation than withCin = 33 pF.
6. Modelling with multilayer ceramic capacitor asthe nonlinear element
So as to demonstrate that the principle holds for differentvarieties of nonlinear capacitor and not varicaps exclusively,results were also obtained with an alternative type. Non-compensated multilayer ceramic capacitors (MLCCs) arewidely available and can give a very large change in
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
Figure 5. Modelled times to decay to 90%, 50% and 10% thresholdlevels, varicap only.
Figure 6. Modelled decay curves using MLCC with Cin = 22 nF.
capacitance with voltage. The nonlinearity in these capacitorsis due to the ferroelectric dielectric; this gives nonlinearitybut also high base capacitances (C with no voltage applied)of typically 100 nF to 10 μF. Currently available componentsare therefore incapable of giving a measureable response inconjunction with input coupling capacitances in the targetrange of 10–100 pF, but larger coupling capacitances can beused to demonstrate the principle of operation and show it tobe independent of the physical effect causing nonlinearity.Non-compensated MLCCs are used primarily where largecapacitance values are required—as such, sufficiently smallvalues are not readily available. Nonlinear MLCCs in thepicofarad range appear to be producible, but until now such acomponent has had no application.
MATLAB simulation was performed using publisheddata for Murata’s GRM188F51H473ZA01D—an MLCC with47 nF base capacitance and maximal nonlinearity. The inputvoltage range was greater than that for the varicap, as a resultof this component’s higher voltage rating. Modelled decaycurves are shown in figure 6, with figure 7 showing decay timeto the appropriate thresholds.
Times are longer than those seen with the varicap due tothe larger capacitance values, but it is clear that the desiredtrend exists.
Figure 7. Modelled times to decay to 90%, 50% and 10% thresholdlevels, MLCC with Cin = 22 nF.
7. Basic experimental setup
A CMOS switch was used to apply the initial voltage whilecomparators were used to measure time-to-threshold. V1 wasbuffered by a low capacitance JFET amplifier prior to beingapplied to each comparator. The circuit was controlled bya custom-designed digital circuit programmed into a fieldprogrammable gate array (FPGA), within which the time wasmeasured between giving the signal to close the switch andeach comparator output flipping to its opposite logic level.Timing was by means of a simple digital counter and 50 MHzclock. The full circuit is shown in figure 8.
8. Uncertainty in practical measurements
One of the most useful features of this measurement systemis that repeat measurements can be made as many times asdesired. In order to minimize uncertainty in the practicalresults that follow, every data point presented was found byaveraging 50 individual readings taken quickly in series. Thevalue shown is simply the mean of the 50 measurements made,while uncertainty is statistically calculated for each data pointby the standard error function
U= (Standard deviation)/√
n. (3)
With n = 50, these statistically calculated uncertaintiesare small in comparison to the values and trends observed.Error bars are plotted on each graph (except those illustratingdrift), but in many cases they are so small that they are obscuredby the markers. For all results taken from a circuit containingthe varicap diode (sections 9 and 11), the largest statisticaluncertainty was 0.015 μs. In the case of the MLCC circuit(section 10), this figure was 0.024 μs.
9. Circuit tests with varicap diode as the nonlinearelement
In this test phase, the nonlinear capacitor shown in figure 8was a ZC830 varicap diode, orientated such that its anode
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
Figure 8. Generic circuit for measuring time delays.
Figure 9. Measured decay times from circuit tests, varicap only.
connected to Cin and its cathode to R and the buffer amplifier–this meant that negative input voltages and positive values ofVinit could be applied to maintain the necessary reverse biascondition, to give a situation comparable to that in simulation.Initially the circuit was tested with a short circuit placed acrossCin, i.e. in a situation where the input voltage was applieddirectly to the anode of the ZC830. With the threshold set at50% of Vinit, the graph of time to decay to threshold againstdc input voltage is shown in figure 9. Similar graphs wereobtained for 90% and 10% thresholds.
From this, it can be seen that the trend has a similar shapeto that seen in modelling; for a given value of Vinit, the timeto decay to the 50% threshold increases as the negative inputvoltage becomes smaller. Error bars that are very small incomparison to the trend give confidence that the trend is real.Generally, this agrees with the predicted performance shownin the ‘Trip Level = 0.5 V’ curve of figure 5, with the gradientbeing steeper as the dc input voltage approaches zero, and
Figure 10. Drift in measurements with no leakage or biasingcircuitry.
flatter (thus less sensitive) for large negative input voltages. Inaddition to this, if a larger value of Vinit is used then the timedelays are not as large; this is because a larger positive valueof Vinit means a larger voltage across the varicap. Since theZC830 has a lower capacitance for a larger voltage, which inturn results in a smaller circuit time constant, this response isexpected. These results confirm the principle of operation.
When the input voltage is coupled to the varicap througha small linear coupling capacitance, as in the real situation,things becomes more complicated. Using the circuit of figure 8with no additional components, it was observed that the decaycurve changed in the expected manner when the dc inputvoltage was varied, but unfortunately it always drifted back toa default curve over time. Correspondingly, measured decaytimes always defaulted to the same values when the test wasrepeated over a long period of time with the same dc voltageapplied. This is shown in figure 10—the drift makes the device
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
Figure 11. Measured decay times—varicap in series with parallelcombination of Cin and leakage resistance.
useless as a sensor without modification as measurementsare not repeatable.
The observed drift is due to the physical nature of thevaricap diode. This is a semiconductor device, requiringproperly defined reverse bias to ensure that the capacitanceis controllable. This cannot directly be achieved in thissituation—a known dc voltage would need to be appliedacross the varicap, something that would prevent intendedcircuit operation. Leakage in the varicap exacerbates this if ameasurement is not taken quickly after the initial disturbance.To operate as intended therefore, there is a requirementfor some leakage through the input coupling capacitance orbiasing by an alternative method.
To check the response with leakage present, the inputcoupling capacitance was replaced with an ultra-low leakagepolystyrene capacitor in parallel with a 10 M� resistor. Theresults for the 50% threshold are shown in figure 11.
The ‘VC only’ trace is for the situation where the dc inputvoltage is connected directly to the varicap, and is includedonly as a reference. The ‘Cin = 0’ trace was taken withno coupling capacitance placed in parallel with the 10 M�
leakage resistance. These results are largely what would beexpected, with larger coupling capacitances giving betterresponses; this is logical since a larger input capacitancevalue will result in a smaller portion of the input voltageappearing across Cin and proportionately more acrossthe sensitive element (the varicap diode). Large values ofinput capacitance give virtually the same response as that seenwhen the input voltage is connected directly to the varicap.While the response at 10 pF is noticeably less, the importantpoint is that there is a response, and importantly, that it isrepeatable. This is significant as it represents the lower end ofthe capacitance range that would be desired. Although theseresults were taken with leakage resistance artificially addedin parallel with Cin and are thus not a true representation ofhow the system would work in reality, they do illustrate animportant point—leakage is required only to bias the varicap,while the coupling capacitance value affects the quality of theresponse. Note that with leakage and no capacitance, there isvirtually no response.
In a real system however, the device must work withoutartificially added leakage resistance, and must instead usea more sophisticated biasing scheme. It was noted that ifthe input voltage was initially strongly positive, then movedquickly to another voltage level and the reading immediatelytaken, then the response appeared reasonably consistent. As aresult of this observation, the circuit was modified such that acontrollable voltage source could be switched in immediatelyprior to making a measurement. This modified arrangement isshown in figure 12.
Figure 12. Modified varicap circuit including capacitively coupled biasing.
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Figure 13. Timing diagram for capacitive biasing.
Vbias was implemented in such a way that the FPGA couldset it to different voltages as required. It was found that thebest way of applying the biasing voltage was to close switch1 as normal, then connect switch 2 to C2. Vbias was then setstrongly negative for 50 μs then strongly positive for 50μs,before setting switch 2 to connect to Cin. There was then aprogrammed delay, before finally opening switch 1 to beginR–C decay. The waveforms for Vbias and the timing sequencewere derived empirically, and the sequence is shown infigure 13. It should be noted at this point that both switcheswere CMOS types, meaning that the system was entirelyelectronic with no moving parts.
It can be seen that the bias source is capacitivelycoupled, rather than being directly connected. While directand resistive biasing methods were attempted, it was foundthat a capacitively coupled source was better at alleviatingthe problem of drift. Additionally, it was the case that ingeneral, large values of C2 gave better results, up to a limitingvalue of about 10 nF. For that reason, the foregoing resultswere obtained with C2 = 2.2 nF, an arbitrary value withinthe desired range. Enhanced performance with capacitivelycoupled biasing can be explained by considering chargestorage at the instant the control signal to switch 2 goes lowat 200 μs. It appears that due to the complex nature of thevaricap, directly coupled bias sources give a loss of varicapcharge during switching. With a large coupling capacitance,however, the stability of the large capacitor causes the biasinginfluence not to be lost entirely.
The precise shapes of the waveforms were not especiallyimportant, provided that Vbias was set strongly positiveimmediately prior to exiting pre-bias mode at 200 μs. Thisstrong positive bias of +10 V was intended to briefly force thevaricap out of its normal reverse bias state and into forwardconducting mode. The logic behind this was that when thedevice was switched from pre-bias mode to normal operationat 200 μs, the varicap would be switching to normal operationfrom a well understood state. The −10 V pulse immediatelypreceding this was added to maximize the rate of change of
bias voltage at 150 μs, in an attempt to supply maximal pulsecurrent to aid the process.
With this in place, it was found that a repeatablemeasurement could be obtained. Results with Vinit = 3 V areshown in figure 14 (again only the results for the 50% thresholdare shown, since those for 90% and 10% are effectively scaledcopies of this). The curves were the same regardless of whetherthe input voltage was swept from −8 V to +8 V or vice versa.
It can be seen that the results follow the general trendof the others, but with some notable differences. Largervalues of Cin give a better response, as expected. Previously,the response was reasonably flat for large negative inputvoltages, and this is the case with these results also. However,previous results were plotted only with negative voltagessince positive voltages caused the varicap to become forwardbiased which prevented normal circuit operation. For theresults from this modified circuit though, this is not thecase, and a response can be seen over a range of positiveand negative voltages. The reason for this is that thesecondary voltage source, controlled by the FPGA and coupledin via C2, causes the varicap to be biased at a particular pointwhen switch 2 is in the lower position (figure 12). When switch2 is then set to its upper position and the voltage sourcethat is being measured is coupled in via Cin, this modifiesthe pre-existing bias. In the previous setup with leakage, thebias was set by the dc source being monitored rather thanbeing modified by it. Thus, over the voltage range shown infigure 14, the reverse bias condition can be maintained. Thegeneral trend is the same as before and is as predicted bytheory–as the input voltage being measured is made morepositive, the time to decay to the threshold level becomesgreater.
In addition, it is clear that with this configuration, thereis no response for input coupling capacitance values less than20 pF. This compares unfavourably with the results obtainedwith artificial leakage present, where a response could be seenfor values as low as 10 pF. This difference comes about becauseof the additional circuitry—switch 2 has capacitance to groundfrom all terminals and these additional parasitic elementsinevitably act to degrade performance. However, electrode-to-conductor capacitances of 20–30 pF are not problematic toachieve with a practically sized electrode.
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
Figure 15. Drift with capacitive biasing circuitry added.
Figure 16. Measured decay time using MLCC as the nonlinearelement and Cin = 22 nF.
With pre-biasing in pace, the device showed good stabilityand gave repeatable measurements with no dependence onprevious values of input voltage. Figure 15 shows how therecorded decay times changed when this circuit was left overthe same period as in figure 10, with the same input voltageapplied.
Clearly there is very little variation in this case, andanalysis over a longer period of time revealed no deviationfrom this. The same was true when the system was switchedoff then on again, and also after temporarily shorting any of thecapacitors. For a given value of input voltage, the output wasalways the same—this is a notable and necessary improvementfrom the previous version that did not include capacitivelycoupled biasing.
10. Circuit tests with MLCC as the nonlinearelement
With no pre-biasing applied to the MLCC and Cin = 22 nF, thegraph of figure 16 was obtained—the input voltage was sweptfrom −50 to +50 V, then back to −50 V.
Clearly this is unsuitable as a sensor as the decay timeis seen to be dependent upon previous Vin values. Anyferroelectric dielectric will experience remnant polarization,causing the charge–voltage plot to be neither a straight line nora simple curve, but a hysteresis loop. Although not mentionedin published component data, it is therefore unsurprising thatresults indicate a dependence on previous polarization states.
To mitigate this, pre-biasing was used once again—its purpose in this case was to force the MLCC intothe same state before every measurement, thereby makingprevious polarization irrelevant. Biasing voltage was thistime connected directly, with the modified circuit shown infigure 17. With a single bias voltage level applied beforemeasurement, a typical set of results for Cin = 22 nF is shownin figure 18.
From these results it is clear that hysteresis can bereduced by suitable pre-biasing. Although no curve showssufficiently reduced hysteresis to allow use over the full range,measurement over part of it is possible—with Vbias = −10 Voperation is possible from 30 V to 50 V, while setting Vbias to0 V gives meaningful data between −50 V and −10 V.Ideally, pre-bias voltage would be sufficiently large to forcethe ferroelectric material into saturation, not possible withthis circuit since the switch rating (15 V) was much lowerthan MLCC saturation voltage (50 V). A future MLCC withsaturation voltage lower than the rating of common CMOSswitches would therefore be very useful. Overall, these resultscompare well with theoretical results, and illustrate that theprinciple applies generally, rather than specifically to oneparticular type of nonlinear component.
11. Results with real electrodes
The previous results with the varicap diode in section 9were obtained with low leakage polystyrene capacitors, whichsuitably represent the coupling capacitance between conductorand electrode. However, in order to show that the desiredresponse could indeed be achieved with real electrodes, thesewere made and the system tested with them. In this situationthe input voltage being measured was applied to an insulatedconductor, and the electrode was added to the outside ofthe insulation layer. It was found that conductor-to-electrodecapacitance could be maximized if the electrode was formed byapplying a layer of silver paint to the outside of the insulationlayer, then wrapping copper tape on top of this. Measurementof the actual capacitance values of such an arrangement usingan LCR meter revealed a capacitance per unit length of about4 pF cm–1. The responses for different electrode lengths areshown in figure 19, again with small statistical uncertainty.
From these results, it can be seen that capacitors formed byplacing real electrodes around conductors do indeed give thesame response as polystyrene capacitors. The 5 cm electrodegives virtually no response, but this is expected given previousresults, since the capacitance for this electrode is about 20 pF.All larger electrodes give an acceptable response, and again,this is repeatable.
These results have implications as to other applicationsfor which the technique may be used. Any circuit node orwire capacitively coupled with at least 20 pF appears to bemeasureable, and while the target range for this work was10–100 pF, situations with larger coupling capacitances canalso be accommodated—indeed, it is preferable to maximizeCin where it is possible to do so.
When operating in a real situation rather than under labconditions, it is the case that Cin may drift slightly over time
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Figure 17. Modified MLCC circuit to include direct biasing.
Figure 18. MLCC circuit test results with pre-biasing.
as the electrode becomes loose, is disturbed slightly, etc. Bymodifying the circuit of figure 12 slightly, an extra switch canbe placed in parallel with the nonlinear capacitor, forming aconventional R–C circuit comprising Cin and R. By performinga charge/discharge cycle as used in normal operation, thevoltage at V1 will decay from Vinit to 0 in a manner governed byconstants Cin and R. As R is a known local parameter, Cin canbe simply derived from the discharge curves. Periodically itmay be useful to find the decay time versus input voltagecurve for the measured value of Cin. To do so, a three-positionswitch replaces the two-position switch 2 in figure 12, withthe third position capacitively coupled to a known local sourcevia a variable capacitor Ccal. By setting Ccal to the same valueas Cin, the known source can be swept to give the voltageversus time curve that forms the lookup table for subsequentmeasurements.
However, the introduction of the calibration procedureperiodically measuring Cin results in larger measurement
Figure 19. Circuit test results with varicap and realelectrode-around-conductor coupling capacitance.
uncertainty than has been shown to be the case with a well-defined Cin. Instead of having only the statistical uncertainty,any error in the periodic measurement of Cin must impact theaccuracy of the voltage measurement. To assess this, the resultsof figure 19 are re-plotted in figure 20, using interpolationwhere required, to show how the voltage read from the lookuptable varies as a function of capacitance, given the samemeasured decay time.
The worst-case value of dVin/dCin is 0.76 V pF–1.How accurately the dc voltage can be measured therefore
depends upon the accuracy with which Cin can be measured,which is in turn dependent upon the uncertainty in timemeasurement when in calibration mode. Firstly, there is theresponse time of the comparators. 200 ns is the typical valuegiven in the datasheet (no maximum given), so the uncertaintyis estimated as 25% of this value, i.e. ± 50 ns. Similarly,the uncertainty in switch response time is estimated as
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Meas. Sci. Technol. 23 (2012) 045001 G McKenzie and P Record
Figure 20. Uncertainty in voltage reading as a result of uncertaintyin Cin.
27 ns. With a timer operating at 50 MHz, there is an additionalerror of up to 1 clock cycle, or 20 ns—this gives a total timinguncertainty for Cin measurement of ± 97 ns. It should be notedthat these issues are not relevant in the measurements from thecircuit with known Cin (figure 14), since once Cin is known,the random uncertainty is the limiting factor.
In standard R–C calibration mode, V1 decays accordingto: V1 = Vinit exp(–t/RC). If the threshold is set to 50% of Vinit,then Cin is calculated using the following equation:
Cin = t
R ln 2. (4)
Uncertainty in time is of greatest significance when thevalue measured is small, meaning when Cin is smallest.Therefore, to get the worst-case value, equation 4 is rearrangedfor t, with 20 pF being used for Cin and a standard value of1 M� for R (the assumed minimum value). The result is that theuncertainty of 97 ns gives a worst-case percentage uncertaintyin t of 0.7%. Uncertainty in R is only 3.5 �; with a minimum Rof 1 M�, this 0.000 35% is negligible meaning the estimatedworst-case percentage error in Cin is 0.7%.
Combining the voltage dependence on capacitance(0.76 V pF–1) with uncertainty in capacitance measurement(0.7%) gives a worst-case error of 0.19 V over the capacitancerange shown. Uncertainty will not increase if larger values of
Cin are used—figure 20 shows that in this case, dV/dC becomessmall, while additionally, percentage error in measured Cin isreduced.
12. Conclusion
This work has proven the theory that R–C decay characteristicscan be modified by an applied dc voltage if a nonlinearcapacitor is included in the circuit; therefore, a dc voltagecan be measured without contacting the conductor in questionif the decay curve is analysed. Modelled and experimentalresults have shown that any suitable nonlinear capacitor canbe used for the purpose, and with a low capacitance varicapdiode, the device is viable as a low dc voltage sensor. Thisappears to be the first time dc voltages have been measuredby monitoring R–C decay in a nonlinear capacitor circuit, andresults show that with readily available commercial electroniccomponents, dc voltages can be resolved to significantly lessthan 1 V.
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