Exploring a new ammeter traceability route for ionisation chamber measurements
EExploring a new ammeter traceability route for ionisation chambermeasurements
S. P. Giblin a) and G. Lorusso
1, 2 National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW,United Kingdom Department of Physics, University of Surrey, Guildford, GU2 7XH, United Kingdom (Dated: 8 March 2019)
We compared the performance of a commercial ammeter and a home-made integrating electrometer in readingionisation chamber currents less than 100 pA. The integrating electrometer charges a capacitor with theunknown current and measures the resulting rate of change of voltage, whereas the ammeter uses a high-value resistor as the feedback element to an amplifier which converts current to voltage. The noise performanceof both systems was very similar for averaging times less than 1000 seconds. Both systems were calibratedusing a reference current source with 1 part per million (ppm) accuracy, revealing an error of 460 ppm inthe electrometer indicated current, of unknown origin. This error is well within the uncertainty budget forradionuclide calibrations, but much larger than the individual uncertainties in the traceable calibrations ofcapacitance, voltage and time. The noise in the ionisation chamber current was much larger than the noisefloor of both instruments, with tests providing strong indication that the excess noise originated in the highvoltage source used for energising the chamber.PACS numbers: 1234
I. INTRODUCTION
Ionisation chambers are of great utility for measuringradionuclide activities and half-lives. The chamber out-puts a current proportional to the activity of the sourceinside the chamber, with the constant of proportional-ity determined by primary calibration methods involv-ing absolute counting of decay events from a dilutedsource . The linearity and stability of the ionisationchamber current measurement is ensured by traceablecalibration of the current measuring instrument. His-torically, these instruments have usually been capacitor-ramp electrometers which integrate the ionisation cham-ber current and allow the current to be calculated ac-cording to I = C dVdt . For ionisation chamber currentsin the picoamp to nanoamp range, voltage ramp ratesof dVdt ∼ C in the picofaradto nanofarad range. Such capacitors are available com-mercially as low-loss air or sealed-gas units possessinglong-term stability at the part-per-million level, and lowsensitivity to temperature and humidity changes. Therelevant calibrations of voltage, capacitance and time areavailable as standard services from national metrologyinstitutes (NMIs), and accredited laboratories, with rel-ative uncertainties less than 10 parts per million (ppm),and in the absence of complicating factors these low un-certainties are transferred directly to the measured cur-rent.In the last 15-20 years, a number of developments haveoccurred in the field of small current metrology whichencourage a fresh look at ionisation chamber current a) Electronic mail: [email protected] readout methods. In response to industry demand, anumber of NMIs have inaugurated calibration servicesfor nanoamp-level ammeters with uncertainties as lowas ∼
10 ppm. Reference currents are usually sourcedby applying a linear voltage ramp to a low-loss capaci-tor (essentially the reverse process of a capacitor-rampelectrometer) . To validate these new services, thefirst international intercomparison of reference currentsources was undertaken . While broadly validating NMIcapability, the comparison could not provide informa-tion at uncertainty levels much below ∼
100 ppm dueto transport instability and environmental effects in thecommercial ammeters used as transfer standards. In par-allel, research into prototype quantum current sources,known as electron pumps, which generate small currentsby moving electrons one at a time , focused attentionon small-current metrology at the lowest possible uncer-tainty level. In this research setting, currents of order100 pA have been measured with combined uncertaintiesof ∼ . . A practical spin-off from the electronpump research has been the ultrastable low-noise currentamplifier, or ULCA . This instrument, following cal-ibration using a cryogenic current comparator (CCC) ,can either source or measure small currents with uncer-tainties as low as 0 . . Recently, different versions of the ULCA havebeen tested, including ones with high gain and small,stable, offset suitable for the measurement of the verylow background currents from ionisation chambers .Inspired by these developments, in this paper we testan alternative traceability route for ionisation chambercurrents: an ammeter calibrated directly using a primaryreference small-current source. We compare this amme-ter method with an established capacitor-ramp method a r X i v : . [ phy s i c s . i n s - d e t ] M a r in which the traceability is to standards of capacitance,voltage and time, and discuss the advantages and limi-tations of each. We also address an important and ne-glected question in ionisation chamber metrology: howdoes the random uncertainty in the measured current de-pend on the measurement time, and what is the optimuminterval between chamber background measurements. II. TRACEABILITY ROUTES
In figure 1 (a), three complete traceability routes forsmall electrical currents are summarized, starting withprimary standards at the top. The electron pump is in-cluded for completeness; although they currently havethe status of research devices, electron pumps offer a verydirect tracebility route and are likely to play a role in pri-mary current metrology in the future . In this paper, wewill be concerned mainly with the first two - the capacitorramp method and the resistor/voltage method.The capacitor ramp method realizes current via therate of change of voltage across a capacitor, and the con-cept can be applied to either the generation or measure-ment of a current. The traceability route for capacitanceis either to the dc quantum Hall resistance (QHR) viaa quadrature bridge and ac/dc transfer resistor, or viathe calculable capacitor, which realizes a small ( < ∼ C × dVdt can consequently be realized with an uncertainty of a fewparts per million, and precision reference current sourceshave mostly used this route .Generation of sub-nA reference currents using a resis-tor and voltage source is less common. This may be be-cause high-value standard resistors, in contrast to sub-nFair-gap capacitors, can have temperature co-efficients aslarge as few tens of ppm per degree, and therefore requireadditional environmental control to reach ppm-level ac-curacy. Calibration uncertainties of high-value resistorshave also been generally higher than low-value capaci-tors, although ppm-level calibration uncertainties of re-sistors up to 1 GΩ are now attainable using CCCs .The ULCA also generates and measures current withrespect to an internal 1 MΩ resistor and an externalDVM, and as already noted, has demonstrated 1-year sta-bility at the ppm level. The resistor and voltage source FIG. 1. (a): Diagram showing routes for traceable generation ofsmall currents via three main mechanisms: capacitor ramping,Ohms law and the controlled transport of charge. Abbreviationsare JVS = Josephson voltage standard, QHR = quantum Hallresistance, DVM = digital voltmeter. The elementary charge isdenoted e . (b): Simplified schematic circuit diagram of an inte-grating electrometer. (c): Simplified schematic circuit diagramof a feedback ammeter. method has the obvious advantage that current can begenerated continuously without being constrained by acapacitor charge-discharge cycle.A problem with the capacitor ramp method is thatthe low calibration uncertainties of the standard ca-pacitors are achieved using voltage-transformer bridgetechniques which work at audio frequencies. Calibra-tions are typically performed at 1 kHz, and the tech-niques can be extended down in frequency to a practi-cal lower limit of ∼
25 Hz. In contrast, capacitor rampmethods for generating or measuring small currents op-erate at frequencies many orders of magnitude lower, inthe millihertz range. One study found that some sam-ples of standard capacitor exhibited unexpectedly largefrequency dependence in the range ∼
10 mHz - 1 kHz,up to several hundred ppm , which is certainly far inexcess of the 1 kHz calibration uncertainty and begins toimpact the uncertainty budgets of NMI-level ionisationchamber readout systems. Either the capacitance needsto be measured at the ramp frequency, which is a labo-rious and non-standard procedure , or the capacitanceuncertainty must be expanded to allow a worst-case sce-nario. This issue reduces somewhat the apparent advan-tages of the capacitor ramp method, and prompts fresh FIG. 2.
Simplified schematic circuit diagram showing the inputstage of an ammeter connected to a non-ideal current source withfinite output resistance R out . The offset current and voltage aredenoted I off and V off respectively, and the current and voltagenoise are denoted I n and V n respectively. consideration of the resistor and voltage method. III. CURRENT MEASUREMENT AND GENERATIONSYSTEMSA. Current measurement systems
The two types of current readout system investigatedin this paper, the capacitor ramp electrometer and thefeedback ammeter, are illustrated schematically in figure1 (b,c). We will refer to them subsequently as the ‘elec-trometer’ and the ‘ammeter’ respectively. Both types ofinstrument use a high-gain amplifier with feedback; thefeedback element is a capacitor in the case of the elec-trometer, and a resistor in the case of the ammeter. Theelectrometer used in this study employs a home-madeamplifier with an external integrating air-gap capacitorof value ∼
500 pF, and an external DVM (Datron model1061) triggered with a calibrated 1 s interval betweenreadings. We denote the current measured by the elec-trometer I E ≡ C corr × dVdt . Here, C corr = C cal + C stray where C cal is the calibrated value of the standard ca-pacitor, and C stray is the stray capacitance correction.For the bulk of the study, excepting the data of figure4 (f,g), the ammeter was a Keithely model 6430 set tothe 1 nA range . The resistive feedback of the amme-ter gives an output voltage = I in R , which is digitized byan analogue-to-digital converter (ADC) internal to theinstrument, and converted to a current reading by theinstrument’s firmware. The feedback resistor ( ∼ B. noise considerations
In figure 2, we present an expanded circuit model forthe input stage of an ammeter connected to a currentsource, including the offsets and noise sources presentin real ammeters, and the finite output resistance R out ofthe current source. Additional noise due to the current source itself is not considered in this model. The voltageoffset and noise are represented by a single source in thediagram for convenience (and likewise for the current off-set and noise) but this should not be taken to imply thatthey are due to the same process or component in the am-plifier. The same circuit describes the electrometer, butwith R replaced by a capacitor. A detailed discussion ofamplifier properties is beyond the scope of this paper, butsome qualitative comments will help with interpretingthe data of sections IV and VI. The total amplifier noiseis the sum of three contributions: the current noise I n ,the thermal noise in the feedback resistor R (in the caseof capacitive feedback, there is no thermal noise), andthe voltage noise V n driving a noise current in the sourceresistance R out22 . Crucially, while the first two contribu-tions are independent of R out , the last one increases ininverse proportion to R out . The reference current sourceused for calibrating the ammeter and electrometer (de-scribed in the next paragraph) has R out = 1 GΩ, whereasan ionisation chamber presents a very high output resis-tance, R out (cid:29) V n to con-tribute more noise during a calibration of the instrumentthan when measuring an ionisation chamber current, anddepending on the relative size of I n and V n (we did notseparately measure these for either the electrometer orthe ammeter) we may expect to see an increase in thenoise when the instrument is connected to the referencecurrent source. Generally, designers of amplifiers have tomake trade-offs, and it is difficult to make both V n and I n arbitrarily small. We note that the measurement of ioni-sation chamber currents is an application in which V n canbe relaxed somewhat in a specialised instrument designdue to the very high output resistance of the source, toenable the smallest possible I n . A commercial ammeter,on the other hand, may offer smaller V n and larger I n , inorder to yield a reasonable total noise when measuringcurrent sources with a wide range of R out .The same general comments also apply to the off-set current and voltage, I off and V off ; in instrumentdesign there is typically a trade-off between the two.We measured V off = 5 mV for the electrometer, and V off ∼ . C. reference current source
Our reference current generator consisted of a cali-brated, temperature-controlled 1 GΩ standard resistor,an uncalibrated voltage source and a calibrated DVM(model Keysight 3458A). The combined type B uncer-tainty in the reference current was ∼ I true , and currentindicated by the instrument, I Ind , as I true = ( g × I Ind ) + I offset , where g is the gain factor. Our calibration deter-mines only the gain factor g . The offset current I offset is automatically removed from the background-correctedmeasurements of activity discussed in section VI, since itis present in the current with and without the radionu-clide source in the ionisation chamber. We calibrated thegain factor of the ammeter every 2-3 days during the mea-surement period, and we denote the current measuredby the ammeter, after adjusting the indicated current forthe gain factor, as I A . Care was taken not to subject thesensitive ammeter preamp unit to mechanical shock, asprevious experience with the EM-S24 small-current inter-comparison showed that even small mechanical shocks,such as plugging a cable into the preamp, could changethe gain factor by several tens of ppm. Following theseprecautions, the ammeter calibration factor changed byless than 5 ppm over 2 − IV. DEPENDENCE OF TYPE A UNCERTAINTY ONAVERAGING TIME
All the radionuclide measurements were performed us-ing the same ionisation chamber, which was of type Vin-ten 671. To assess the type A (statistical) uncertaintyafter a given averaging time, we placed a sealed Ra-226source in the chamber and measured the current for pe-riods of several hours. Raw data from ammeter measure-ments is shown in figure 3 (a). The ammeter was set tointegrate each data point for 10 power line cycles (PLC),with the auto zero function disabled, and consequentlythe raw data set consists of 5 data points per second.In figure 3 (b), the same data has been block-averagedso that each plotted point is averaged over 85 secondsof measurement time. A plot of the ionisation chambercurrent from the same Ra-226 source, measured usingthe electrometer, is shown in figure 3 c. In this plot,each data point is obtained from one voltage ramp cycle.The ramp cycle lasted 85 s, so the data points in figures3 b,c can be directly compared, i.e. each data point cor-responds to the instrument integrating the current signalfor the same amount of time. The offset of ∼ . ∼
50 fA over the first few hours and continuing a down-ward drift more slowly for the remainder of the measure-ment time. The rapid drift visible at the start of thisdata set was rather atypical of the performance of thisinstrument, and was not the result of mechanical shock.
FIG. 3. (a): raw ammeter data obtained while measuring theoutput of an ionisation chamber containing a Ra-226 source.(b): The data in (a) averaged in 85-second blocks. (c) Datafrom the same source/chamber combination measured using acapacitor ramp electrometer. Each ramp takes seconds. (d):Allan deviation as a function of averaging time τ of the data inplot (a) (open triangles), plot (c) (filled diamonds) and an addi-tional data set obtained with the ammeter disconnected from theionisation chamber to measure its noise floor (open diamonds).The diagonal solid line is a guide to the eye with slope / √ τ .The vertical double arrow indicates the difference between theammeter noise floor and the noise when measuring the ionisa-tion chamber current, and the horizontal dashed lines indicaterelative random uncertainties of . and . . The instrument was powered up and running in acquisi-tion mode for several days prior to the start of the dataset. We cannot rule out the possibility that the drift isdue to a change in the ambient temperature, coupled toa temperature dependence of the ammeter’s gain-settingresistor, but this is unlikely as calibrations of the amme-ter spread over two weeks showed the gain to the stableat the 10 − level. In contrast to the ammeter data, thecurrent measured by the electrometer appears to be sta-tionary in time. Next, we employ the Allan deviation tomore quantitatively investigate this observation.The Allan deviation is a statistical tool developed as away of assigning a meaningful statistical uncertainty todata with a non-stationary mean . It is widely used intime and frequency metrology, and its use in electricalmetrology is becoming more widespread, for example tocharacterize the stability of voltage standards and cur-rent comparator bridges . Here, we briefly summarizeit. The Allan deviation σ A is computed from a time-seriesof data points evenly spaced over a total time T . Thecomputation yields σ A as a function of averaging time τ ,for τ < ∼ T /
4. For the case of frequency-independent noise, σ A ( τ ) = σ/ √ τ , where σ is the standard deviation of thedata; in other words, the Allan deviation is equal to thestandard error of the mean, and decreases as the squareroot of the measurement time. However, in the presenceof frequency-dependent noise, the standard error of themean is no longer a meaningful measure of the type Auncertainty. Two examples of frequency-dependent noiseare 1 /f noise, in which the Allan deviation is indepen-dent of τ , and random-walk, or 1 /f noise, in which theAllan deviation increases as the square root of τ .The Allan deviation of the time-domain data from fig-ure 3 (a) and (c) is shown in figure 3 (d). Note thatthe first data point for the electrometer is at τ = 85 s,the time for one integration ramp, whereas the amme-ter data starts at τ = 0 . σ A for τ < σ A ( τ ) ∝ / √ τ . For τ > /f noise,in which further increases in the averaging time do notresult in any further decrease in the type A uncertainty.The lowest type A uncertainty achievable with the am-meter, based on this data set, is ∼ I A .The electrometer, on the other hand, continues to follow σ A ( τ ) ∝ / √ τ out to the longest time-scale probed bythis data set, τ ∼ σ A ∼ I E .Some insight into the behaviour of the ammeter canbe gained by plotting the Allan deviation of a time-seriesof data taken with the instrument left open-circuit (opendiamonds in figure 3 (d)). This exhibits a transition to1 /f noise at τ ∼
10 s, which is due to the low frequencybehaviour of its input bias current noise. A small ad-ditional contribution may be due to the ADC voltagemeasurement . Referring to section III, the superiorstability of the electrometer at long averaging times isprobably a consequence of it having a more stable offsetcurrent and voltage than the ammeter. We might alsopropose that the electrometer has a more stable gain-setting element (the feedback capacitor) than the amme-ter. However, in section VI, and referring to the insetto figure 5 (a), we see that the ammeter gain is stableat the level of 10 − on a time-scales of a few hour, sothe 10 − limit to the type A uncertainty discussed in theprevious paragraph is unlikely to be due to instability inthe resistive gain element.The analysis presented in this section is not intendedto be a definitive comparison of the two types of currentmeasuring instrument, nor should the ammeter data beinterpreted as definitively describing the particular makeand model of instrument used in this study . Rather, itis intended to demonstrate a methodology for evaluatingthe type A uncertainty achieved following a given aver-aging time. For example, referring again to figure 3 (d),if a statistical uncertainty of 50 fA (0 .
1% of the signalfrom the Ra-226 source) was desired, it is only neces-
FIG. 4. (a): Ammeter current as a function of ionisation cham-ber voltage, with the ionisation chamber energised with a low-noise laboratory DC supply. The Ra-226 source in the chamberis the same as in figure 3. (b,c): Ionisation chamber current withthe chamber energised using (b): the low-voltage source and (c):the high-voltage source. In each data trace, the source is initiallyin the chamber, and is then removed. (d): Allan deviation ofsections of data with the chamber empty from plots (b) and (c).Open symbols: LV source, filled symbols: HV source. (e): As(d), but with the Ra-226 source in the chamber. (f): Amplitudespectra of current noise from an empty chamber energised withthe LV and HV sources. (g): as (f), but with the Ra-226 sourcein the chamber. sary to integrate the current for 30 s using either typeof instrument. Knowledge of the stability of the currentmeasuring instrument is also important when designinga protocol for measuring the chamber background cur-rent. One possible such protocol would be to measurethe background current once a day, and subtract thesame background from all calibrations performed thatday. In this case, the Allan deviation of the readout cur-rent for τ = 1 day would yield the minimum meaning-ful statistical uncertainty achievable in any calibration.Since instruments generally suffer from 1 /f or randomwalk behavior at long time-scales, a more robust proce-dure would be to measure a new background signal everytime the chamber is empty, i.e. in between calibrationsof different sources. V. INVESTIGATION OF EXCESS NOISE
A remarkable feature of the data in figure 3 (d) is theroughly factor of 100 increase in the short-averaging-timenoise when the ammeter is connected to the energisedionisation chamber. This excess noise is indicated by avertical double arrow. The excess noise is not due to thecable connecting the ammeter to the ionisation cham-ber. Separate measurements showed that the cable onits own, or indeed the cable connected to the chamber,but with the high voltage (HV) source disconnected fromthe chamber, increased the noise by a negligible amountcompared to the situation with the ammeter input leftopen circuit. The statistical nature of current genera-tion in the ionisation chamber can be expected to adda shot-noise contribution, but we do not believe this isa significant contributor to the total noise because therewas only a small decrease in the total noise (less thana factor of 2) when the source was removed from thechamber.To investigate the nature of the excess noise, we re-placed the HV source with a low-noise laboratory volt-age source (Yokogawa GS200), which we will refer to asthe low-voltage (LV) source. This source was limited toa maximum of 32 V, but as shown in figure 4 (a), thechamber current almost reached saturation at this volt-age using the same Ra-226 source employed in the mea-surements reported in section IV. In figures 4 (b) and (c)we show data measured using the ammeter, in which thesource was initially in the chamber, and was then with-drawn from the chamber. The data of figures 4 (b) and(c) were obtained using the LV and HV voltage sources,set to 32 V and 1455 V, respectively. The lower currentnoise when using the LV source is immediately appar-ent. Allan deviation plots of sections of the data fromfigures 4 (b) and (c), shown in panels (d) and (e) show,however, that the reduction in noise using the LV sourceis rather more complicated than might appear from thetime-domain data plots. With the chamber empty, thereduction in noise using the LV source is indeed dramatic,at least a factor of 20 for averaging times from 0 . . V/A followed by a Keysight 34461A integrating volt- meter sampling 1000 times a second. The bandwidth(3 dB point) of the transimpedance amplifier is 150 Hz.Time-domain data traces were transformed in software toyield the amplitude spectra scaled in units of pA/ √ Hz (figures 4 (f) and (g)). The spectra have peaks at multi-ples of the 50 Hz power line frequency with both voltagesources, but the striking difference between the sources isat frequencies below about 50 Hz, where the HV sourcegenerates a broad background with an amplitude morethan ten times that of the LV source. The backgrounddue to the HV source persists even if its variable voltageis turned down as low as 10 V, although it disappears ifthe voltage is set to zero. This data convincingly showsthat the HV source is the origin of a large part of the theexcess noise first seen in figure 3 (d). We did not attemptto investigate the origin of the noise further, for exampleby directly measuring the voltage noise spectral densityof the two voltage sources. It is nevertheless clear thatelimination of excess noise due to the HV power supply,by filtering or improved design, would result in reduc-tions in the amount of time required to achieve a givenresolution in a measurement of ionisation chamber cur-rent, and more dramatic reductions in the time requiredto measure the background current. VI. ABSOLUTE AGREEMENT BETWEEN TWOREADOUT SYSTEMSA. Calibration of electrometer using reference currentsource
We now return to the comparison between the amme-ter and the electrometer. In this section, we investigatehow well the two systems agree in background-correctedmeasurements of a range of radioactive sources. As al-ready noted in section II, the gain factor of the ammeterwas regularly calibrated using a reference current sourceconsisting of a 1 GΩ standard resistor and a calibratedDVM. Here, we also calibrated the gain factor of the elec-trometer using the same reference current source. For allthe calibrations, the reference current was periodicallyswitched between a nominal zero setting, and 50 pA,yielding a difference current ∆ I cal = 49 .
995 pA. the dif-ference currents ∆ I A and ∆ I E were extracted from theinstrument readings. Figure 5 (a) shows values of ∆ I A (top-left inset) and ∆ I E (main plot) extracted from cal-ibrations of the ammeter and electrometer respectively,over times of several hours. The most striking differencebetween the two instruments is that the values of ∆ I E exhibit much more statistical scatter than those for ∆ I A (note the different y-axis scales for the main panel of fig-ure 5 (a) and the inset). This could be a consequence ofthe specialised design of the electrometer amplifier mod-ule: as discussed in section III, the input voltage noiseof the amplifier module will cause excess noise when itis connected to the 1 GΩ reference current source, andthe electrometer may have a larger input voltage noisethan the ammeter. However since we did not directlymeasure the voltage noise for either the electrometer orthe ammeter, this remains a conjecture.After averaging the statistical fluctuations in the cali-bration data of figure 5 (a), we find that the mean cur-rent difference indicated by the electrometer, (cid:104) ∆ I E (cid:105) , isoffset from ∆ I cal by a statistically significant amount:(∆ I cal − (cid:104) ∆ I E (cid:105) ) / ∆ I cal = (460 ± × − . This error,460 ppm, is much larger than the uncertainty in the ca-pacitance, voltage and time components used to calculate I E , although still much smaller than the uncertainties inthe radionuclide-specific ionisation chamber calibrationfactors. We now consider the possible causes of this er-ror.The most likely cause of the error is non-linearity ofthe voltage ramp. In a previous study on another typeof capacitor-ramp electrometer, non-linearity of the V ( t )ramp was at the level of a few parts in 10 for currents inthe range of 10 pA to 100 pA . The non-linearity wasassumed to arise due to dielectric storage, or other non-ideal properties of C stray . However, it could not be satis-factorally modeled, and the measured non-linearity wasused to assign empirical type B components to the un-certainty budget for the electrometer . Measurementsof V ( t ) were also made on the electrometer under inves-tigation in this study, and they also showed non-linearityat the level of a few parts in 10 . More extensive char-acterisation of the voltage ramp over a range of currentsare needed to clarity this error mechanism.As already noted in section II, a possible source of errorin capacitor-ramp electrometers is frequency-dependencein the feedback capacitor. We measured the frequencydependence of the capacitor (a sealed-gas unit of ∼
500 pF) over the range 50 − . However, thisstudy was based on a small sample of capacitors, andwe cannot conclusively rule out capacitor frequency de-pendence as the cause of the 460 ppm gain error in theionisation chamber electrometer.Finally, the error may be simply an artifact due tothe input resistance of the electrometer in conjunctionwith the 1 GΩ output resistance of the reference cur-rent source. The sign of the error (the indicated currentis less than the actual current) is consistent with thismechanism. The measured 460 ppm error would implyan input resistance of 460 kΩ, which is quite high but notimplausible. Future calibrations, using reference currentsources with different output resistances, will clarify thismatter. In the following comparison between the amme-ter and electrometer, we simply treat the calibration ofthe electrometer as yielding a correction factor, in thesame manner in which we calibrated the ammeter. FIG. 5. (a): The main plot shows the current indicated by thecapacitor ramp electrometer when supplied with a known cur-rent of . pA from a calibrated source. Each data pointis averaged from ∼ minutes of voltage ramps, and the errorbars indicate the standard error on the mean of the current cal-culated from the individual ramps. Horizontal dashed lines showthe calibrated current (upper line) and the mean of the indicatedcurrents (lower line). The upper left inset shows the current in-dicated by an ammeter when supplied with the same calibratedcurrent. The inset shares the same time axis, and averaging timeper point is the same as for the main plot, but note the differenty-axis scales of the inset and main plot. (b): Agreement betweenthe current measured by the electrometer and ammeter, whenconnected to an ionisation chamber in a series of measurementsof four different radionuclides. Red open points: electrometercurrent as indicated. The red dashed line with error bar showsthe weighted mean. Blue filled points: electrometer current cor-rected for the calibration factor determined from plot (a). Theblue dashed line with error bar shows the weighted mean. Eachmeasurement is corrected for background, and error bars indicatethe type A uncertainty. The nuclide and approximate current areindicated above each pair of data points. B. Background-corrected measurements using bothreadout systems
As a direct comparison, the electrometer and ammeterwere both used to measure background-corrected ionisa-tion chamber currents from four different radionuclides.Each measurement consisted of a raw data set similarto that shown in figure 4 (c), from which the back-ground corrected currents I AC and I EC were obtained.To ensure that random geometrical factors due to sourceplacement inside the chamber did not affect the compar-ison, the source was only put into the chamber once foreach comparison. So, for example the ammeter wouldbe used to measure first the empty chamber, then thesource. Next the electrometer would be used to mea-sure the source followed by the empty chamber. Thesocket at which the instruments were connected and dis-connected from the chamber was mechanically isolatedfrom the chamber via a cable to avoid disturbing the po-sition of the source when the instruments were swapped.As detailed, I AC already incorporates a correction fac-tor from the ammeter calibration. I EC was optionallycorrected, based on the calibration detailed in the previ-ous sub-section. Figure 5 (b) shows the normalised dif-ference between the two background corrected currentsboth with and without the calibration correction appliedto the electrometer current. After applying the correc-tion, the weighted mean of the 4 points yields the av-erage (cid:104) I AC − I EC I EC (cid:105) = ( − . ± . . ± . ∼ . VII. CONCLUSIONS
We compared examples of a feedback ammeter andan integrating electrometer, and we can conclude thatthe feedback ammeter, calibrated using a reference cur-rent source, can be considered as a viable alternative tothe integrating electrometer traditionally used for ioni-sation chamber readout. Measuring ionisation chambercurrents of a few tens of picoamps at an uncertainty levelof 0 . . .
01% for a current of 50 pA after 1000 secondsof averaging. However, when calibrated using a referencecurrent source, the electrometer was found to be in errorby 0 . .
01% to be achieved in justa few seconds of measurement time. We have also pre-sented the Allan deviation as a useful statistical tool forevaluating the stability of current measuring instrumentsas a function of measuring time. This helps the designof calibration protocols which make most efficient use ofthe available time to reach a desired uncertainty level.
ACKNOWLEDGMENTS
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