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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 4, AUGUST 2007
A Current Source for Picoammeter Calibration
Luca Callegaro, Vincenzo D’Elia, and Bruno Trinchera
Abstract—A current source, which is to be employed in the calibration of low-current meters (picoammeters and electrometers),
is presented here. The output current range is 100 fA to 100 pA
and is directly traceable to calibrated standards of dc voltage,
capacitance, and time period. The source is based on a lowfrequency (≈1 mHz) trapezoidal signal generator, which charges
and discharges a gas-dielectric capacitor; the voltage is monitored
with a voltmeter that is triggered by a precision time base. The
source has been employed during March 2006 for the Italian participation to the supplementary comparison EUROMET.EM-S24
and will be part of an extension of the Italian national standard
of dc current. However, being composed of low-cost electronics
and common commercial instrumentation, the source can also find
useful application in secondary calibration laboratories.
Index Terms—Calibration,
generators.
current
measurement,
signal
I. I NTRODUCTION
T
HE generation of traceable dc currents having nominal
values below the nanoampere level is of great interest for
the calibration of current detectors, electrometers, picoammeters, and electrochemical transducers [1].
Current sources made from reference voltage sources and
high-value resistors [2] tend to perform poorly below the picoampere level. This is because resistors of values above the
gigaohms range have high voltage, temperature, and humidity
coefficients and low stability; furthermore, low-current meters
have significant voltage burden,1 which constitutes a cause of
error in the measurement of the applied voltage.
An interesting alternative for the generation of low-value dc
currents is to apply a linear voltage ramp to a differentiating
capacitor. Reference [3] gives a simple and effective realization of the idea; references [4]–[6] describe metrology-grade
realizations.
The following describes an implementation of the technique
based on a purposely built generator and commercial instrumentation, which is suitable for the calibration of current meters
in the 100-fA to 100-pA range.
II. T ECHNIQUE
The basis of the technique consists in applying a linear
voltage ramp v(t), through a differentiating capacitor C, to the
Manuscript received June 30, 2006; revised March 28, 2007.
The authors are with the Department of Electrical Metrology, Istituto
Nazionale di Ricerca Metrologica, 10135 Torino, Italy (e-mail: lcallega@
inrim.it).
Digital Object Identifier 10.1109/TIM.2007.900128
1 For
example, Keithley mod. 6430 has a maximum voltage burden of 1 mV.
Fig. 1. Block schematics of the experimental setup. A, meter; G, ramp
generator; V, sampling voltmeter; C, differentiating capacitor; T, trigger time
base source; PC, data acquisition computer.
Fig. 2. Experimental setup. Labels on the photo correspond to block schematics of Fig. 1. The size of the generator described in Section III-A can be
appreciated.
input of the meter under calibration. If the ramp is known, a
displacement current i(t), i.e.,
i(t) = C
dv(t)
dt
(1)
can be indirectly determined as a calibrated stimulus.
Fig. 1 shows the block schematics of the setup. A is the meter
under calibration. The ramp generator G is connected to a
sampling voltmeter V and to the high-voltage port of capacitor
C. The low-voltage port of C is connected, either directly (by
mating panel connectors on both cases) or with a short cable
length, to the input of A. V and A are triggered by the precision
timer T. Readings from V and A are acquired and stored by
PC. A photo of the source is given in Fig. 2.
If v(t) is a continuous piecewise linear function, to each
slope of v(t), a stable current value I is generated, and (1)
is valid even if a (constant) voltage burden is present on the
input of A. A symmetric trapezoidal shape permits both the
0018-9456/$25.00 © 2007 IEEE
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CALLEGARO et al.: CURRENT SOURCE FOR PICOAMMETER CALIBRATION
1199
current enters an integrator4 having feedback capacitor C3. The
integrated signal v(t) is shown in Fig. 3, is available as output,
and drives also the modulator threshold.
Losses of C3 cause small deviations of the ramp from
perfect linearity. To compensate the effect, a feedback current
generated by an active network is added to the integrator input;
the network is trimmed until a ramp as linear as possible is
obtained. The remaining deviations are caused by dielectric
absorption [8], [9] and could be reduced by a more complex
feedback network [5], which are only taken into account here
during data processing.
Each linear piece of the trapezoidal ramp has a duration of
≈200 s. Since the ramp span is ±10 V, the slope is 100 mV s−1
within a few parts in a thousand. When the variable reference is
chosen, the voltage slope can be varied.
Fig. 3. (Continuous line) Voltage output v(t) of generator G, as measured
by sampling voltmeter V. (Dotted line) Calibration output current i(t), as
computed from v(t) and capacitance C with (1).
B. Ramp Measurement
Two voltmeters V, namely an Agilent Tech. 34401 digital
multimeter (6.5 digits, with an accuracy of 400 µV on the 10-V
scale) and an Agilent Tech. 3458A (8.5 digits), are supported
by the acquisition program, which is specifically built for signal sampling. Results are consistent within the corresponding
accuracies of the two instruments.
C. Data Acquisition and Processing
Fig. 4. Simplified electrical schematics of the generator G of Fig. 1. “Digital”
part that feeds the integrator having transfer function given by R1 and C3. R5
injects a current to compensate C3 losses.
calibration of two current points, i.e., ±I (during ascending and
descending slopes), and of the meter offset (during horizontal
slopes, when v(t) is constant). Fig. 3 shows an example of
the trapezoidal wave output of G as measured by V and the
corresponding computed output current i(t).
III. I MPLEMENTATION
A. Generator
A simplified schematics of the voltage ramp generator G
is shown in Fig. 4. A voltage reference Vref (either fixed
at 2.5 V or variable with a potentiometer) is chopped by a
delay generator and enters an AD6302,3 modulator; the voltage
output is transformed in a small current with resistor R1; such
current is proportional to the final current i(t) of Fig. 3. The
2 All brand names in the paper are used for identification purposes. Such
use implies neither endorsement by Istituto Nazionale di Ricerca Metrologica
(INRIM) nor assurance that the equipment is the best available.
3 Analog Devices AD630 Balanced Modulator/Demodulator, ±1 gain, employed as a symmetric waveform generator [7].
Both V and A are triggered simultaneously by T, which is
a purposely built quartz digital synthesizer, with f ≈ 950 mHz,
calibrated against Italian national frequency standard. Data are
acquired via a general-purpose interface bus driven by a very
simple C program with no user interface. Recorded voltage and
k
, which are acquired at times tk , are
current samples vk and Im
simply stored continuously.
The entire data processing is conducted offline with a Matlab
program and the Statistics toolbox. The program is able to
identify different ramps of the voltage waveform and process
each ramp separately. For each ramp, the evaluation of the
meter error ∆ is given by the following algorithm:
• the point-per-point difference ∆k is computed, i.e.,
vk+1 − vk
k
(2)
∆k = Im − C
tk+1 − tk
• acquired points k corresponding to transients are automatically eliminated (both by bounds on maximum acceptable
|∆k | and by discarding a fixed number of points after a
ramp transition);
• ∆k can be affected by an additive error gvk due to the
nonzero conductance g of C. To keep the whole experimental information, the error ∆ of A is found by robustly
fitting the couples (vk , ∆k ) with a straight line; the fit is
then evaluated at V = 0.
In this way, it is possible to take into account the slow variations
of i(t) caused by residual nonlinearities in the voltage ramp (or
4 Burr-Brown OPA2111, Dual Low Noise Difet Operational Amplifier,
√
±2 pA bias current, 0.8 fA/ Hz current noise. The second section of the
amplifier is used to generate the feedback current.
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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 4, AUGUST 2007
by drifts in the generator). Algorithm steps are repeated for each
ramp; horizontal sections give instrumental offsets, which are
averages (for positive and negative voltages) that the user may
want to subtract to find the final result.
IV. C APACITORS
The differentiating capacitor C must have a very low parallel
conductance g, a minimal dielectric absorption, and a very
small frequency dependence since it will be calibrated in ac
regime (typical frequency of 1000 or 1592 Hz) and operated
near dc. Hence, it must be a gas- or vacuum-dielectric capacitor.
Several metrology-grade gas-dielectric capacitor models
have been tested: Agilent 16380A series (C = 1 pF, 10 pF,
100 pF, and 1 nF), General Radio 1404 series (C = 10 pF,
100 pF, 1 nF), General Radio 1403-K (C = 1 pF), Sullivan
C8001 (C = 10 pF), C8002 (C = 100 pF), and C8003 (C =
1 nF), which are all calibrated against Italian national standard
of capacitance by substitution with an automated capacitance
bridge.5
The ac–dc relative capacitance difference for gas-dielectric
capacitors is either assumed to be implicitly negligible [5]
or that its contribution to uncertainty is small (e.g., 10 µF/F
[6]). Older papers [10], [11] have indeed shown a frequency
dependence caused by thin-film layers deposited on electrode
surfaces; unfortunately, to our knowledge, no data are available
for commercial capacitor models.
To measure this ac–dc difference, a measurement setup
that is similar to that described in [12] has been constructed.
The measurement consists in a delicate charge measurement
(resolution required: at least 100 fC). Very preliminary results
of measurements on General Radio 1404 1000-pF capacitors
give an ac–dc relative capacitance difference below 200 µF/F,
which is different for different units of the same capacitor
model. Older units (about 30 years since manufacture) appear
to have a larger ac–dc difference than newer units. Before
including these corrections in the model or the uncertainty
budget, extensive testing with the setup will be necessary. At
present, possible ac–dc capacitance difference is taken into
account as an uncertainty contribution.
V. R ESULTS
A. Calibration Tests
Tests of the current source have been conducted by calibrating commercial picoammeters (Keithley mod. 6514, 6517, and
6430 have been employed; extensive tests concentrated on mod.
6517 and later on mod. 6430) on current values of ±100 fA,
±1 pA, ±10 pA, and ±100 pA. Fig. 5 shows an expanded view,
for the positive ramp, of the current generated by the source i(t)
and of the corresponding reading im (t) of the picoammeter.
For each current, around ten full ramps have been conducted,
each ramp duration being ≈800 s; hence, a complete calibration
(four current values) requires about 9–10 h of measurement.
5 Andeen-Hagerling mod. 2500 A ultraprecision capacitance bridge. Instrument stability when measuring, e.g., 100 pF, is better than 1 µF/F.
Fig. 5. Expanded view of the (continuous line) calculated i(t) current from G
and (dotted line) corresponding readings im (t) of A, during a positive voltage
slope for the generation of a nominal current of 100 pA and measurement with
Keithley mod. 6517. Residual nonlinearity of the voltage ramp and the effect of
the parallel conductance of C can be observed.
TABLE I
TYPE-B EVALUATION OF THE SOURCE UNCERTAINTY uS (I)
B. Uncertainty
A Type-B evaluation of source uncertainty uS (I) of the
generated current I is shown in Table I. The contributions that
are taken into account are as follows:
• capacitance
• calibration, 2 µF/F, 1:1 substitution with Italian national standard of capacitance;
• temperature dependence, 8.6 µF/F for 1-pF standards; 1.4 µF/F for 10-, 100-, and 1000-pF standards;
• ac–dc deviation (see Section IV): a relative uncertainty contribution of 30 µV/V has been considered safe;
• ramp voltage measurement: calibration, 5 µV/V (Agilent
mod. 3458A, dc sampling, 10-V range, within 90 days
after calibration);
• triggering: frequency meter calibration, 1 µHz/Hz;
• compensation of capacitor leaks in the fitting process, 5 ×
10−18 · I + 10 aA.
The calibration uncertainty uC (I) of a specific meter must
also take into account meter noise,6 displaying resolution, and
6 Meter noise is caused by intrinsic noise of the meter electronics, which may
be strongly affected by input capacitance C, and by the source noise filtered
by the acceptance analog and digital bandwidths of the meter. The noise of the
source alone is of little significance, and we prefer to treat all noise present as
“meter noise.”
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CALLEGARO et al.: CURRENT SOURCE FOR PICOAMMETER CALIBRATION
drifts (mainly of thermal origin [6]). Such effects vary strongly
between different models and may be dominant, particularly
in the lowest current ranges. Because the algorithm that is
employed for data processing includes nonlinear (robust) data
treatment, a complete description of uC (I) evaluation will be
presented elsewhere.
VI. C ONCLUSION
A dc current source that is working in the range 100 fA of
100 pA has been developed. The source will be part of the
Italian national standard of dc current to extend its range toward
low currents. The uncertainty of the generated current is adequate for most demanding calibrations. Despite this, the source
is simple, employs low-cost electronics and standard instrumentation that is typically available in calibration laboratories,
and could prove useful for calibrations at secondary level.
R EFERENCES
[1] M. Breten, T. Lehmann, and E. Bruun, “Integrating data converters for
picoampere currents from electrochemical transducers,” in Proc. IEEE
ISCAS, Geneva, Switzerland, May 28–31, 2000, pp. V711–V712.
[2] G. Landis and M. Godwin, “Portable precision dc voltage–current transfer
standard for electrometer calibration,” Rev. Sci. Instrum., vol. 53, no. 8,
pp. 1290–1291, Aug. 1982.
[3] R. A. Pease, “What’s all this tempco stuff, anyhow?” Electronic Design,
Jun. 1997.
[4] G. Rietveld and H. Heimeriks, “Highly sensitive picoampere meter,” in
Proc. CPEM Conf. Dig., May 28–31, 1996, pp. 332–333.
[5] G.-D. Willenberg, H. N. Tauscher, and P. Warnecke, “A traceable precision current source for currents between 100 aA and 10 pA,” IEEE Trans.
Instrum. Meas., vol. 4, no. 2, pp. 436–439, Apr. 2003.
[6] H. E. van den Brom, P. de la Court, and G. Rietveld, “Accurate subpicoampere current source based on a differentiating capacitor with
software-controlled nonlinearity compensation,” IEEE Trans. Instrum.
Meas., vol. 52, no. 2, pp. 554–558, Apr. 2005.
[7] AD639 Data Sheet, Norwood, MA: Analog Devices. see Fig. 12, General
Purpose Function Generator. [Online]. Available: http://www.analog.com/
UploadedFiles/Obsolete_Data_Sheets/55889558331308887AD639.pdf
[8] R. A. Pease, “Understand capacitor soakage to optimize analog systems,”
Electronic Design, pp. 125–129, Oct. 1982.
[9] K. Kundert, “Modeling dielectric absorption in capacitors,” Internet
Draft, 2005. [Online]. Available: http://www.designers-guide.org/
Modeling/da.pdf
[10] A. V. Astin, “Measurement of relative and true power factors of air capacitors,” J. Res. Natl. Bur. Stand., vol. 21, pp. 425–456, Oct. 1938.
1201
[11] B. D. Inglis, “Frequency dependence of electrode surface effects in
parallel-plate capacitors,” IEEE Trans. Instrum. Meas., vol. IM-24, no. 2,
pp. 133–150, Jun. 1975.
[12] V. Bego, J. Butorac, and G. Gas̆ljević, “Measurement of electrode surface
effects in air capacitors using a precise coulombmeter,” IEEE Trans.
Instrum. Meas., vol. 38, no. 2, pp. 378–380, Apr. 1989.
Luca Callegaro was born in Venice, Italy, in 1967.
He received the Laurea degree in electronic engineering and the Ph.D. degree in physics from the
Politecnico di Milano, Milano, Italy, in 1992 and
1996, respectively.
Since 1996, he has been with the Department of
Electrical Metrology Department, Istituto Nazionale
di Ricerca Metrologica (formerly Istituto Elettrotecnico Nazionale Galileo Ferraris), Torino, Italy, where
he was a member of the Scientific Council from 1998
to 2005. He is currently in charge of the research
line on ac electrical quantities and of Italian national standards of capacitance,
inductance, ac resistance, and ac voltage ratio. From 2003 to 2006, he was
an Adjunct Professor of electronic measurements at Politecnico di Torino. His
current research interests are on traceable measurements of low-level noise in
circuits and devices at audio frequency.
Vincenzo D’Elia was born in Torino, Italy, in 1965.
He received the high school degree in electronics
from IPSIA “G. Plana,” Torino, in 1988.
After working in a telecommunication company,
in 1996, he joined the Department of Electrical
Metrology, Istituto Nazionale di Ricerca Metrologica
(formerly Istituto Elettrotecnico Nazionale Galileo
Ferraris), Torino. He is currently involved in impedance measurements.
Bruno Trinchera was born in 1973. He received
the Laurea degree in physics from the University
of Torino, Torino, Italy, in 2001 and the Ph.D. degree in metrology from the Politecnico di Torino, in
2005. His research on radiation thermometry toward
the Ph.D. degree was conducted at the Istituto di
Metrologia “Gustavo Colonnetti” [now merged in the
Istituto Nazionale di Ricerca Metrologica (INRIM)],
Torino.
In 2005, he joined the Department of Electrical
Metrology, INRIM, where he currently works on
high-accuracy impedance comparison systems based on digital signal synthesis.
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