Download Guidelines on the determination of the sensitivity and calibration of

Guidelines on the determination of the sensitivity and calibration of ratio error of the Room
Temperature Current Comparator (RTCC)
MIKES, PTB, January 2015
Introduction
A low frequency room temperature current comparator (LFCC or RTCC) is designed for accurate
comparison of two AC currents at very low frequency (frequency range 0.2 Hz – 1 Hz). It is used in an
AC resistance bridge for establishing and maintenance of the ratio of currents equal to the ratio of the
number of turns in the coil windings. The required ratios in the RTCC can be chosen depending on the
ratio of the measured resistors. For accurate and reliable scaling of the currents, the calibration of a
current comparator should be periodically performed at all operating frequencies. The main method of
calibration is based on the measurement of the deviation from 1:1 for all ratio windings, staring from 1
turn coils and consequently increasing the number of turns using a binary build-up procedure.
In Fig. 1 a simplified diagram of the RTCC is presented. The windings of two different coils are wound
on the same high-permeability toroidal core: 1) a selected number of ratio windings and 2) a detection
winding. The RTCC is completed by electrostatic and magnetic shields (Cu foil and two annealed µmetal cans). The detection coil represents the inductive component of a parallel LC circuit. The
alternating currents to be compared have the frequency of this circuit’s resonance. These currents with
amplitudes I1 or I2 will flow through ratio windings with numbers of turns N1 or N2, respectively.
Toroidal core
I1
Rdet
N1
Ratio coil
I2
Ndet
C
Ldet
G
Vdet
Detection
coil
N2
Electrostatic and magnetic shields
Fig.1 Equivalent circuit of the RTCC with the ratio and detection windings and the parallel capacitor
for tuning the LC circuit to the required resonance frequency.
Sensitivity of the RTCC
The detector’s sensitivity Si(f) is defined as the ratio of the AC voltage in the resonant circuit, Vcal(f)
and the sum of the input currents generated in any of the ratio windings, or in the case of using N1 and
N2 :
Si (f) = Vcal(f) / Ical(f) = Vcal(f) / [I1 (f) N1 + I1 (f) N2]
(1)
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Si(f) is expressed in terms of V / A turn.
In [1] it was shown that the sensitivity of a current comparator operated at low frequencies may be
represented as:
Si(f) = 2 k f µA Nd / d,
(2)
where f is the frequency, Nd is the number of turns in the detection winding, µ is the initial permeability
of the magnetic core, expressed in H/m, A is the area of the magnetic core cross section in m2, k is the
coefficient of tuning, and d is the mean diameter of the magnetic toroid in m. With reducing the
frequency of operation (approaching DC for a better representation of DC resistance in resistance ratio
measurement) the sensitivity is reduced, but it can be compensated by increasing µA, k and Nd. The
coefficient k depends on the Q factor of the resonance circuit (Q=2πfLdet/Rdet) and can be maximized by
reducing the resistance Rdet of the detection coil and the dielectric losses in the winding self-capacitance
and in any other connected external conductance G. The higher the number of detection turns Nd, the
magnetic permeability µand the cross section area A of the toroid - the higher a sensitivity can be
obtained and the lower a ratio error can be detected. In a current comparator the magnetic core acts as
an indicator of zero magnetic flux, and does not transfer power from primary to secondary coil as in
voltage transformers.
The scheme of calibration of the sensitivity of the tested coils is presented in Fig.2. The measurement
can be performed by calibration of the reading of the Lock-in amplifier at each operational frequency f,
by feeding a small known current dIcal(f) into the tested coils connected in series, (or “N1+N2”
connection), and by measuring the corresponding voltage, dVcal(f).
Fig.2 Scheme of calibration of sensitivity of the tested coils
Before sensitivity measurement, it is necessary to determine the resonance frequency. As the sensitivity
depends on the frequency, it is necessary to measure the sensitivity at each operational resonance
frequency.
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Determination of ratio error
Generally, a deviation d from a 1:1 ratio (or ratio error) of two windings, (N1=N2) can be determined
when a current Imax is fed into these windings (connected in opposite polarity). Due to misbalance of
the ampere-turns, a small residual current, dIdet(f), is sensed by the detection coil. An error d can be
defined as:
d = dIdet(f) / ∑ [Imax(f)*N1 - Imax(f)*N2)]
(3)
where dIdet(f) is the residual current which can is detected during application of the same current,
Imax(f), into the two tested coils.
Estimation of the value of the current dIdet(f) is based on the measurement of the voltage dVdet(f)
induced in the detection coil and from the known sensitivity Si(f) or, dIdet(f) = dVdet (f) / Si (f).
Using the preliminary calibrated sensitivity in the used windings, Si (f) = Vcal (f) / Ical (f), a ratio error can
be expressed as:
d = [(Vdet(f)/Si (f)]/∑ [Imax(f)*N1 - Imax(f)*N2)]
= [(Vdet(f)/{dVcal/dIcal)}(f)] /∑ [Imax(f)*N1 - Imax(f)*N2)]
(4)
At fixed frequency a simplified relation for the ratio error can be defined as:
d = (Vdet / Si) / [Imax N1 - Imax N2], or d = (Vdet / [dVcal/dIcal]) / (Imax N1 – Imax N2]
(5)
and determined as a detected current dIdet(f) (estimated by measurement of the voltage dVdet(f) at the
resonance frequency using a lock-in amplifier) to the maximum current passing into the calibrated
windings.
In Fig 3 a simplified scheme of calibration of the RTCC with a lock-in amplifier is presented. A signal
generator (Agilent 33250) is used for setting the currents (up to 50 mA) at the frequency range 0.2 Hz 1 Hz in the windings (“N1-N2”) to be calibrated. The measured voltage dVdet(f) is proportional to the
residual current in the resonance circuit and is detected by the lock-in amplifier at the measured
frequency.
3
Vout = 1 V
R = 100 Ohm
Iout = 10 mA
at 1 Hz
Ratio
windings
Detection
coil
Generator
Agilent 53350
Lock-in
PE7265
16 t
C = 28 uF
16 t
RTCC
Fig 3 Simplified scheme of calibration of RTCC with applied current Imax = 10 mA, which is fed into
N1 - N2 ratio turns, the voltage of the resonance circuit is measured by a lock-in amplifier.
The guideline for the measurement of sensitivity and calibration of RTCC:
Resonance frequency measurement
1. Measurement of a resonance curve of the resonance circuit formed by detection coil and the
parallel capacitor to define the resonant frequency peak for each used capacitors. Connect an
output of a Lock-in amplifier, (see Fig.2) through an output resistor (with value, depending on
the sensitivity of the used ratio coil, for example, Rout=10 MOhm) to any of the ratio coil to
supply a suitable current.
2. Increase the current into ratio coil and measure the signal in Lock-in amplifier using settings for
X and Y component and make “auto-phase” function in Lock-in.
3. By changing the frequency of the output signal of Lock-in (near the resonance, in the range of
about 20 mHz- 40 mHz) – measure an output of the Lock-in, (using R and Q components) and
define the maximum of the resonance curve.
4. Repeat measurement of resonance for each capacitor defining the resonances in 0.2 Hz – 1.0 Hz
range.
Sensitivity measurement
5. Connect output of a signal generator, (for example Agilent 33250) in according to the circuit in
Fig. 2, through a resistor (for example,10 MOhm, its value depend on the number of turns of the
calibrated windings) to the ratio windings connected in series direct (N1+N2) polarity.
6. In signal generator, set the required resonance frequency, according to the previous
measurement of the resonances and the used capacitor and set the output current (for example,
f=0.719 Hz, Vout=1 mV, Rout=10 MOhm, Ical =0.1 nA).
7. Connect output of the detection coil of resonance circuit to the input of Lock-in amplifier (for
example PE7265) and check the settings of amplifier and the setting of internal reference signal.
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8. Increase output current Ical so that to get relatively large signal in X and in Y component and
repeat “auto-phase”, so that maximum signal was in X component.
9. Set the current Ical to lower value and measure an output voltage (X component) on detection
coil at the corresponding resonance frequency Vcal.
10. Estimate sensitivity Si = Vcal / Ical
11. Repeat these measurement (making “auto-phase” before measurement at each new frequency)
and estimate sensitivity for all operational frequencies.
Ratio error measurement
12. Connect output of a signal generator through a 100 Ohm resistor to the ratio windings
connected in series opposite polarity in according the scheme on Fig.3.
13. Set the required resonance frequency, according to the used capacitor connected in resonance
circuit.
14. Connect output of the detection coil of resonance circuit to the input of Lock-in amplifier (for
example PE7265) and check the settings of amplifier and reference signal.
15. Increase output voltage and corresponding current Imax of a signal generator up to the value,
when the voltage on the detection coil can be detected and measured. Measure this voltage Vdet
on the resonance circuit at each operation frequency.
16. Estimate the value of the deviation from the ratio according to the equation (5):
d = (Vdet / [dVcal/dIcal]) / (Imax N1 – Imax N2]
An example of the resonance frequency measurement with LFCC-B is presented in Fig.4. Examples of
sensitivity measurement and calibration of the ratio error for the developed RTCC are presented in the
Figures 5 - 11 below.
140
143 mHz
218 mHz
364 mHz
511 mHz
718 mHz
Sensitivity (V / A t)
120
100
80
60
40
20
0
100
200
300
400
500
600
700
800
Frequency (mHz)
Fig. 4. The resonance frequencies of the resonance circuit formed by the detection coil of LFCC-B and
set of five capacitors.
Examples of the sensitivity measurements for the windings with number of turns 8, 16, 32 and 64 using
1 nA current at 0.71 Hz and for the 512 turn winding using current 10 pA are presented in Fig. 5 a) and
4 b) accordingly.
5
800
4000
1 nA in 8-64 t coils
at 0.71 Hz
64 t.
10 pA in 512 t coils
at 0.71 Hz
600
32 t.
2000
16 t.
1000
Voltage (nV)
Voltage (nV)
3000
400
200
8 t.
0
A
15:18
B
C
D
E-2
E-1
15:38
15:58
Time
a)
0
16:12
A
B
C
16:22
16:32
D
16:42
Time
b)
Fig. 5. Sensitivity test of detection coil, measured with chopper amplifier for 8 to 64 turn coil at 0.71
Hz with gain 104 and b) for 512 turn coil with chopper amplifier gain of 105.
Summarized comparative results of the sensitivity measurements for two LFCC are presented in Fig.6.
These measurements have been done using a Lock-in amplifier (SR 850). A 0.4 nA current was biased
from the output of this device through a 10 MΩ resistor into 100- or 512-turns ratio windings of LFCCA or LFCC-B, respectively. Before being connected to the input of the lock-in, the AC voltage across
the detection coil has been pre-amplified by using an ultra-low noise chopper amplifier [2]. The resonant frequency covers the range from 1.02 Hz (LFCC-A, using C=28 µF), down to 0.144 Hz (LFCC-B
and using C=700 µF), for the quality factors we found values from 25 to 12.
120
Sensitivity, V/A-t
100
LFCC-B
LFCC-A
80
60
40
20
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, Hz
Fig. 6. Resonant-frequency dependent sensitivity of two LFCC prototypes.
An example of the sensitivity and calibration of the ratio error for 16:16 turns winding is presented in
Fig. 7. Maximum current (supplied from functional generator Agilent 33250A), used in this
measurement was: Imax=50 mA (peak value).
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During calibration of LFCC-B with different windings, the value of the used current, dIcal (for
sensitivity measurement), depend on the tested winding and is usually in the range of 0.1 A for 1 turn
coil, and down to 10 pA for 2048 turn coil. The results of the calibration for different number of turns
are presented in Figures 8 - 11. In Fig. 8 the deviations from 1:1, measured at 722 mHz for the coils
starting from one turn and up to 16 turn coils are presented.
Four one turn coils are placed over the wounded cables with the ratio windings and are separated by 90
degree relatively each other. It is seen that the largest deviations (for one turn coils) is about 5 parts in
10-8, and these deviations are varied for different combinations of the used coils. One turn coils are the
worst case of coupling between coils and have the maximum ratio error. For the 1:1 ratio with 4 turn
coils, (formed from series connection of four one turn coils and four turn coil), the deviation is below
10·10-9. The estimated deviation d from 1:1 for the number of turns more than 8 turns are below 5·10-9.
16d-sh /16e-2
20
-8
Ical=10 A
Vdet, V
15
-5
Vcal = 2 10 V
10
Ical= 50 mA
5
-7
Vx = 10 V
0
18:24
18:29
18:34
18:39
18:44
Time
Fig. 7. Sensitivity and calibration of ratio error measurement for 16:16 turn windings at 0.72 Hz.
Results of the measurement of deviations from 1:1 ratio for the four different combination of 512:512
turn coils (named 512-a, 512-b, 512-c and 512-d) measured at 722 mHz are presented in Fig. 9. It is
seen that the deviations of the tested combinations are within 3·10-9.
Deviation from 1:1 ratio in LFCC-B for different number of turns, which have been performed at 0.143
Hz – 0.722 Hz frequency range is shown in Fig.10.
50
40
Ratio error, 10
-9
2:2
1:1
30
20
4:4
10
16:16
8:8
0
0
5
10
15
20
25
30
35
Number of turns
7
Fig. 9. Ratio error in LFCC-B measured at 722 mHz for different coils, starting from 1:1 turn and up to
16:16 turn windings.
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4
Deviation, x10
-9
c-b
c-b
2
0
c-a
c-d
c-d
b-d
b-a
-2
--
c-b c-d
--
b-c
c-a c-b c-d b-d b-a b-c
combination of 512 coils
Fig.9. Deviation from 1:1 for 512 / 512 turn coils, for different combination of four (a, b, c, d) 512 turn
coils at 722 mHz.
Deviation from 1:1 for 1024 / 1024 turn coils for combination of four 512 turn coils connected as
(b+c)/(a+d) measured at 722 mHz, 515 mHz , 370 mHz, 224 mHz and 143 mHz are presented in Fig.
10.
at 722 mHz
at 515 mHz
at 370 mHz
at 224 mHz
at 143 mHz
1
-9
Deviation (x10 )
2
0
-1
-2
error bars are nor shown, but at least 0.5 10
0
200
400
600
-9
800
1000
Frequency, mHz
Fig. 10. Deviation from 1:1 for 1024 / 1024 turn coils for combination of four 512 turn coils
(b+c)/(a+d) at 722 mHz, 515 mHz, 370 mHz, 224 mHz and 143 mHz.
Measurements at 143 mHz and 224 mHz have been done with the use of chopper amplifier with gain
3·105. It is seen that the deviations in the measured frequency range are within 1·10-9. During
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sensitivity measurement it was observed the influence of the applied current on the measured
sensitivity. With increase of the applied current the sensitivity was reduced, means that probably there
is influence of the non-linearity of the magnetic permeability in the magnetic core. An example of the
results of measurement of sensitivity with different currents, in the frequencies in the range 143 mHz –
718 mHz is presented in Figure 11. With increase of applied current, possibly the magnetic flux in the
core goes to saturation region and the sensitivity is reduced.
160
143 mHz
218 mHz
364 mHz
511 mHz
718 mHz
140
120
S (V/AT)
100
80
60
40
20
0
0.01
0.1
1
10
100
1000
I (nA)
Fig. 11. Sensitivity of LFCC-B, measured with currents 0.01 nA - 1 uA, using 512 turn winding in
frequency range 143 mHz - 718 mHz.
[1] P.N. Miljanic, N. L. Kusters, and W. J. M. Moore, “The development of the current comparator, a
high-accuracy AC ratio measuring device”, Trans. AIEE (Commun. Electron.), vol. 81, pp. 359-368.
Nov. 1962.
[2] D. Drung and J.-H. Storm, “Ultralow-Noise Chopper Amplifier with Low Input Charge Injection”,
IEEE Trans. Instrum. Meas., vol. 60, no. 7, pp. 2347-2352, Jul. 2011.
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