Technical information

Performance of the primary-standard resistance thermometry
bridge model CTR9000 (F900)
WIKA data sheet IN 00.31

The model CTR9000 primary-standard resistancethermometry bridge is designed specifically for resistancethermometry to provide the best possible accuracy. Workon validating the performance lasted 1 ½ years. During thistime a large number of tests were being performed. This
report provides details of some of the key tests used todetermine the more critical aspects of the CTR9000 (F900)
performance.
The work was carried out in the research and development
department, which is not air-conditioned, ambient
temperatures therefore varied between about 16 °C and30 °C. This environment is not ideal for precision electricalmeasurement. It is therefore realistic to expect that theCTR9000 (F900) should equal or exceed the performanceindicated by these tests when used in most temperaturelaboratories, provided good measurement.

Model CTR9000 primary-standard resistancethermometry bridge, version 20 ppb accuracy

Accuracy
A key performance parameter for the model CTR9000(F900) primary-standard resistance thermometry bridge isits accuracy, since this ultimately limits the measurement
uncertainty that can be achieved using the bridge.
The high accuracy of ±20 ppb claimed in the specification isdifficult to validate. This is due to the uncertainty of the tests
used and the difficulty, in finding suitable products for use insuch tests.
Following approaches were taken to validate the accuracy:
Internal consistency check
The model CTR9000 (F900) primary-standard resistancethermometry bridge uses a ratio transformer to make themeasurement (figure 1):

WIKA data sheet IN 00.31 ∙ 03/2015

Fig. 1: Measurement concept
Ratio transformer
I:nRS

Detector
RXPage 1 of 6

The two resistances RS and RX carry the same current. Theratio transformer is used to balance the voltage developed
across an unknown resistance (RX) against that across aknown standard resistance (RS). Since the ratio of the voltage
across the primary and secondary of an ideal transformer isequal to the turns-ratio (n), the ratio of the resistances RX andRS then equals the turns-ratio:
RX = n ∙ RS (at balance)
The ratio transformer is actually a series of cascaded
transformers. Each transformer has tappings in decimal
intervals (10:1, 10:2, 10:3 ... 10:9) and provides one decadeof resolution for the bridge. Since the tapped secondary
comprises a number of individual windings, it is possible toconnect any two of these windings “back-to-back” and use asensitive detector directly to measure the difference between
them. From this we can calculate the linearity errors thatwould occur when the winding segments are built up into thecomplete secondary winding.

However, this approach does not subject the windings to
the common voltages they will experience in practice. Thisis important since the complex interwinding capacitance
relationships will inject current that depends on thesecommon mode voltages. The approach used was therefore toconnect all the segments of the secondary in their intended
arrangement and to compare these with a reference winding.
The ratio transformer has two “extra” windings that normally
drive subsequent decades and one of these was used as thereference in the measurement.
The most significant ‘decade’ actually provides a ratio up to
1.2 to give the required range for thermometry. This decade
effectively determines the measurement linearity, since it ishere where the signals are greatest and therefore where any
ratio errors have the most impact on the measurement.
The winding inter-comparison was made on this decadein order to confirm the resistance thermometry bridge
measurement linearity. The results (with measurementuncertainties) are shown in figure 2.

Fig. 2: Non-linearity caused by ratio transformer errors

Error/ppb of UNITY

+1.0

0.0

Uncertainty shown with k = 2
-1.0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

Ratio
This test confirms that the non-linearity caused by ratio
errors in the transformer is less than 1 ppb and is therefore
insignificant compared with the specified performance of
20 ppb.
This test measures linearity only; it does not check whether
the full winding accurately provides a ratio of unity. Anyerrors in either the zero or unity ratio measurements further
contribute to the total measurement accuracy achieved by
the resistance thermometry bridge.

Page 2 of 6However, it is straightforward to check “unity” performance byconnecting the potential terminal for RX to RS.
It is also easy to check “zero” performance by connecting
a four-terminal short-circuit in place of RX. These test
functions are built into the bridge and made available via
front panel keys. They provide a simple and useful instrument
performance check.

WIKA data sheet IN 00.31 ∙ 03/2015

Complement check
Although the model CTR9000 (F900) primary-standard
resistance thermometry bridge is equipped with a UNITY
self-test function, it is desirable to check the accuracy of theratio measurements when using actual resistors.

This was overcome in the tests by using reed relays to swap
over connections to the resistors within a few milli-seconds, atime frame that is short enough to have no negligible impact
on the resistance.

This can be achieved by connecting two resistors of similarvalue to the bridge and measuring the ratio, then swapping
over the resistors and re-measuring the ratio. The ratios
should be the reciprocal of each other so that the productof the two ratios should be unity. The measurement error istherefore half the difference between the product of the tworatios and unity.

The temperature coefficient of the resistors (2 ppm/°C) meanthat a 1 mK change in temperature yields a 2 ppb error. The
resistors used in the test were therefore chosen to havematched temperature coefficients, they were used in a stabletemperature environment and the measurements were taken
quickly in order to minimise the effect of temperature coefficient on the measurement.

Two Wilkins resistors were used in the tests. Although thetemperature coefficient and power coefficient of these resistors are low, they are significant at the level of measurement(ppb) we are working at. The interruption of the power tothe resistors whilst they are being swapped over manuallycauses the temperature and therefore the resistance of theresistors to change significantly followed by a relatively longrecovery.

The result of complement checks in a number of resistancethermometry bridges is shown in table 1. The complement
checks confirm that the ratio accuracy of the bridge at unity is
within specification.

Table 1: Complement errors measured

CTR9000 (F900) S/N

R1/R2

R2/R1

R1/R2 x R2/R1 Error/ppb

7869005009

1.000037014

0.999963000

1.000000013-6.5

78669003007

1.000032194

0.999967804

0.999999997

1.57869001005

1.000035132

0.999964862

0.999999992

4

Comparison with a traceable IVD

For this, a ratio test unit (RTU) was used, which is aninductive voltage divider (IVD) of our own design that is used
as a company reference standard.

The uncertainties (k = 2) for both measurements are shownby the “error bars”. Interestingly, the resistance thermometry
bridge “error” is a mirror image of the calibration ‘error’ determined by PTB.
This suggests that the calibration ‘errors’ determined in thistest are the result of “errors” in the values assigned by PTB in
their calibration and are not real. This does not mean that thePTB values are wrong, since the nominal or design values for
the RTU are comfortable within the uncertainties declared byPTB.

The RTU provides ratios in integer multiples of elevenths;
this particular ratio set is useful as it exercises all the digitsof every decade when used over the range zero to unity andthereby provides a thorough check of the ratio tappings. The
RTU was sent to PTB, the national standards laboratory ofGermany for calibration.

With the uncertainties available on the PTB calibration of
the RTU, it is not possible to use this test alone to confirm
the accuracy. However, the striking mirror image relationshipbetween the two results together with the design calculations
for the RTU support the view that it is legitimate to use thenominal RTU ratios in the test.

Although the design calculations and measurements on theratio transformer indicate that the model CTR9000 (F900)
primary-standard resistance thermometry bridge achieves
the stated accuracy, it wanted to find some way of providing
a performance check for the whole instrument that was
traceable to national standards.

WIKA data sheet IN 00.31 ∙ 03/2015

Page 3 of 6

If WIKA use the nominal design values for the RTU in thecalibration test, we find that the errors are very small.
The maximum error is only 14 ppb and the standard deviationis 5 ppb.

measurement system easily achieve the stated 20 ppb
accuracy. Additionally, the comparison of the resistancethermometry bridge against the RTU indicates that thelinearity of the complete) instrument is within its specification.

The internal consistency checks confirm that the linearity of
key components within the resistance thermometry bridge

NoiseAlthough not part of the formal specification of the instrument, the noise performance of the model CTR9000 (F900)
primary-standard resistance thermometry bridge is vitalin determining the measurement uncertainty that can beachieved with this equipment.
The resistance thermometry bridge measures resistanceratio by balancing the voltage across the known andunknown resistances using a ratio transformer. The complex
electronics surrounding the transformer serve to ‘bootstrap’
the transformer so that the magnetising currents in the transformer do not load the resistances significantly as this would
lead to measurement errors. These circuits do not directly
form part of the measurement circuit, so their contribution tonoise is limited to the noise on the very small bias currents
drawn by the amplifiers that are connected to the potential
leads of the resistance RS.

The null balance detector used also contributes to themeasurement noise. The bridge impedance is matched to thenoise impedance of the detector using a transformer in orderto optimise measurement noise. For an ideal transformer, any
resistance ‘seen’ through a transformer has its impedance
transformed by 2:1.
The detector system noise (referred to the detector amplifierinput) can be viewed as an equivalent voltage noise (VN) andcurrent noise (IN) as shown in figure 3.
The easiest way to determine the contribution of detector
noise to the total measurement noise is to refer the detector
noise components to position XX.

Fig. 3: Noise matching system used
Ratio transformer
I:nAXRSImpedance matching transformer
I:mPre-amplifier

VNBINXRXDetectorCGuardamplifier

AC bridge

Page 4 of 6Detector with impedance matching

WIKA data sheet IN 00.31 ∙ 03/2015

At this point the impedance of the bridge is:
RB = RX + n ∙ 2 ∙ RS
Note:
When measuring low resistances (high-temperatureSPRTs or cryogenic applications), the lead resistances are
significant and need to be included in the calculation ofbridge impedance.
For the purpose of this analysis they are ignored, so thenoise VN at X-X is given by:
VN ∙ 2 = [m ∙ IN ∙ RB] ∙ 2 + [ VN ] 2
The optimum (lowest VN 2) value for m (transformer setting)is determined by differentiating this expression w.r.t. m andsetting this to zero to yield:
Minimum noise when:
VN = m ∙ 2 ∙ R ∙ BConsidering that an ideal transformer transforms any
impedance by n2, this is equivalent to stating that optimum
noise performance is achieved when the transformer
matches the detector noise impedance to the measurement
circuit impedance. This noise matching facility enables theresistance thermometry bridge to approach the fundamental
Johnson Noise limit over the normal resistance measurement
range used in thermometry.

An Excel spreadsheet has been produced that calculates thetheoretical noise figure for the resistance thermometry bridge
for any operating conditions (this can be supplied to model
CTR9000 (F900) primary-standard resistance thermometry
bridge customers to assist in predicting uncertainty budgets).
These predict that for a 10 Ω resistance measured at 25 °C
the resistance thermometry bridge (set to 10 Ω impedance)
would exhibit an RMS ratio noise of 62 ppb at 0.7071 mA and9 ppb at 5 mA.
The corresponding measurements were made using Wilkins
standard resistors in a temperature stabilized oil bath, withthe results shown in table 2.
Table 2: Calculated and measured noise figures

Test current

Calculated
RMS noise

Measured
RMS noise

0.7071 mA

62 ppb57 ppb

5 mA

9 ppb

5 ppb

The measurements confirm that the noise performance of
the is as predicted by the design calculations and closely
approaches the fundamental Johnson Noise limit.

For example:
The fundamental Johnson Noise on a 25.5 Ω standard
platinum resistance thermometer (SPRT) at 0 °C measured
with a 0.5 Hz bandwidth is 893 pV and the measurement
noise achievable with a properly configured CTR9000 (F900)
is equivalent to only 958 pV (only 7 % above the fundamentallimit).

WIKA data sheet IN 00.31 ∙ 03/2015

Page 5 of 6

Bridge current accuracy
The accuracy of the bridge current is important because of
the self-heating effect in an standard platinum resistancethermometer (SPRT). This causes the resistance of the SPRT
at a given temperature to be dependent on the measurement
current to an extent that is significant at the target uncertainty
level of 20 ppb.
The accuracy of the bridge current is therefore important ifthe SPRT is to be used as a transfer standard thermometerat a stated current or if the bridge current is to be varied
to allow extrapolation back to the zero-power resistance.
The bridge current was measured using a Keithley model
2000 multimeter to measure the voltage developed across acalibrated Wilkins resistor.

Table 3: Bridge current error

The errors between the measured and expected current for
all bridge settings are shown in table 3.

2This test confirms that the current accuracy is comfortably
within the specified Ω ±0.1 %.

Bridge setting in mAError in %50√20.01

20√20.01

50
20

10√2
105√2
52√2
√2
1

0.5√2
0.5

0.2√2
0.2

0.1√2
0.1

-0.01
-0.01
0.02
0.05

-0.02
-0.04
-0.03
-0.04
-0.01
0.02
0.01

-0.01
0.00

-0.01
0.02
0.05

Conclusion
As stated at the beginning, the above test results are alimited selection of the extensive tests carried out on themodel CTR9000 (F900) primary-standard resistancethermometry bridge over the last 18 months.
However, these tests are the ones that address the mostimportant performance criteria for this instrument (accuracy,noise and bridge current accuracy). These tests confirm theperformance of this resistance thermometry bridge to be wellwithin its performance specification.

The resistance thermometry bridge is designed to be as
immune to environmental effects (particularly electrical noiseand temperature) as possible. It should therefore be possible
for users to achieve the specified performance.
It is however important for users to set up the primarystandard resistance thermometry bridge correctly in orderto achieve this performance. In particular, users must set
the bridge gain correctly (as documented in the operatinginstructions).

Page 6 of 6

WIKA data sheet IN 00.31 ∙ 03/2015

WIKA Alexander Wiegand SE & Co. KG
Alexander-Wiegand-Straße 30
63911 Klingenberg/GermanyTel.
+49 9372 132-0
info@wika.de
www.wika.de03/2015 EN© 2015 WIKA Alexander Wiegand SE & Co. KG, all rights reserved.
The specifications given in this document represent the state of engineering at the time of publishing.
We reserve the right to make modifications to the specifications and materials.