Setup for the dynamic calibration of bridge amplifiers from DC up to 10 kHz


ACTA IMEKO 
ISSN: 2221-870X 
March 2019, Volume 8, Number 1, 19 – 24 

 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 19 

Setup for the dynamic calibration of bridge amplifiers from 
DC up to 10 kHz 

Leonard Klaus, M. Florian Beug, Thomas Bruns 

Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany 

 

 

Section: RESEARCH PAPER  

Keywords: dynamic bridge amplifier calibration; traceability; dynamic measurement; dynamic bridge standard 

Citation: Leonard Klaus, M. Florian Beug, Thomas Bruns, Setup for the dynamic calibration of bridge amplifiers from DC up to 10 kHz, Acta IMEKO, vol. 8, 
no. 1, article 4, March 2019, identifier: IMEKO-ACTA-08 (2019)-01-04 

Section Editor: Maija Ojanen-Saloranta, VTT Technical Research Centre of Finland, National Metrology Institute MIKES, Finland 

Received August 15, 2018; In final form October 10, 2018; Published March 2019 

Copyright: © 2019 IMEKO. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits 
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited 

Corresponding author: Leonard Klaus, leonard.klaus@ptb.de 

 

1. INTRODUCTION 

Mechanical quantities, such as acceleration, force, torque, and 
pressure, are often measured with transducers, based on strain 
measurement by means of strain gauges, or sensor elements, 
based on the piezoresistive effect. These sensing elements 
change their resistance proportionally to the strain (strain gauge) 
or the compression/tension (piezoresistive element). However, 
both transducer principles require signal conditioning by bridge 
amplifiers. 

In many applications, these mechanical quantities change 
rapidly over time, thus requiring a dynamic calibration in order 
to be traceable. Until now, bridge amplifiers – as well as the 
corresponding transducers – have almost exclusively been 
calibrated statically. 

To overcome this problem, a joint European project [1], [2]  
researched the necessary procedures, measuring devices, and 
mathematical tools to establish dynamic calibration. For signal-
conditioning electronics (including all types of measuring 
amplifiers), it is known that deviations between static and 
dynamic behaviour exist [3]. These deviations may influence 
dynamic measurements significantly. Therefore, one outcome of 

this project was a newly developed dynamic bridge standard [4] 
that enables bridge amplifier calibration from a static regime 
(DC) up to frequencies of 10 kHz. This bridge standard is 
incorporated in the calibration setup described here.  

This paper is a revised and extended version of [5]. 
 
 

 

Figure 1: Wheatstone bridge circuit with four resistive sensing elements 
𝑅1 … 𝑅4, excitation voltage 𝑈Exc, and bridge output voltage 𝑈Br. 

ABSTRACT 
Measurements of mechanical quantities are often carried out with transducers with a bridge output. The output signals are conditioned 
using bridge amplifiers. If dynamically changing quantities are going to be measured traceably, the bridge amplifier must be calibrated 
dynamically. 
This paper describes a dynamic bridge amplifier calibration setup based on the new PTB dynamic bridge standard. The calibration is 
carried out by the synchronous sampling of the bridge amplifier output voltage and a reference signal provided by the calibrated dynamic 
bridge standard. The dynamic bridge standard enables calibrations in a frequency range from DC (static calibration) up to 10 kHz. An 
overview of the different measurement uncertainty contributions is given, and the first measurement results show good agreement 
with a previously established measurement setup. 

mailto:leonard.klaus@ptb.de


 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 20 

2. DYNAMIC BRIDGE STANDARD 

Bridge amplifiers are always connected to some type of 
Wheatstone bridge circuit, as depicted in Figure 1. The resistive 
sensing elements (e.g. the strain gauges or piezoresistive sensor 
elements) are connected as a quarter bridge (one sensing element 
of variable resistance), half bridge (two sensing elements), or full 
bridge (four sensing elements) in order to maximise the output 
signal of the bridge. What all configurations of a Wheatstone 

bridge have in common is that the output voltage level 𝑈Br 
depends on the bridge excitation voltage 𝑈Exc (in this case a DC 
voltage) featuring a ratiometric output, which is typically given in 

mV V⁄ . The excitation voltage is supplied by the bridge amplifier. 
The output of the bridge amplifier is therefore proportional to 
the ratio of the bridge output voltage to the excitation voltage. 

As a result, the bridge output voltage 𝑈Br has no connection 
to ground. In the bridge amplifier calibration, this bridge voltage 

𝑈Br must be ratiometrically provided by the dynamic bridge 
standard based on the excitation voltage, undertaken in the form 
of a calibrated voltage ratio and phase. 

The dynamic bridge standard working principle is based on 
two multiplying digital-to-analogue converters (MDACs), which 
generate output voltages proportional to their reference voltage 
without dependency to ground. This reference voltage is chosen 

as the bridge excitation voltage ±𝑈Exc . A schematic diagram of 
the dynamic bridge standard components can be seen in Figure 
2. Subsequent to the MDAC outputs, a resistive 1/400 voltage 
divider supplies the small output voltages as required for the 
bridge amplifier calibration. The load of a strain gauge transducer 

is simulated by a load resistance of 350 Ω. The output voltage of 
the two MDACs is used as reference for the phase calibration. 
For this purpose, it is conditioned by buffer amplifiers to avoid 
any influence on the MDAC output and is fed to connectors 
placed on the front panel. 

The waveforms generated by the MDACs, which can be 
either static or time-dependent (arbitrary or sinusoidal), are 
programmed by using an optical computer link. 

3. IMPLEMENTATION OF A CALIBRATION SETUP 

For the calibration of a bridge amplifier, not only is a bridge 
standard required, but additional data acquisition hardware, a 
proper data analysis, and a measurement uncertainty evaluation 
are also required.  

The calibration setup incorporates the dynamic bridge 
standard described as well as a data acquisition system featuring 
two synchronised sampled data channels. The connection of the 
different components, including the device under test (DUT), is 
depicted in Figure 3. 

                                                           
1 Commercial instruments are identified in this paper only to adequately specify the experimental setup. Such identification does not imply recommendation by 

PTB, nor does it imply that the equipment identified is necessarily the best available for the purpose. 

The dynamic behaviour of an amplifier can be described by 

its frequency dependent complex transfer function 𝐻 (i𝜔), with 

its input 𝑋(i𝜔) and its output 𝑌(i𝜔) giving 

𝐻(i𝜔) =
𝑌(i𝜔)

𝑋(i𝜔)
 . (1) 

More commonly, it is given as a magnitude response 𝐴(𝜔) 
and phase response 𝜑(𝜔), giving 

𝐴(𝜔) =
𝐴𝑌 (𝜔)

𝐴𝑋(𝜔)
 , (2) 

𝐴𝜑(𝜔) = 𝜑𝑌 (𝜔) − 𝜑𝑋 (𝜔) , (3) 

with the magnitudes 𝐴𝑋, 𝐴𝑌, and phase angles 𝜑𝑋 ,  𝜑𝑌 of the 
input and output. Based on the magnitude and phase responses, 
the associated complex transfer function can be derived and vice 
versa [3]. 

In the case of the calibration of a bridge amplifier, the 

amplifier’s magnitude excitation at the input 𝐴𝑋 is well known, 
because the dynamic bridge standard is calibrated. For the 
determination of the magnitude response, only the output of the 

amplifier 𝐴𝑌 needs to be analysed. This could be done by means 
of a calibrated sampling system or even a calibrated AC 
voltmeter. The phase response determination requires the phase 

measurement between the output of the bridge amplifier 𝜑Y(𝜔) 
and the dynamic bridge standard’s reference signal, since this 
signal has a calibrated phase relation to the input of the bridge 

amplifier 𝜑X(𝜔). 

4. DATA ACQUISITION 

In our setup (Figure 4), we simultaneously sample the bridge 
amplifier output and the dynamic bridge standard reference 
signal by means of two synchronous sampling data acquisition 
channels. The hardware used for the data acquisition is a PXIe 
system with a high-resolution digitiser card from National 
Instruments (PXI-59221), which has a flexible resolution of 18 
bits to 24 bits. With sampling rates applicable to the calibration 

of bridge amplifiers (𝑓s ≪500 kHz), the resolution is 24 bits. The 
PXI-5922 digitiser card was thoroughly analysed in terms of its 
dynamic properties, precision, and metrological suitability [6], [7]. 
Additionally, automated calibration procedures exist for this 
acquisition card at PTB (Section 6), as it is widely used in the 
Realization of Acceleration working group. 

The oscillators of the different systems, namely the oscillator 
of the dynamic bridge standard and of the data acquisition 
system, are synchronised in order to avoid spectral leakage. The 
dynamic bridge standard is equipped with an optical clock input. 
The PXIe system is equipped with a timing and synchronisation 

 

Figure 2. Schematic overview of the dynamic bridge standard. 

 

Figure 3. Components of the dynamic bridge amplifier calibration setup. 



 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 21 

card (PXIe-6672), which features a stable oscillator (TCX0). Its 
one-year stability is in the range of a few 106 [8]. The 20 MHz 
reference frequency for the dynamic bridge standard is then 
generated by direct digital synthesis (DDS) based on the 

10 MHz TCX0 oscillator. The electrical frequency output 
provided by the PXIe card is converted to an optical link as 
required by the bridge standard. 

Dynamic bridge excitation signals are generated by two 
MDACs with a sampling frequency that is a fraction of the 
reference frequency. Based on this sampling frequency, the 
sinusoidal waveforms can be generated based on a finite number 
of data points per oscillation period, which are then repeatedly 
output. The sampling frequencies and the acquisition time of the 
data acquisition were chosen based on two criteria: 

1) The sampling rate should be multiples or integer 
fractions of the bridge standard’s sampling rate. 
Generally, it would not be favourable to sample with a 
higher sampling rate than the signal generation rate. 
However, the chosen digitiser card has a minimum 
sampling rate of 50 kS/s, requiring a down-sampling of 
the data after acquisition. This decimation process is 
carried out by calculating an averaged decimated 
waveform from the original data. 

2) The sampling rate was chosen in order for us to achieve 
a finite number of samples for the selected number of 
oscillations requiring acquisition. The corresponding 
acquisition time should include an integer number of 
periods of the excitation frequency. 

The sampling frequency of the chosen digitiser cannot be 
chosen arbitrarily. It is chosen as an even integer divider of the 
sampling frequency of 120 MS/s for the bitstream input of the 
incorporated delta-sigma analogue-to-digital converters (ADCs) 
and must be in a range of 50 kS/s and 15 MS/s. 

5. DATA ANALYSIS 

The acquired and synchronously sampled waveforms of the 
two input channels make up the input for the data analysis. One 
data channel is the reference output of the dynamic bridge 
standard, and therefore contains a signal with a known relation 
to the input of the transducer, while the second data channel 
contains the voltage output of the device under test.  

The transformation of the time series data into the frequency 
domain is carried out by means of digital Fourier transform 
(DFT). Because of the synchronised generation and acquisition 
frequencies, spectral leakage can be avoided. The sampling of full 
periods of the sinusoidal waveform allows us to go without any 
windowing prior to the DFT. 

Based on the outcomes of the two DFTs and the calibration 
results of the dynamic bridge standard, the magnitude and phase 
responses of the DUT at each excitation frequency can be 
calculated as described in Section 3. The magnitude response is 
derived only based on the output of the device under test, as the 
input magnitude is known from the bridge standard’s calibration 
data. The phase response (i.e. the frequency-dependent phase 
delay) requires input from both measurement channels, as the 
absolute phase position cannot be derived from calibration data. 

For each frequency point, repeated measurements are carried 
out (the number of repetitions can be set), and the mean and the 
standard deviation are calculated, giving information about the 
stability of the input-output relation of the DUT for each 
calibration frequency. 

6. MEASUREMENT UNCERTAINTY EVALUATION 

The measurement uncertainty is evaluated according to the 
Guide to the Expression of Uncertainty in Measurement (GUM) 
[9] and Supplement 1 thereto (GUM S1) [10] by means of Monte 
Carlo simulations. 

GUM distinguishes between two types of measurement 
uncertainty contributions, both of which are considered for the 
measurement uncertainty estimation: 

1) Type A uncertainty contributions: These can be 
determined by the statistical analysis of measurements. 

2) Type B uncertainty contributions: These include all 
contributions that cannot be estimated by statistical 
analysis. They may include datasheet content, results 
from calibrations (of, for example, components of the 
setup), operator know-how, records from previous 
measurements, or other prior knowledge. 

The measurement is modelled by means of mathematical 

model function 𝑓 propagating all the input quantities 𝑋1 … 𝑋𝑛 to 
the measurement result 𝑌, giving 

𝑌 = 𝑓(𝑋1, 𝑋2, … , 𝑋𝑛) . (4) 

Each input quantity can be described mathematically by its 
distribution, which leads to estimations of the value of the input 
quantity and its uncertainty. Depending on the sources of 
information about the input quantity and its properties, the 
corresponding distributions (Gaussian distributed, rectangularly 
distributed, etc.) are assigned.  

Independent calibrations of the components of the 
calibration setups are incorporated in the uncertainty estimation 
as sub-models, i.e. the distributions of the calibration results are 

assigned to the according input quantity 𝑋. This is the case for 
the two components detailed below.  

6.1. Calibration of the dynamic bridge standard 

The bridge standard was calibrated in advance by calibrating 
the resistive voltage divider, the MDACs, and the signal 
conditioners of the outputs. The expanded measurement 
uncertainties (U(k=2)) of this calibration are 0.03 % (magnitude) 
and 0.05° (phase angle) for frequencies up to 1 kHz and 0.05 % 
(magnitude) and 0.1° (phase angle) for frequencies above 1 kHz 
and up to 10 kHz.  

 

Figure 4. Dynamic bridge amplifier calibration setup, consisting of the bridge 
amplifier under test (top), the dynamic bridge standard (middle), and the 
data acquisition system (bottom). 



 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 22 

There are systematic effects, which are in the same order as 
the expanded measurement uncertainty for the magnitude 
transfer function and less than 0.2° for the phase angle at 10 kHz. 

6.2. Calibration of the digitiser channels 

The two digitiser input channels were calibrated dynamically 
using a voltage calibrator. In typical conditioning amplifier 
calibration setups, it is not necessary to calibrate the data 
acquisition hardware so thoroughly if the input and output are 
acquired simultaneously and a second measurement with 
swapped input channels is carried out. In this case, possible 
influences due to the different input channel characteristics can 
be corrected. However, in the case of the dynamic bridge 
standard, this procedure is not applicable: As the magnitude 
response is only derived from the bridge standards output 
(Section 3), all influences due to the digitalisation need to be 
determined. 

The calibration of the digitiser channels was carried out using 
a Fluke 5700A voltage calibrator (which was itself calibrated 
dynamically beforehand). For the calibration, both input 
channels were connected to the voltage calibrator’s outputs, and 
the voltages of known magnitude and frequency were generated. 
From the acquired signal, the root mean square (RMS) value was 
derived for each frequency point of the calibration. The digitiser 
card shows a characteristic transfer function, which could be 
compensated for as it is only dependent on the sampling rate [6], 

[7]. Figure 5 shows the calibration results for a sampling rate of 
50 kS/s (the same rate used for the calibration measurements). 

The stable local oscillator of the PXIe timing and 
synchronisation card was calibrated traceably to PTB’s frequency 
standards by means of a distributed frequency signal. 

The different measurement uncertainty contributions are 
depicted in Figure 6, and detailed information about the different 
type B contributions, including their distributions, is given in 
Table 1. 

6.3. Statistical analysis of the measurements 

The type A uncertainty contributions are also analysed. The 
stability of the measurement setup and of the different DUTs are 
assessed by carrying out many repeated measurements in a short 
time (referred to as ‘repeatability’ in Figure 6) and by repeating 
the calibration at larger intervals, including the disconnection of 
all cables and turning the calibration devices and devices under 
test off between measurements (referred to as ‘reproducibility’). 

A complete evaluation of the type A uncertainty contributions 
requires extensive measurements with different DUTs and 
numerous repetitions, which have not yet been carried out.  

6.4. Correction of systematic effects 

Both the signal acquisition card and the dynamic bridge 
standard show a frequency-dependent change in their transfer 
function. GUM recommends a correction of all systematic 
effects. However, if necessary, it is possible to treat those 
systematic effects as uncertainty contributions [11]. Both the 
magnitude-related systematic contributions are in the same range 
as the random measurement uncertainty component of the 
calibration of the dynamic bridge standard. Therefore, in the first 
step, these are not corrected; rather, they are included in the 
measurement uncertainty estimation as input quantities. In 
future, these could be corrected to reduce the resulting 
measurement uncertainty for the bridge amplifier calibration. 

 

Figure 5: Calibration results for a PXI-5922 digitiser card. The relative 
deviations are given in blue, and the assigned measurement uncertainty 
U(k=2) is red. The sampling rate was 50 kS/s, and the input voltage span ±5 V. 

 

Figure 6. Ishikawa diagram of the measurement uncertainty contributions for 
a dynamic bridge amplifier calibration. 

Table 1. Type B measurement uncertainty contributions of the calibration setup. 

Input quantity Uncertainty contribution Distribution 

Dynamic bridge standard (magnitude) 𝑢rel ≤ 2.5 × 10
−4 Gaussian 

Dynamic bridge standard (phase) 𝑢 ≤ 0.05° Gaussian 

Dynamic bridge standard systematic (mag.) 𝑢rel ≤ 5 × 10
−4 Gaussian 

Frequency standard 𝑢rel = 1 × 10
−10 Gaussian 

Stability TCX0 (1 year) 𝑢rel = 1 × 10
−6 rectangular 

Temperature stab. TCX0 (0 °C – 55 °C) 𝑢rel = 2 × 10
−6 rectangular 

Skew 𝑢 = 5 × 10−10 s rectangular 

Cal. PXI-5922 (magnitude) 𝑢rel ≤ 2.5 × 10
−6 Gaussian 

PXI-5922 systematic deviations (magnitude) 𝑢rel = 6 × 10
−4 Gaussian 

PXI-5922 DC accuracy (magnitude) 𝑢rel = 5 × 10
−4 and 

𝑢 = 1 × 10−5 V 

rectangular 

rectangular 



 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 23 

6.5. Application of the Monte Carlo simulation 

The measurement uncertainty evaluation is carried out by 
means of a Monte Carlo simulation according to GUM S1. For 
this purpose, repeated simulations of the measurement are 
carried out. The different input quantities are modelled according 
to their input distributions. The resultant distribution of the 
output describes the measurement results, including uncertainty. 

7. FIRST MEASUREMENT RESULTS 

To obtain a first impression of the performance of this new 
setup, measurements are carried out with a bridge amplifier 
under test, which had previously been dynamically calibrated. 
The previous calibration had been carried out with an earlier 
prototype of the dynamic bridge standard in conjunction with a 
sampling voltmeter [12]. The results of the magnitude and phase 
responses are given in Figure 7 and Figure 8, respectively. 

The chosen bridge amplifier shows only small deviations (in 
the range of a few 10-3 for the magnitude response) from the 
ideal behaviour in the chosen frequency range. The measurement 

results agree very well both in terms of magnitude and phase, 
despite that the individual frequency responses of the 
corresponding bridge standards have not yet been compensated 
for. The differences between the results of the two 
measurements are even slightly smaller than the largest single 
type B measurement uncertainty contribution. 

8. CONCLUSION 

This paper describes a dynamic bridge amplifier calibration 
setup based on the new PTB dynamic bridge standard. The 
output of the bridge standard and the DUT is sampled 
synchronously by a high-precision digitiser. A synchronisation of 
the oscillators of both the data acquisition system and the bridge 
standard avoids spectral leakage. 

The new calibration setup enables the dynamic calibration of 
bridge amplifiers according to the measurement conditions 
required by ISO 4965-2 [13], in which a dynamic signal on a 
constant bias is stipulated. 

The first measurement results of the new setup agree very well 
with measurements previously carried out with a prototype of 
the dynamic bridge standard. 

REFERENCES 

[1] C. Bartoli et al., Traceable dynamic measurement of mechanical 
quantities: Objectives and first results of this European project, 
International Journal of Metrology and Quality Engineering 3, 3 
(2013) pp. 127-135,   
DOI: 10.1051/ijmqe/2012020. 

[2] C. Bartoli et al., Dynamic calibration of force, torque, and pressure 
sensors, in Proc. of the Joint IMEKO International TC3, TC5 and 
TC22 Conference 2014, Cape Town, South Africa, 2014, 
https://www.imeko.org/publications/tc22-2014/IMEKO-TC3-
TC22-2014-007.pdf. 

[3] L. Klaus, T. Bruns, H. Volkers, Calibration of bridge-, charge-, and 
voltage amplifiers for dynamic measurement applications, 
Metrologia 52, 1 (2015) pp. 72-81,   
DOI: 10.1088/0026-1394/52/1/72. 

[4] M. F. Beug, H. Moser, G. Ramm, Dynamic bridge standard for 
strain gauge bridge amplifier calibration, in Proc. of the 2012 
Conference on Precision Electromagnetic Measurements 
(CPEM), 2012, Washington DC, USA, pp. 568-69,   
DOI: 10.1109/CPEM.2012.6251056. 

[5] L. Klaus, M.F. Beug, T. Bruns, A new calibration set-up for the 
dynamic calibration of bridge amplifiers from DC up to 10 kHz, 
in Proc. of the 23rd TC3, 13th TC5 and 4th TC22 IMEKO 
International Conference, Helsinki, Finland, 2017,  
https://www.imeko.org/publications/tc3-2017/IMEKO-TC3-
2017-011.pdf. 

[6] G. Rietvield et al., Characterization of a wideband digitizer for 
power measurements up to 1 MHz, IEEE Transactions on 
Instrumentation and Measurement 60, 7 (2011) pp. 2195-2201,  
DOI: 10.1109/TIM.2011.2117330. 

[7] F. Overney et al., Characterization of metrological grade analog-
to-digital converters using a programmable Josephson voltage 
standard, IEEE Transactions on Instrumentation and 
Measurement 60, 7 (2011) pp. 2172-2177,   
DOI: 10.1109/TIM.2011.2113950. 

[8] National Instruments Corporation, NI PXIe-6672 User Manual, 
2010. 

[9] Bureau International des Poids et Mesures, et al., Evaluation of 
Measurement Data – Guide to the Expression of Uncertainty in 
Measurement, 2008. 

[10] Bureau International des Poids et Mesures, et al., Evaluation of 
Measurement Data – Supplement 1 to the Guide to the 
Expression of Uncertainty in Measurement – Propagation of 
Distributions using a Monte Carlo Method, 2008. 

 

Figure 7. Magnitude response calibration results of a bridge amplifier using a 
prototype of the bridge standard (blue) and of the actual setup (red). 

 

Figure 8: Phase response calibration results of a bridge amplifier using a 
prototype of the dynamic bridge standard (blue) and of the actual setup 
(red). 

http://dx.doi.org/10.1051/ijmqe/2012020
https://www.imeko.org/publications/tc22-2014/IMEKO-TC3-TC22-2014-007.pdf
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http://dx.doi.org/10.1088/0026-1394/52/1/72
http://dx.doi.org/10.1109/CPEM.2012.6251056
https://www.imeko.org/publications/tc3-2017/IMEKO-TC3-2017-011.pdf
https://www.imeko.org/publications/tc3-2017/IMEKO-TC3-2017-011.pdf
http://dx.doi.org/10.1109/TIM.2011.2117330
http://dx.doi.org/10.1109/TIM.2011.2113950


 

ACTA IMEKO | www.imeko.org March 2019 | Volume 8 | Number 1 | 24 

[11] I. H. Lira, W. Wöger, Evaluation of the uncertainty associated with 
a measurement result not corrected for systematic effects, in 
Measurement Science and Technology 9(6) (1998) p. 1010,  
DOI: 10.1088/0957-0233/9/6/019. 

[12] L. Klaus, Entwicklung eines primären Verfahrens zur Kalibrierung 
von Drehmomentaufnehmern mit dynamischer Anregung, PTB 

Report MA-93, 2016, pp. 59-61, pp. 146-50,   
DOI: 10.7795/110.20160714. 

[13] ISO/TC 164/SC 5, ISO 4965-2:2012, Metallic Materials – 
Dynamic Force Calibration for Uniaxial Fatigue Testing – Part 2: 
Dynamic Calibration Device (DCD) Instrumentation, 
International Organization for Standardization, 2012. 
 

 

http://dx.doi.org/10.1088/0957-0233/9/6/019
http://dx.doi.org/10.7795/110.20160714