Adaptation of metrology-grade ac current source in velocity mode of Planck-Balance 2: direct referencing induced voltages with ac quantum voltage standard

The adaptation of developed metrology-grade ac current source (MCS) to the velocity mode of measurements of the Planck-Balance 2 as a means for generating ac mechanical oscillations is presented. The universality in operating with the MCS unit especially practical for the Planck-Balance setup for frequencies of 0.1 Hz–20 Hz (including but not limited to the negligence of a broader range of 0.01 Hz up to several hundred Hz) and for amplitudes of up to 10 mA with 16 (offset with 14)-bit effective resolution is demonstrated. MCS allows generating complex ac waveform signals as waveform synthesizers by adding to the original signal an extra five independent harmonic components, each of which with an adjustable resolution of 10 ns for phase and 16-bit for amplitude. Additionally, the MCS is supported by an external clock at 10 MHz frequency which serves also as a common reference time base for the comparison between the direct output signal of MCS, or of the induced voltage in the coil of the Planck-Balance resulting due to the applied current by MCS, with the ac quantum voltage standard at the required accuracy levels.


Introduction
In many precision electromagnetic and mechatronic systems, knowledge of the input electrical parameters and the thereupon-dependent output signals define the limits of system performance and guide future research and development directions.The Kibble balance (KB) [1][2][3] which are developed to realize the primary standard of mass directly traceable to the Planck constant is one such state-of-the-art metrology-grade system.In these systems, it is necessary to perform measurements of multiple parameters, such as length, voltage, etc with high accuracy, high precision, and extraordinary levels of relative measurement uncertainties reaching several parts per billion (ppb).It is evident that some of the parameters have only a subtle appearance and do not necessarily enter the general measurement equation directly, despite their change.Therefore, their influence is considered in the uncertainty budget of the measurement results.For example, one of the pillars on which the operation of the KB system is based is the magnet-and-coil assembly for which the electromagnetic Bl (B represents the magnetic field density that crosses the wire of the electric current-carrying coil with total l length) factor needs to be identified from two different measurements with at least below 10 −8 relative measurement uncertainty [4].The other is the electric current which appears either as a compensation current equivalent to that of the gravitational force acting on the mass piece to be calibrated or as a drive current which is required to apply to the current-carrying coil to guide its motion in the magnetic field in a highly predictable manner.In most of the KB systems, this electric current is applied as a constant dc value with extraordinary resolution, and at the same time it needs to be known or measured in a likewise manner.However, in recent studies [5][6][7] there are presented more setups operating on the KB principle that tend to require ever more versatile electric current sources that provide a high degree of knowledge or control over these electric currents.For example, previously it even introduced a quantum-based (analog-to-digital converters) system as a precise current sensor for applications in high-precision weighing systems [8].In such systems, mass comparisons are made using electric currents as intermediate quantities; therefore solutions for measuring the lowest possible current differences are highly demanded.In the Planck-Balance 2 (PB2) system, which is a table-top version of the KB performing mass calibration traceable to the Planck constant for the E2 class of weight pieces [5,9] (e.g. with ppm level of combined relative measurement uncertainty for 10 g), the traveling length of the coil is short and the mass values to be compensated are also small in comparison with KB systems.During the velocity mode of measurements, an ac electric current is used to create mechanical oscillation at ±40 µm [5] in order to induce sufficiently large and measurable voltages in the coil, instead of relatively big and constant dc value which is commonly used in KB systems.In the literature, besides some custom-developed and well-characterized current reference standard systems [10] with sufficiently high temporal stability, information about the current sources used in the KB system is typically absent or it is given only in terms of their stability or in the ways they are used to compensate for coil current effects [11].
In this work, we introduce a metrology-grade current source (MCS) used in the velocity mode of measurements in the PB2 setup.We focus particularly on adapting MCS operation in ac mode at frequencies ranging between 0.1 Hz and 10 Hz.We also tested the opportunities (a) for reducing the statistical error in mass determination which is typically present in the force mode of measurements due to the noise of the current source.However, the same noise is still apparent in the velocity mode.And (b) we tested for compensation of the phase shift between the applied electric currents, the induced voltages in the coil, and the measured voltages by voltmeters which are typically due to the complex mechanical-electromagnetic structure of the PB2.More specifically, represented by such basic elements of the scheme as the frequency-dependent induction of the coil, or the electrical impedance of different components of the measurement circuit, etc [12,13].Several comparison measurements were performed between the output signal of the MCS and commonly used current sources used in precision measurements (HP3245A) [14] to test the basic characteristics and advantages offered by the system.The MCS can be complemented by an external 10 MHz reference clock which offers beneficial optionality over other commercial current sources.To the best of our knowledge, most of the precision current sources available on the market are not supported by sufficiently stable internal clocks, and also their synchronous operation inside an electrical measurement scheme with all other coupled components of the circuit cannot be achieved with respect to a common reference time base.Moreover, most commercially available multifunctional sources do not allow for generating quasi-dc and ac signals at the bordering frequencies which arguably span between mHz up to 10 Hz, or if they do, then with low-stability, -reproducibility and -resolution (e.g.Fluke 5720A, Keithley 2400/6200, Clarke-Hess M151/5050, Keysight B2961B/2B, HP3245A, etc).We also perform comparison measurements between the signal of the MCS measured as a voltage drop over a stable precision resistor or as an induced voltage in the coil of the PB2, relative to the signal generated by the quantum ac programmable Josephson voltage standard (AC PJVS) [15][16][17].Results of the measurements using different amplitudes of ac electric current of up to 1 mA for which the induced voltages range up to a 0.5 V level, alongside the method of generating distorted ac signals or reconstructing the original single component sine signal by adding or subtracting (suppressing) additional components of up to the 5th harmonics of the signal are presented.

System description and core electrical setup
In this section, we present the basic concept design and the parameters of the MCS without accounting for the detailed particularities of the electronic design.There are still various options for upgrading the system and achieving minor improvements by specific choices made for the electronic components.In figure 1 the block diagram of the MCS is presented.The digital-to-analog converters supported via the direct digital synthesizer (DDS) that is implemented on the FPGA, are utilized to generate a single arbitrary, periodic output from a freely programmable Look-up-table with a resolution of 16-bit and a memory length of 10 −6 .The digital signal output of the DDS can be adjusted further by digitally preprogrammed offset and amplitude values on the board of the programmable gain amplifier.The DDS is pre-configured to operate internally at a 10 MHz update rate with a 100 MHz internal clock rate.On the main board (on FPGA) of MCS it is synchronized with the external 10 MHz reference clock making the phase noise equal to that of the reference clock.
In short, the MCS provides an ac current output with up to ±1 mA amplitude with 14-bit resolution for adjustable gain.This leads to achieving an effective resolution of the applied current at 0.5 nA steps, whereas the offset value can be adjusted with 16-bit resolution.The frequency is adjustable for the range covering from 10 mHz up to several hundred Hz.The MCS allows generating of complex ac waveform signals as waveform synthesizers following equations (1) and (2).We are able to add an extra independent five harmonic components to the original fundamental signal.Each harmonic component can be adjusted with a resolution of 10 ns for phase and 14-bit for amplitude.Thus, by superposition of all the components, the effective output electric current is constructed as where I T (t) is the total (overall) effective output electric current, with an independent I 0 dc offset component, the sum of all superimposed I n ac components, and I ε noise component (to be discussed later).I S is the fundamental component and I 1 , I 2 , I 3 , I 4 , and I 5 are successive harmonic components to be added or subtracted.I An is the amplitude of the nth harmonic component, φ n is the phase angle between the fundamental and nth harmonic components, and f n is the frequency of the nth harmonic defined by the fundamental frequency f S and the order number of the harmonic component.Dropping the independent dc component of the electric current, which effectively serves to maintain the offset load (or the imbalance of the lever arms), the dynamic performance of the current source can be described by the total harmonic distortion plus noise as follows Besides the apparent harmonic distortions which could be modeled and subsequently compensated to a considerable extent from the original MCS output signal, there can be additional obscured noise components (e.g.50 Hz line voltage frequency) affecting adversely either the motion of the drive and measurement coils, or the final result of the measured induced voltage.Furthermore, when integrated with the PB2 setup and its electrical measurement infrastructure, which represents a complex electromechanical system, additional unwanted frequency-dependent noise components can originate.According to initial test measurements at an isolated state the current source shows the following floor noise, distributed along the 1 mA range for different frequencies as @DC @1 Hz @10 Hz The load impedance is limited to a maximum of the supply voltage of U load (max) = ±7 V which is pre-adjusted such to correspond to the actual operational conditions defined by the electrical parameters of the measurement circuit of the velocity mode of the PB2 setup, primarily for the current carrying coil which is represented as a floating load with resistance R coil drv = 180 Ω, and frequency dependent inductance L coil drv = 150 mH @1 Hz.The timing of the MCS operation is maintained according to the diagram provided in figure 2, allowing also to directly couple with the operation of PJVS.
As a time reference, we used a GPS disciplined oven stabilized quartz oscillator.It is coupled to all systems used in the velocity mode of measurements.The frequency is accurately  measured with a frequency counter with relative uncertainty better than 10 −8 .Thus, the general signal trigger, the triggering frequency of the current source f MCS and the actual fundamental frequency f S of the output current signal (including all the harmonics) is accurately synchronized.In figures 3 and 4, the block and data acquisition diagram, and the core electrical schematics of the velocity mode of measurements where the MCS is integrated, are presented.
The schematics in figure 4 represent only the core components that in the ideal case of velocity mode measurements should be considered, thus several aspects of the measurement circuit, including for the MCS and PJVC, are omitted.For example, the Keysight 3458A voltmeter receiving the 'CLK In' signal indirectly, by receiving a sample trigger from the PJVS system which is set to operate in the Master Mode.Throughout the system, the distribution of the 10 MHz clock and trigger signals were supplemented with inductive decouplers.The measurement coil in which the voltage is induced is fixed from the load carrier of the electromagnetic force compensation (EMFC) balance.In effect, it is rigidly fixed on one side of the lever arm inside the EMFC balance, whereas the drive coil is fixed directly on the opposite side of the lever arm.The distance ratio of the lever arms where both coils are rigidly fixed, the positions of both coils from the pivot point of the lever arm, as well as the total effective loads apparent on opposite sides of the lever arm, are different (see [5] for more details).To compensate for this imbalance, an offset dc current is used that can also be used upon necessity to compensate for drift effects.Alternatively or additionally, a compensation method is used by adding or removing a required amount of ∆m offset load from the offset mass pan to avoid possible electrical influences or interferences of the dc electrical current component.

Measurement system verification
Initially, several measurements were made using additional current sources to compare the performance of the MCS and its suitability.Following the schematics in figure 4(b) (without PJVS), an electric current was supplied to the drive coil at 1 Hz frequency using MCS, HP3245A, and dSpace.In the case of dSpace, in-house built additional voltage-to-current (V/C) converters and a servo control of the coil position were used.The resulting voltage induced in the measurement coil in each case was measured with the same voltmeter under the same parameter configurations (aperture time 700 µs, sampling time 1 ms, voltage range 1 V).The comparison of all three measured signals shows no obvious difference (see figure 5(a), however when subtracting the first harmonics obtained by a sine fit [18] from each measured signal it is possible to distinguish from the remaining noise of the amplitude spectral densities a substantial characteristic differences.In particular, as expected, it is seen that the higher order harmonics (2nd, 3rd,...) apparent in each signal from which the highest magnitude distortions (including the noise) demonstrate the low-grade dSpace system.After several systematically performed comparison measurements between the MCS and the HP3245A a slightly better performance of the MCS was observed with few minor differences.. Despite the digital programming possibilities provided by the HP3245A current source (according to practical experience and device manuals) in generating an electric current with (quasi-ac) arbitrary waveforms, its usage is less suitable for fulfilling the development tasks of this work.E.g. due to insufficient size of the internal memory for storing the synthesized digital signal of relevant length and precision, the communication delay between the consequent measurements with differing parametrizations of the waveform, and importantly, the absence of any possibility for triggering of each individual sample of the waveform, for measurement synchronization and for providing the general data acquisition synchronicity.
In figure 6, an example of a comparative analysis of one of the test measurements is provided to demonstrate the possible interference of the harmonic component.Two measurements are made by applying the same amplitude ac electric current with the MCS to the drive coil at 1 Hz frequency and measuring the induced voltage at the measurement coil.From these two signals, one is modeled by compensating the 1st to 5th harmonic components, effectively containing only the fundamental component of a signal and other noise sources (equations ( 4) and ( 5)) The magnitudes of these harmonic components are found in prior measurements empirically by subtracting from the original signal the possible absolute value numerically and thus tuning the output current signal of the MCS such to obtain nearly 100% compensation (cancelation).In both cases, the induced voltage signals from PB2 are measured, and a simple linear single-component sine fitting algorithm is applied.In figure 6(a), the resulting fitting data (visually overlapping at the presented scale) of the measured induced voltage signals are presented.In figures 6(b) and (c) the difference between the fitted data and the measured induced voltage signals are shown, for the time and frequency domains, respectively.It can be observed that while the fundamental component (frequency f S ) in such test measurements is naturally cancelled out, the higher harmonics are still present in the first uncompensated signal, which however, is clearly compensated in the second signal where the initial correction (subtraction) is applied.
At the fundamental frequency 1 Hz and for the small amplitude U ind = 0.02 V (typically up to 0.35 V for the 10 Hz frequency) of induced voltages in the PB2 velocity mode, the resolution of the higher harmonics compensated signal can be evaluated (see figure 6(c)).Along the frequency spectra between 0.2 Hz to 10 Hz the residual signalremaining additional distortions (or higher order harmonics) plus additional noises and without any additional treatment or filtering-is below residual U ind = 200 nV.In relative terms resulting residual U ind /U ind / √ n <1 ppm, where n = 9 is the total number of the periods of the oscillations for this particular case.
In the next stage of verification, the results of the interferometric measurements of the actually occurring mechanical oscillations are included in the analysis in reference to the measured induced voltages.
Analogous to the previous case, two identical output electric current signals are generated with MCS and applied to the drive coil of PB2.Similarly, in the second signal, all the harmonic components are compensated.In this case, the amplitude of the applied electric current is one order of magnitude higher than previously, and the oscillation frequency is set to be 5 Hz.The resulting induced voltage in the measurement coil and the amplitude of the coil motion are measured.
In figure 7 the comparison of measurements with and without harmonic compensated ac electric current signals are presented.It can be observed from the results that the induced voltage measurements and the interferometric coil motion measurements are consistent with one another.Thus, the possible potential distortions corrupting the desired ideal singlecomponent sine wave signal can be modeled (and eliminated) initially, before the input of the PB2 setup to obtain at the output of the PB2 setup a measurement signal with maximally reduced uncertainty contributions.The measurement results presented in figure 7 (see also figure 6), shown in relative terms and without any additional signal treatment, demonstrate about 1 ppm of currently achieved upper limits on the residual noise level apparent in the velocity mode measurements of PB2 setup.
Other possible obvious electrical or digital data evaluation or filtering improvements can still be made to minimize the remaining apparent noise sources in the system.However, in the next section, direct comparison and thus direct verification results of the induced voltage measurements made against the AC PJVS quantum voltage standard will be presented.

Realization of AC PJVS referenced measurement
The realization of PB2 velocity mode measurements directly referenced against the voltages created by the quantum AC PJVS is performed in accordance with the electrical schematics provided in figure 4. In order to validate the measurements, initially, the measurement configuration is set up with a test shunt resistor (see figure 4(a)).Here, the resistor is used as a quasi-identical replacement of the PB2 setup and the voltage drop across the resistor is measured similar to measurements of the induced voltage at the coil in the velocity mode.The presence of the resistor in the schematics can also be seen as analogous to the state of PB2 velocity mode measurements with a non-moving measurement coil, which has to be assumed here only with its own coil resistance.Herewith, the characteristic performance of the MCS and AC PJVS is obtained in their fully isolated state, meaning that all parasitic low-frequency influences and noise sources of the PB2 are absent completely, and AC output signal U test of MCS is directly compared with the ac voltage output U PJVS of AC PJVS (see figure 4(c) and equations ( 6) and ( 7)).
Electrically, such differential voltage measurement is reduced to a measurement of the residual voltages using one voltmeter with the advantage of lower noise level and direct traceability to the SI units, where one of the signals is the AC PJVS voltage output and the other one is the signal to be characterized.In a similar manner as in the previous validation measurements (without AC PJVS) the required additions or compensations of the higher order harmonics from the U test (or later U ind ) signal can be made and further be compared with U PJVS .Systematic measurements including also the PB2 setup was made and all the measured data for different input parameters (t, f S , f n , ϕ S , ϕ n , U S , U An ) were evaluated.Also, different parameter configurations of the voltmeters for measuring the resulting residual voltage signals were tested, particularly, the sampling time that is closely connected with the signal frequency (see figure 1) and the aperture time of measurements.In figure 8 three identical measurements using different aperture times are presented.
The PB2 setup allows us to obtain measurements by altering the measurement routine to include or cover only different isolated stages of the involved subsystems (see figure 4).The following three main measurement configurations were tested within the scope of the current study.
(i) Resistor-Electrical measurement infrastructure is the same and a simple resistor is used as a replacement of the PB2 (replacement to induced voltage measurements).The MCS is driving current through a resistor which is connected (floating) in differential measurement mode with AC PJVS to the voltmeter (see figure 4(a)), (ii) Simplified-model-Electrical measurement infrastructure is the same and the PB2 is connected with minimally required electrical connections.The drive coil is connected with MCS and the measurement coil (floating) in differential measurement mode with AC PJVS to the voltmeter (see figure 4(b)), (iii) PB2-Electrical measurement infrastructure is the same and the PB2 is connected in its full operational mode (including all main and minor subsystems).The drive coil is connected with MCS and the measurement coil (floating) in differential measurement mode with AC PJVS to the voltmeter (see figure 4(b)).
The systematization of the measurement results is summarized in table 1 and figure 9.The stepwise-approximated waveform generated by AC PJVS consists of 20 sample points per period of oscillation.For sampling the voltage measurements (digitization) we use Keysight 3458A voltmeter preset for 1 V measurement range.In future, we expect improved type A measurement uncertainty when using the 100 mV measurement range, obviously for all those induced voltage measurements that have amplitudes lower than 100 mV.The sampling rate and the aperture time were chosen to correspond to the apparent limits of the voltmeter and the preset mask of sample points of the AC PJVS voltage steps in order to capture the measurement points accordingly.As an example, in the case of data point number 11 (see figure 9), having 20 sample points of AC PJVS per period leads to a 50 ms total interval time per sample which is further separated into three segments, the initial two of which are the 10 ms of initial delay (first 1/5th), then 30 ms aperture time (next 3/5th).
Successive measurements of U ind − U PJVS for different input electric currents (amplitudes and frequencies) demonstrate the variability of controlling the operation of the PB2 in the velocity mode.The obtained results in terms of relative uncertainty of the voltage measurements show nominally even several tens of ppb for the case of measured voltage drop over a resistor.Notice that one of the main contributing factors leading to obtaining larger relative measurement uncertainty is the small amplitude of the induced voltages, which is a direct consequence of the chosen small electric current (or the small mechanical oscillation amplitudes, or very small or very large oscillation frequencies).Such small values were chosen to test the practical limits of the PB2 velocity mode operation in combination with the MCS.As an example, at  1 Hz and 8 Hz oscillation frequencies with the corresponding effective voltage amplitudes of 27 mV and 15 mV result in relative uncertainties at 20 ppm level, whereas at 4 Hz, 8 Hz, and 10 Hz frequencies with the effective amplitude of 300 mV (for all frequencies) the relative uncertainties are considerably smaller and are distributed at the level of 0.4 ppm up to 1 ppm.The measurements, which are grouped in figure 9 with symbol (red cross marker-resistor), represent the isolated operation of the MCS and AC PJVS.In comparison with the measurements grouped with other symbols and (square marker-PB2 and circle marker-simplified model of PB2) it is evident the contribution of the PB2 setup on the change of the noise level.It can be evaluated from the results presented in figure 9 that at the isolated MCS and AC PJVS state for the same amplitude (0.3 V, items 1 and 3) but for different frequencies of signals the difference is negligible and only the one with the reference 2.5 V voltage signal exhibits slightly lower noise level at the order of several tens of ppb difference.When comparing items 2 and 3, it is obviously evident that under identical parameter settings, the one with greater amplitude shows better relative measurement uncertainty.Also, it can be observed from figure 9 items 5 and 6 in comparison with item 10 that there are no obvious differences observable between the measurement modes 'with-' or 'without compensation', all three measurements were made for 0.3 V amplitude but for different frequencies.However, in the case of the measurements shown by items 7 and 8 which are made for the same 0.118 V amplitude and the same frequency, the noise level reduction at the order of ppm is already observable.
There are several factors mixed in the measured signal at different operational frequencies that lead to an increase in noise level.Some of the higher-order harmonic components still require careful evaluation to be eliminated from the signal; similarly the other non-harmonic higher-order noise components.However, some characteristic behavior can still be seen when making a comparison between the measurements grouped by red cross marker (resistor) and all others (PB2).The evaluation of our preliminarily obtained results suggests that to a certain level of confidence it can be speculated that the noise increase is due to non-linear BL, temperature/offset drift, frequency-dependent mechanical misalignments, or frequency-dependent impedance effects, both internal on the resistor/coil side and external on the measurement device side.Therefore, it can by no means be attributed to the base level of the electrical performance of the MSC, capacities of resolving the residual voltages, finding equivalence between the two voltage signals (induced and AC PJVS), and a proper synchronization thereof or in general the overall established measurement infrastructure.
The measurement results presented in figure 9 demonstrate also the level of digitization error (approaching the practical limits) of the best in its class state-of-the-art voltmeters.Notice that due to the constant nature of the induced voltages in most classical KB systems in practice, a longer integration time at the level of several seconds and higher (typically NPLC 10) in voltage measurements is used to obtain the lowest possible noise and therefore better results for relative measurement uncertainties.This, of course, comes with the cost of time lags during data processing and some other inevitable considerations and device-specific engineering drawbacks.In our study, we allowed optional time periods for resolving the residual voltages from the difference signal (induced by PB2 and applied by AC PJVC ac voltages) defined by the aperture time being experimentally tested to be from 20 ms up to 100 ms.In our case, this is on the expanse that the noise level is increasing.
Depending on the value of the signal frequency and the duration of the signal period, the noise level can also be affected.This dependence in part is due to a combination of factors such as the quantized nature of reference voltage, the possibilities of discretizing stable voltage steps with AC PJVS along the generated reference ac voltages, and the duration of a single step (see figure 8) on the one hand, and the ability to find and further adapt an ac induced voltage with identical amplitude and frequency on the other hand.
We expect to improve these preliminary obtained relative uncertainty values when we have enough measurement data to carry out a more thorough systematic and statistical analysis, including a portion of the contributions originating from the total or partial compensation of the higher-order harmonic distortions.We also leave the investigation on finding (tuning the system) the optimal parameter set of measurements that may lead to obtaining the best and smallest achievable relative uncertainties for future work.This is also because such a search can qualify as a technical task pertaining to each individual system.Nevertheless, the development of a more generalized and robust measurement system and a more simplified measurement routine is crucial for the realization of ac voltage measurements in velocity modes of table-top systems that already demonstrate only an order of magnitude away relative uncertainties than that of DC voltage measurements known from classical KB systems.
As mentioned, our primary goals were the demonstration of the developed AC MCS and its capabilities, its adaptation into and the conceptualization of a newly developed measurement routine within the velocity mode of measurements in the PB2 setup, and the SI-traceable AC PJVS referenced ac type of induced voltage measurement.Due to this, the study of several other important factors remains beyond the scope of current work.One such factor is the long-term stability of the offset point that requires only several nA up to 10 nA DC electric currents for compensating the observed typical drifts during the measurement process.This drift in effect has two major causes within the PB2 setup: the mechanical misalignments appearing during the measurement process and the thermal effects affecting primarily the magnetic field (temperature coefficient about 300 ppm K −1 ) and therefore the change of the Bl factor of coil-magnet assembly.Additionally, whereas this drift is less likely to be originating within the MCS itself, other minor noise effects (both dc and ac) are apparent within the MCS and within the connection of the MCS with the drive coil of the PB2.These noise effects are partially due to the crosstalk with the passive background noises within the PB2 system and surrounding it, and also due to some other parasitic noise effects that are inevitable while connecting the electrical infrastructures of MCS, PB2, and AC PJVS together.However, some simple improvements have already been undertaken to operate with AC PJVS system which is highly sensitive to external electrical disturbances and to prevent noise leakages into the overall system.

Conclusion
We present operational capacities of newly developed MCS and its adaptation to the velocity mode of measurements of the PB2 setup (PB2 -is a table-top version of the KB system) as a means for generating ac mechanical oscillations and induced ac voltages in the measurement coil.Various test measurements with the MCS unit are demonstrated at the most practical operational parameters of the PB2 setup.Particularly for the oscillation frequencies of 0.1 Hz-20 Hz (however, not limited to the negligence of a broader range of 0.01 Hz up to several hundred Hz) and for amplitudes of up to 1 mA with 16bit effective resolution.The MCS allows generating complex ac waveform signals analogous to a waveform synthesizer by adding to the original single frequency component signal an extra five independent higher harmonic components each of which with an adjustable resolution of 10 ns for phase and 16bit for amplitude.Additionally, the MCS is supported by an external clock at 10 MHz frequency which serves also as a common reference time base for all the peripheric electronics of the PB2 setup and AC PJVS system.Thus, in this paper is discussed the comparison measurements between the direct output signal of MCS with the ac quantum voltage standard at the required accuracy levels.More importantly, we presented the comparison between the measured induced voltages in the coil of the PB2 as a result of the applied drive electric current by MCS against identical ac voltages generated with AC PJVS system.Difference measurements between the induced voltages and AC PJVS voltages are made by initially adjusting these two signals to match their average amplitudes and be synchronous with their phase and frequency.The residual voltages and their standard deviations are evaluated for different sets of input parameters in order to validate the adapted measurement concept as well as to obtain the main contributing factors on system performance and influential noise sources.Among other results presented, we demonstrated an SI-traceably made (AC PJVS referenced) ac voltage measurements in PB2 setup that at an isolated state of operation (see item resistor in figure 9) achieves relative measurement uncertainty of several tens of ppb, whereas at the fully operational state and for enough big amplitudes of the induced voltages V = 0.3 V (see item PB2 in figure 9) we have preliminarily achieved values distributed from 0.4 ppm to 1 ppm level, to be improved further.

Figure 1 .
Figure 1.Basic concept design of the MCS.

Figure 2 .
Figure 2. Timing of MCS and the compensation of the phase shift.

Figure 3 .
Figure 3. Block and data acquisition diagram of the velocity mode.The item Current Source is used interchangeably for indication of the MCS or HP3245A.The interferometric and photodiode position sensor measurements, which remain out of the scope of discussions in this work, are made in the background to track the proper operation of the PB2.

Figure 4 .
Figure 4. Core electrical schematics of the velocity mode measurements of PB2 in combination with MCS and PJVS.The schematics in (a) show a measurement configuration where a test (shunt) resistor is used as a quasi-identical replacement of the PB2 setup, and the voltage drop across the resistor is measured similar to measurements of the induced voltage in the velocity mode.(b) Actual measurement schematics with PB2 setup, where the MCS generated ac electric current is applied at 'drive coil' and the induced voltage is measured at 'measurement coil'.(c) Block diagram showing all possible measurement configurations that were realized within this study.

Figure 5 .
Figure 5. (a) Comparison of the amplitude spectral densities of the induced voltages using MCS and two other current sources and (b) the remaining noise when the fundamental component is subtracted from each signal.

Figure 6 .
Figure 6.Comparison of the induced voltage measurements at 1 Hz oscillation frequency as a result of two applied electric currents of the MCS, one of them is pre-modeled without the higher order harmonics, (a) fitting data (b) residuals-difference between the fitted data and actually measured induced voltages (c) the FFT of the residuals-with and without harmonic compensations, orange line shows the voltage noise at the level of 200 nV.

Figure 7 .
Figure 7.Comparison of the measurements at 5 Hz oscillation frequency with and without harmonic component compensations obtained from (a) the interferometric measurements of the motion, (b) the induced voltage measurements, and (c) direct velocity measurements.In all cases, the results are presented as FFT of residuals relative to signal amplitude.

Figure 8 .
Figure 8.(a) Model representation of both induced (or test) and the AC PJVS voltages, and associated sampling and aperture times, (b) RMS of the induced voltage U ind at f S = 1 Hz signal frequency with total N = 125 oscillations using T S = 50 ms (20 Hz) sampling time and three different aperture time T A = 20 ms, 30 ms, and 40 ms, (c) standard deviation of the RMS as a function of the aperture time.

Figure 9 .
Figure 9.The relative uncertainty of voltage difference U ind − U PJVS measurements in terms of the measured standard deviation of voltage difference (type-A uncertainty at k = 1) over nominal voltage amplitude and the square root of the number of measurement cycles (periods) as a function of oscillation frequency.As an example, in the case of data point number 11 the frequency is 1 Hz, and the nominal mean value of RMS amplitude of the signal with 500 oscillation periods is measured to be approximately 15.7852 mV with 2.3 µV standard deviation (see example data of figure8).