Josephson Arbitrary Waveform Synthesizer as a Reference Standard for the Measurement of the Phase of Harmonics in Distorted Waveforms

Abstract

We have used the Josephson arbitrary waveform synthesizer (JAWS) to provide traceability for the phase of the harmonics, relative to their fundamental frequency, of a distorted waveform. For distorted waveforms with rms values from 0.154 to 0.2 V and harmonic magnitudes from 5% to 40% of the fundamental, our system can generate odd harmonics up to the 39th with best phase uncertainties from 0.001° to 0.010° (k = 2.0), depending on the harmonic number and harmonic magnitude. We anticipate that the ability of the JAWS to generate distorted waveforms with the lowest possible uncertainty in the magnitude, and phase spectra will make it a unique tool for low-frequency spectrum analysis.

I. Introduction

HARMONIC analysis is used in electricity networks, communications, characterization of systems and materials, and acoustics and vibration. While the traceability of harmonic magnitude measurements to ac–dc transfer measurement standards is well established (see [1]), there is a gap in the traceability for the phase of the harmonics relative to the fundamental.

The Josephson arbitrary waveform synthesizer (JAWS) [2] has been successfully implemented in a number of applications for ac metrology, such as the calibration of ac voltmeters, evaluation of thermal-to-voltage converters used in ac–dc transfer voltage standards [3]–[6], impedance bridges [7], and Johnson noise thermometry [8]. Comparisons of JAWS with programmable Josephson voltage standards and with other JAWS have shown agreement within some parts in 10⁸ [9]–[11], depending on the frequency and signal magnitude. Budovsky [12] proposed the use of the JAWS for the calibration of the phase of harmonics of distorted waveforms relative to the fundamental. Based on [12], we use the JAWS to generate precisely distorted waveforms that contain harmonics of known magnitude and phase.

The primary application of this paper is to provide traceability for the phase of the harmonics for power analyzers used in power systems and appliance certification. Target uncertainties for this application range from 0.001° to 0.010°, depending on the relative harmonic magnitude and the harmonic number.

In this paper, which is an extension of [13], we describe the experimental setup and report experimental results of the evaluation of the JAWS as a harmonic phase standard. The uncertainty components of the system are given and summarized in an uncertainty budget.

II. System Description

The measurement system is shown in Fig. 1. The JAWS [14] contains a continuous-wave (CW) generator, a ternary pattern generator, two broadband radio frequency (RF) amplifiers, two arbitrary waveforms generators (AWGs), two voltage-to-current (V/I) converters, two NIST Josephson junction arrays (JJA), and microwave circuit designs [15]. At the input and the output of each RF amplifier, a combination of cascaded inner conductor type dc blocks and attenuators is connected, shown as capacitors in Fig. 1.

Fig. 1.

Block diagram of the JAWS system.

The CW generator is referenced to a 10-MHz signal derived from a cesium beam atomic clock. A 24-bit flexible resolution digitizer is used to check the quantization of the JJAs. To minimize common mode and other noise sources, the digitizer, the RF amplifiers, and the voltage-to-current converters are battery powered for isolation.

The JJAs are programed to produce two arbitrary waveforms of the same harmonic content and rms value but with a relative phase difference of 180°. While the application requires only one JJA, the use of two channels enables additional possibilities, as discussed in Section III. Two digital sampling systems have been used to measure the arbitrary waveforms—one based on two precision sampling multimeters [16] (digitizer1) and the other based on the National Instruments PXI5922¹ (digitizer2). For all the experiments, the sample period of digitizer1 was set to 70 μs and the aperture time 50 μs. The sampling frequency of digitizer2 was 100 kHz.

A number of precisely known waveforms of 60-Hz fundamental frequency and different harmonic phases have been generated, containing the 3rd, 5th, 7th, 9th, 11th, 23rd, 31st, and 39th harmonics. These harmonics are commonly found in power systems and referenced in power quality documentary standards. The number of the harmonics was chosen to keep the signal-to-noise ratio of the harmonics relative to the noise floor of the spectrum analysis high enough to allow phase resolution better than 0.001°. In some cases, we used waveforms with fundamental frequencies other than 60 Hz. Two types of waveforms were used: 1) a waveform containing the fundamental and one of the above harmonics at a time (referred to as “one harmonic”) and 2) waveforms with the fundamental and all of the above harmonics at the same time (referred to as “all harmonics”). Fig. 2 shows two “all harmonics” waveforms with an amplitude of 0.140-V rms. Each of these waveforms has harmonic amplitudes equal to 10% of the fundamental, with one waveform having harmonics with a phase angle of 90° between the each harmonic and the fundamental, and the other with a phase angle of 0° between each harmonic and the fundamental. A third “one harmonic” waveform has the same rms amplitude as the “all harmonic” waveforms but contains only the 3rd harmonic at 90°.

Fig. 2.

Typical test waveforms used in the evaluation of the JAWS as standard for the phase of the harmonics of a distorted signal.

III. System Evaluation

Because of the errors that can occur in a practical realization of a JAWS [11], [14], [17]–[19], to evaluate the performance of the JAWS as a harmonic standard, it is important to show that the following.

1. The phase of the generated waveform is independent of the specific JJA.

2. The biasing electronics do not affect the operation of the system.

3. The phase of the harmonics is independent of the repetition frequency and of the RF pattern of pulses used to produce a particular distorted waveform (i.e., if a particular distorted waveform can be obtained using more than one pattern of pulses and repetition frequencies, then the resulting distorted waveforms should be the same).

4. The phase of each generated harmonic does not depend on the total harmonic content. In this section, we present several experiments aimed at providing evidence that these conditions are met.

A. Comparison With AC–DC Voltage Transfer Standards

To obtain confidence in the operation of the JAWS we compared the magnitude of both the sine wave and distorted waveforms generated by the JAWS with the National Measurement Institute Australia (NMIA) ac–dc transfer standards based on thermal-to-voltage converters. For the sine wave evaluation, we measured the ac–dc difference of a calibrated Fluke 792A ac–dc transfer standard with a 0.2-v single-frequency sine wave at frequencies of 100, 400, 1000, and 5000 Hz (Table I). The ac–dc differences measured by both the systems agree within their respective standard deviations.

TABLE I.

AC–DC Difference of a Fluke 792A Transfer Standard for a Single-Frequency 0.2-V Sine Wave Measured by the JAWS and the Conventional AC–DC Transfer System of NMIA

	JAWS		Conventional ac-dc Standard
Frequency (kHz)	ac-dc Difference (μV/V)	Standard Deviation, (μV/V)	ac-dc Difference (μV/V)	Standard Deviation. (μV/V)
0.1	+ 12.1	1.2	+ 14	1.6
0.4	+ 6.2	0.7	+ 7	2.3
1	+ 2.4	0.8	+ 2	8.5
5	+ 1.8	0.7	+ 3	5.5

For the distorted waveforms, we used digitizer1 as a transfer standard to measure the magnitude of the JAWS harmonics. Fig. 3 shows the magnitude errors of digitizer1 for “all harmonics” waveforms with various ratios of the magnitude of the harmonics to the fundamental. The magnitude errors of digitizer1 measured for similar waveforms using the thermal power comparator of NMIA applying the technique described in [1] also did not exceed 0.001% of the fundamental.

Fig. 3.

Harmonic magnitude error of digitizer1 for various ratios of the harmonics to the fundamental. The error bars indicate the standard deviation of the measurement.

B. Harmonic Phase Measurements

A number of experiments, with both the single-frequency sine waves and distorted waveforms, have been conducted to demonstrate that the phase of the signals generated by the JAWS is independent of the JJA used and the bias electronics (which include the CW generator, the pattern generator, the RF amplifiers, the voltage-to-current converters, and the AWGs).

For the sine wave test, we generated two single-frequency sine waves of 0.158-V rms with a nominal phase difference of 180° and used two channels of digitizer1, whose relative phase shift was nulled prior to the measurement, to measure the phase difference between these sine waves. The agreement was within 0.00003° at 60 Hz and better than 0.0003° up to 1 kHz. The 60-Hz result was confirmed with digitizer2 operated as a lock-in amplifier.

Next, as part of a distorted waveform test, we calibrated digitizer2 with two different JJAs from the same chip, driven by the same bias electronics, using the “10% all-harmonics” waveform specified above. The results of the two measurements agreed within 0.001° [Fig. 4(a)]. Then, the two JJAs were used to generate the same waveform, but driven by different bias electronics [Fig. 4(b)]. For all the harmonics up to the 23rd, the results agreed within 0.001°. As the harmonic number increased the disagreement also increased but was still within the uncertainty of the measurement. The error bars in Fig. 4 indicate the standard deviation of the measurement.

Fig. 4.

Phase error of digitizer2 measured using two different JJAs driven by the same (a) bias electronics and (b) different bias electronics.

Insight into the sensitivity of the JAWS to the bias electronics can also be gained using waveforms of different fundamental frequencies. We used the JAWS to measure the phase errors of digitizer1 at 65 Hz, and the phase errors of digitizer2 at 400 Hz (Fig. 5). Digitizer1 shows a linear dependence of the phase error with the harmonic number. This is due to an uncancelled timing error in the sampling of the DSVMs of digitizer1. Because it is used as transfer standard, this dependence is not important. This experiment also gives insight into the phase error introduced by the inductive voltage that is generated across the JJAs due to compensation current flowing into the on-chip inductances. The phase angle error introduced by the inductive voltage across the array is not significant up to the 39th harmonic of 60 Hz, but in other applications where the fundamental frequency is greater than a few kilohertz, this voltage can introduce a significant phase error in the measurement.

Fig. 5.

Phase error for digitizer1 calibrated with “all harmonics” waveforms with fundamental frequencies 60 and 65 Hz and digitizer2 calibrated with “all harmonics” waveforms with fundamental frequencies 60 and 400 Hz.

To investigate the effect of the cable connecting the output of the JJA chip at low temperature to the measurement electronics at room temperature, a “10% all harmonics” wave-form was generated and measured with digitizer2 for three different cable lengths (1, 2, and 4 m). The results (Fig. 6) agree within 0.001° for all the harmonics. For comparison, Fig. 6 shows the simulated phase error values of a combination of a 1-m transmission line having nominal characteristics of the actual coaxial cable at room temperature (Table II) and digitizer2. The simulation is based on [20]. The simulated and the measured phase errors agree within the standard deviation of the measurements.

Fig. 6.

Phase error of digitizer2 for different cable lengths (1, 2, and 4 m). The Calc L = 60 nH and Calc L = 6 nH points correspond to a simulated 1-m transmission line having the characteristics in Table II.

TABLE II.

Parameters Used in the Simulation for the Effect of the Transmission Line connecting the JJA Output to Digitizer2

Characteristic	Value	Source
Characteristic impedance	50 Ω	Specifications
Line capacitance	94 pF/m	Specifications
Load resistance	1 MΩ	Specifications
Load capacitance	60 pF	Specifications
Length	1 m	Assumed
JJA output inductance	6 nH	[21]
	60 nH	[22]

Finally, we investigated the performance of the JAWS when spurious pulses are added to the pattern of the RF pulses driving the JJA. For this reason, in a “10% all harmonics” waveform, we replaced the first m 00_HEX bytes that appear in the ideal pattern of pulses with m 01_HEX bytes, effectively adding m pulses to the ideal RF pattern of pulses. The results of the corresponding harmonic phase measurements are shown in Fig. 7(a). Fig. 7(b) shows the corresponding spectra. When adding up to 15 pulses, the harmonic phase stays within 0.001° for all the harmonics up to the 23rd. For the higher harmonics, the results agree within one standard deviation of the measurements. Adding further spurious pulses can affect the quantization of the JJA and lead to higher phase errors.

Fig. 7.

Effect of spurious RF pulses in the bias pattern of the JJA on (a) phase error of digitizer2 for an ideal waveform (ideal), ideal wave-form with the first 15 “zero” bytes (00_HEX) replaced by 15 “one” bytes contain (01_HEX) and ideal waveform with the first 25 “zero” bytes (00_HEX) replaced by 25 “one” bytes (01_HEX) and (b) magnitude spectra of an ideal RF pattern, pattern containing 15 spurious pulses, and pattern containing 100 spurious pulses.

C. Effect of Different Repetition Frequencies and RF Patterns

To investigate whether the phase of the harmonics is independent of the repetition frequency and of the RF pattern, we generated two “10% all harmonics” waveforms with the same rms value (0.12 V) using two different pulse repetition frequencies (Fig. 8).

Fig. 8.

Phase error of digitizer2 for two “10% all harmonics” waveforms with different RF pulse repetition frequencies.

Next, we fixed the repetition frequency at 15.0528 GHz and used different patterns of RF pulses to generate four voltages (0.158-, 0.117-, 0.078-, and 0.039-V rms) of a “10% all harmonic” waveforms using one of the JJA. These waveforms were measured with digitizer2 (referred to as direct measurement). Then, a precision inductive voltage divider with known ratio errors (Sullivan F9200), connected as shown in Fig. 9, was used to produce four waveforms of the same rms values and harmonic content by scaling an 0.140-V waveform (indirect measurement). Fig. 10(a) shows the difference between the direct and indirect phase measurements for the four voltages. This experiment was also conducted for an “all harmonics” waveform with each harmonic 20% of the fundamental [Fig. 10(b)]. The results in Fig. 10(a) and (b) show that the performance of the JAWS is independent of the voltage.

Fig. 9.

Setup for the generation of distorted waveforms with different rms values from a waveform generated using the JAWS and scaling it with an inductive voltage divider.

Fig. 10.

Phase error of digitizer2 for different voltages and liquid helium levels for waveforms measured directly using the setup of Figs. 1 and 9 for “all harmonics” waveforms with magnitude of each harmonic of the fundamental (a) 10% and (b) 20%.

Finally, the experiments were repeated with the helium level in the dewar varied from its highest to its lowest operational level. The results in Fig. 10(a) and (b) show that this change does not significantly affect the phase of the harmonics.

D. Evaluation of the JAWS for Different Phase Angles and Distortion

In all the experiments presented above the harmonics were at 90° from the fundamental. To show that the JAWS can produce accurate waveforms with other harmonic phases, we generated 1) three “10% all harmonics” waveforms where all the harmonics had phase angles 0°, 60°, and 90° to the fundamental, respectively, and 2) an “all harmonics” waveform having phase angles 90°, 60°, 0°, 90°, 60°, 0°, 90°, and 60° for the 3rd, 5th, 7th, 9th,11th, 23rd, 31st, and 39th harmonics, respectively. Fig. 11 shows that the phase errors for each harmonic, measured by digitizer1, agree within one standard deviation.

Fig. 11.

Phase error of digitizer1 for a 10% “all harmonic” waveforms with phase angles all phases at 0°, all phases at 90°, all phases at 60°, and phase shifts of 90°, 60°, 0°, 90°,60°, 0°, 90°, and 60° for the 3rd, 5th, 7th, 9th, 11th, 23rd, 31st, and 39th harmonic, respectively.

An ideal JAWS has infinitely small phase resolution. In a practical system, the phase resolution is limited by the signal-to-noise ratio of the JAWS. The resolution of the JAWS was verified at 90° for incremental changes of 0.0001°, 0.0005°, and 0.001°. Three “all harmonics” waveforms with phase angles 90.0001°, 90.0005°, and 90.001°, respectively, were generated with the JAWS and measured with digitizer2 (see Fig. 12). The resolution is as expected up to the 11th harmonic, after which the standard deviation of the measurements increases up to 0.004°.

Fig. 12.

Phase difference of digitizer2from 90° for incremental changes of 0.001°, 0.0005°, and 0.0001°. Solid lines: nominal values.

To be a true harmonic phase standard, the JAWS must be able to generate waveforms of the same ratio of the harmonics to the fundamental but with different total harmonic contents of the composite waveform. This can be shown by demonstrating equivalence between “one harmonic” and “all harmonics” waveforms for the same ratio of the harmonics to the fundamental. This equivalence is also important as a matter of convenience in experimental design because low-frequency waveforms have pulse patterns that require about 50 MB of storage and takes several minutes to calculate. For this purpose, digitizer1 was first used to measure “one harmonic” waveforms and then an “all harmonics” waveform (Fig. 13). The difference between the two sets of measurements did not exceed 0.001°.

Fig. 13.

Phase error of digitizer1 measured with one harmonic at a time and all harmonics simultaneously. The error bars indicate the standard deviation of the measurement.

Finally, we generated an “all harmonics” waveform with monotonically decreasing harmonics, inversely proportional to the harmonics number “1/N,” with harmonic phases of 90° for all the harmonics. Fig. 14 shows the results for “all harmonics” waveforms with the amplitude of each harmonic to the fundamental 5%, 10%, 20%, and 1/N, respectively. For all the waveforms, the phase error of each harmonic is less than 0.001°. For harmonics higher than the 11th, the standard deviation of the measurement increases up to 0.004°.

Fig. 14.

Phase error of digitizer2 for different harmonic magnitudes relative to the fundamental.

It should be noted that for the waveforms used in the evaluation of the system, the current margins of the JAWS depend mainly on the voltage. The current margins range from 0.6 mA at 0.1 V to 0.4 mA at 0.2 mV. The distortion of the generated voltages does not have a measurable effect on the margins.

IV. Uncertainty Analysis

The major uncertainty components of the system include the uncertainty introduced by the delta-sigma modulation producing the RF bias pattern, delay of the RF paths connecting the outputs of the pattern generator to the JJAs, resolution of the digitizer2 used to monitor the quantization of the array, length of the cable used to connect the output of the JJAs with the instrument under test, the rounding, resolution of the JAWS, and the standard deviation of the measurements.

Table III shows the uncertainty budget based on [23] for harmonics up to the 10th when the magnitude of each harmonic relative to the fundamental is 10%, and the rms voltage is 0.154-V rms. We have included a type-B uncertainty component to account for the discrepancies between different experiments (item 3 in Table III). This uncertainty component was estimated from the maximum deviation (d_max) between different experiments reported in Section III, as d_max/√12 ([23, Sec. 4.3.7]).

TABLE III.

Typical Uncertainty Budget for a 0.154-V RMS, Fundamental Frequency 60 Hz, Each Harmonic up to 10% of the Fundamental, up to the 9th Harmonic

Item	COMPONENT	TYPE	DIS	Standard uncertainty (°)
1	Code generation error	B	GAU	0.0001
2	NI resolution	B	GAU	0.0003
3	Maximum deviation between different experiments	B	GAU	0.0005
4	rf delay	B	GAU	0.0001
5	Cable length	B	GAU	0.0001
6	Rounding	B	REC	0.0001
7	Std Dev of Measurements	A	GAU	0.0010
8	Phase resolution	B	REC	0.0001
	Combined Standard Uncert.,		0.0006 °
	Effective Total DOF, n		24.6
	95% Coverage Factor, k		2.07
	95% Expanded Uncert., U		0.0013 °

We prepared a number of uncertainty budgets for harmonic ratios to the fundamental 5%, 10%, 20%, and 40% for harmonics up to the 9th, from the 11th to the 19^th, and from the 21st to the 39th. The resulting uncertainties for specific harmonic ranges (e.g., from the mth harmonic to the nth harmonic U_m–n(°)) can be fitted to equations of the form

$$U_{m-n}(°)=aR(\%{)}^{-b}+c$$ (1)

where R(%) is the ratio of the harmonic to the fundamental, expressed as percentage. Table IV shows the coefficients a, b, and c of (1). For example, for 10% ratio of the harmonics to the fundamental, R(%) = 10, the calculated uncertainties from (1) are 0.0013° for harmonics 3–9, 0.0019° for harmonics 11–19 and 0.0096° for harmonics 21–39. Table V shows the best and worst uncertainties of our system for a voltage with rms value of 0.154 V.

TABLE IV.

Coefficients of (1) for Ratios of Harmonics to the Fundamental from 5% to 40%

Range of harmonics	a	b	c
n<9	0.00212	0.247	0.0001
11≤n≤19	0.00225	0.098	0.0001
21≤n≤39	0.00511	0.059	0.0052

TABLE V.

Best and Worst Cases Uncertainties for a Waveform With RMS Value of 0.154 V

	Uncertainty (°)
R(%)	n<9	11≤n≤19	21≤n≤39
5	0.0016	0.0020	0.0098
40	0.0010	0.0017	0.0093

V. Conclusion

The results reported in Section IV show that the JAWS exhibits consistent results as a phase standard with expanded uncertainties from 0.001° to 0.010° depending on the harmonic number and harmonic magnitude. These results were obtained for different JJAs driven by different RF paths, distorted waveforms having different number of RF pulses driving the JJA, different bias electronics, different voltages and different distortions, at different helium levels, and different cable lengths connecting the output of the JAWS to the phase measurement equipment. The JAWS gives consistent results for waveforms with fundamental frequencies 60, 65, and 400 Hz. It was also demonstrated that the introduction of a certain amount of spurious RF pulses does not affect the harmonic phase of the JAWS waveforms within the claimed uncertainties.

This paper was motivated by the need to provide traceability to power analyzers used for testing appliances and monitoring voltage and current harmonics in power systems according to the 61 000 series documentary standards of the International Electrotechnical Commission. The fundamental frequency for these applications corresponds to the mains frequency. However, the traceability of harmonic phase is also important in other applications such as audio processing, communications, seismology and geophysics, and the characterization of systems and materials. While the measurement requirements (e.g., voltage and frequency range and the related uncertainties) in these applications are different from the characterization of power analyzers, the JAWS can, nevertheless, provide an ultimate quantum standard of harmonic phase.

Biography

Dimitrios Georgakopoulos (A’11–M’12–SM’12) was born in Athens, Greece, in 1972. He received the B.Eng. degree in electrical engineering from the Technological Educational Institution of Piraeus, Egaleo, Greece, in 1996, the M.Sc. degree in electronic instrumentation systems from the University of Manchester, Manchester, U.K., in 1999, and the Ph.D. degree in electrical engineering and electronics from the University of Manchester Institute of Science and Technology, Manchester, in 2002.

From 2002 to 2007, he was a Research Scientist with the National Physical Laboratory, Teddington, U.K. In 2007, he joined the National Measurement Institute, West Lindfield, NSW, Australia, as a Research Scientist, where he has been involved in the development of quantum voltage standards and low-frequency electromagnetic compatibility standards.

Dr. Georgakopoulos is a member of the Measurements in Power Systems IEEE Committee (TC-39) and a member of the American Association for the Advancement of Science, USA.

Ilya Budovsky (M’00–SM’03) was born in 1964. He received the B.E. degree in electrical engineering from the Technical University of St. Petersburg, St. Petersburg, St. Petersburg, Russia, in 1987, and the Ph.D. degree from the D. I. Mendeleyev Research Institute for Metrology, St. Petersburg, in 1995.

Since 1991, he has been with the National Measurement Institute Australia, formerly the National Measurement Laboratory of CSIRO, where he became a Leader of the Low-Frequency Standards Group in 1997 and a manager of the Electricity Section in 2009. He is responsible for the development and dissemination of Australian measurement standards for electricity, magnetism, and time.

Dr. Budovsky is a fellow of Engineers Australia and the Australian Representative to the Consultative Committee for Electricity and Magnetism, where he chairs the working group on interregional coordination.

Samuel P. Benz (M’01–SM’01–F’10) was born in Dubuque, IA, USA, in 1962. He received the B.A. degree (summa cum laude) in physics and maths from Luther College, Decorah, IA, USA, in 1985, and the M.A. and Ph.D. degrees in physics from Harvard University, Cambridge, MA, USA, in 1987 and 1990, respectively.

In 1990, he joined the National Institute of Standards and Technology (NIST), Boulder, CO, USA, as a NIST/NRC Post-Doctoral Fellow, where he became a permanent Staff Member in 1992. Since 1999, he has been the Project Leader of the Quantum Voltage Project at NIST, where he has been a Group Leader of the Superconductive Electronics Group since 2015. He was involved in broad range of topics within the field of superconducting electronics, including Josephson junction array oscillators, single flux quantum logic, ac and dc Josephson voltage standards, Josephson waveform synthesis, and noise thermometry. He has authored or co-authored over 250 publications. He holds three patents in the field of superconducting electronics.

Dr. Benz is a fellow of NIST and the American Physical Society. He is a member of Phi Beta Kappa and Sigma Pi Sigma. He was a recipient of the three U.S. Department of Commerce Gold Medals for Distinguished Achievement, the 2016 IEEE Joseph F. Keithley Award, twice the IEEE Council on Superconductivity Van Duzer Prize, and the R. J. McElroy Fellowship from 1985 to 1988 to work toward the Ph.D. degree.

Gleb Gubler (M’11) was born in St. Petersburg (former Leningrad), Russia, in 1972. He received the M.S. and Ph.D. degrees from St. Petersburg State Polytechnical University, Russia, in 1995 and 1998, respectively. His Ph.D. thesis was on analog-to-digital conversion techniques based on sigma-delta modulation.

In 1998, he joined the Measurements and IT Sub-Faculty, St. Petersburg State Polytechnical University, as an Acting Assistant Professor and an Assistant Professor from 2001 to 2006. Since 2006, he has been a Senior Research Scientist with the Electric Energy Laboratory, D. I. Mendeleev Institute for Metrology, St. Petersburg. As a Principal Developer and Keeper, he is in charge of maintaining the National Standard of Electrical Power. His current research interests include digital signal processing; signal conditioning, precision measurements of electrical quantities and power quality parameters, and metrology for smart grids.