Research on AC voltage measurement method based on high-speed comparison and Josephson Junction Arrays Voltage Standard

The overall structure diagram of the AC voltage measuring device based on the JVS used in this paper is shown in Figure 1. The device is make up with JVS, comparator, independent isolated power supply, pulse trigger interrupt timer and microprocessor.

Figure 1.

Schematic diagram of the AC voltage measuring device based on the quantum DC voltage reference

The Josephson junction array consists of 2N Josephson junction sub-array, including N sub-arrays forming a positive voltage and N other sub-arrays forming a negative voltage, each Josephson junction sub-array has an output tap connected to the comparator. The Josephson junction array can provide a specific numerical DC quantum voltage reference for the high-speed comparator by changing the bias state of the Josephson junction array.

Each comparator in the unit has a unique model, and each comparator is powered by separate, electrically isolated power sources. One end of the two comparison inputs of each comparator is connected to a Josephson junction sub-array, and the other end is connected to the tested voltage. In order to ensure that the device does not introduce non-necessary uncertainties such as resistance, the feedback loop is not set in the comparator circuit at the output end, and only the 1μF electrolytic bypass capacitor and 10 nF ceramic bypass capacitor at both ends of the power supply. The 1μF electrolytic bypass capacitor is placed within 0.5 inches of the power pin to reduce any potential voltage fluctuations from the power supply; the 10 nF ceramic bypass capacitor is placed beside the power pin and acts as a charge reservoir for the power supply during high-frequency signal switching. The output point of positive and negative voltage intermediate node is marked as E₀, on the basis of this point, and the output voltage is E₁+, the output voltage across the n Josephson junction sub-array is E_n+; and a Josephson junction sub-array is marked E₁-, the output voltage across the n Josephson junction sub-array is E_n-, and n<N. The comparator connected to E_n+ is labeled P_n+, the comparator connected to E_n- is labeled P_n-, and the comparator connected to the ground is labeled P₀.

In this paper, we use heterogeneous discrete Fourier interpolation to reproduce the measured signals. The repetition accuracy is influenced by the number of set comparators, the accuracy of the voltage reference, and the accuracy of the sampling time. In order to ensure that the influence of the sampling time accuracy on the accuracy of the recurrence signal is as small as possible, this paper uses the picosecond 16-channel precision time timer with the measurement resolution up to 5ps and the measurement stability is better than 0.6ps@1000s. The timer has 16 independent time timing modules. When the comparator jumps to output the trigger signal, the ramp voltage generation circuit is triggered to work to generate the ramp voltage, and the ADC records the digital amount of the ramp voltage conversion AD0. And the integer part N₀ of the trigger time is recorded by the FPGA timer of the 100 MHz clock, and then the calibration module calculates the phase difference T₀ between the trigger time and the system clock according to the digital quantity AD0, and finally calculates the exact time T= N₀T₀ + T₀ of the microprocessor. At this time, T₀ is the sampling interval of 10ns of the FPGA timer of the 100 MHz clock.

The AC voltage measurement method based on JVS proposed in this paper focuses on the direct comparison between the quantum DC voltage reference and the measured signal, including the following steps:

The normal phase input of each comparator is connected to the defined Josephson junction sub-array output tap, and the reverse phase input is connected to the measured signal. At this time, the Josephson junction sub-array voltage output acts as the comparator output signal jump threshold. When the measured signal exceeds the threshold voltage comparator output signal jump, the picosecond level 16-channel precision timer is triggered to work. As shown in Figure 2, a sinusoidal voltage signal is sampled. The microprocessor records the jump time of the comparator and the serial number of the comparator, and the corresponding DC voltage value can be found according to the serial number of the comparator. Convert the serial number of the comparator into the corresponding voltage reference value, that is, P_n+ to the corresponding reference voltage E_n+, and P_n- to the corresponding reference voltage E_n-, and match it with the corresponding trigger time. At this point, the microprocessor has collected all the physical quantities used to reproduce the measured signal.

Figure 2.

Schematic diagram of the measured sinusoidal voltage signal sampling

The microprocessor can reconstruct the measured signal waveform after receiving at least one complete period of signal and a sampling point. The non-uniform discrete method of Fourier is widely utilized in signal repetition and power grid parameter estimation as it has a small computational amount and strong noise resistance. Therefore, using this method and measuring the voltages of Josephson junction sub-arrays and the timer, the waveform of the measured AC voltage can be reconstructed.

The reconstruction of the measured signal waveform is conducted by using the sampling period extension mode. As shown in Figure 2, if nine comparators are used, the reference voltage are -2.8V, -2.1V, -1.4V, -0.7V, 0V, 0.7V, 1.4V, 2.1V, 2.8V, respectively, there are eighteen points are sampled in a period. And the initial signal sequence (U_i,t_i) can be obtained, where U_i is the ith voltage value, t_i is the triggering time of the ith pulse, and i=0,1,⋯,17. Then, the initial signal sequence is extended for at least three cycles to eliminate the boundary effect of the interpolation method. Finally, the intermediate periodic signal is extracted from the obtained results as the final repetition signal.

Due to the lack of simulation conditions for Josephson junction array in Multisim, a DC voltage source was used instead of it as the reference in actual simulation. The simulation schematic circuit is shown in Figure 3. To test whether the AC voltage measurement method based on quantum DC voltage reference proposed in this article can compensate for the shortcomings of PJVS equipment in the field of wideband voltage traceability, this simulation mainly focuses on measuring and testing high-frequency signals. The signal generator outputs eight sets of sine wave signals with peak values of 3V at 1kHz, 5kHz, 10kHz, 50kHz, 100kHz, 500kHz, 800kHz, and 1MHz as high-frequency test signals. The comparator uses Multisim ultra-high speed comparator AD8561AN. In the dual power supply mode, the typical transmission delay time is only 6.5ns, and the typical rise and fall times do not exceed 3.8ns, which can meet the high-frequency and high-precision AC voltage measurement requirements of this method. The comparator’s dual power supply pins are equipped with 1F electrolytic bypass capacitors and 10nF ceramic bypass capacitors. The 1F electrolytic bypass capacitor can reduce any potential voltage fluctuations from the power source; A 10nF ceramic bypass capacitor is placed next to the power supply pin, serving as a charge storage reservoir for the power supply during high-frequency signal switching, improving the stability and measurement accuracy of the comparator. And a 5k pull-up resistor is set up, with one end connected to the 5V power supply pin and the other end connected to the output pin, to improve the comparator’s load capacity. Due to the lack of picosecond-level multi-channel precision time timers in Multisim, multi-channel oscilloscopes are used for timing in actual simulations. In simulations, the input resistance and bandwidth are both infinite, and the propagation delay error can be ignored. This can effectively replace picosecond-level multi-channel precision time timers. Finally, record the transition time of each comparator using the multi-channel oscilloscope and reproduce the test signal using MATLAB.

Figure 3.

Schematic diagram of the simulation circuit

Configure the simulation circuit according to the above method, and set up 9 sets of AD8561AN ultra high speed comparators with reference threshold voltages of 2.8V, 2.1V, 1.4V, 0.7V, 0V, -0.7V, -1.4V, -2.1V, and -2.8V, respectively. When the input frequency of the measured signal is 50kHz, the reproduced waveform is shown in Figure 4. The maximum reproduced error is about 0.00017V. Considering the magnitude of the measured voltage is 3V, the fiducial error is 0.00017/6×100%≈3.×10^-5%.

Figure 4.

Surmograph of the 50 kHz measured sinusoidal voltage signal

In order to further verify the effectiveness of the proposed method in this paper, simulation measurements were conducted on the measured AC voltage signal with frequencies of 1kHz, 5kHz, 10kHz, 50kHz, 100kHz, 500kHz, 800kHz, and 1MHz. This frequencies range covers most medium and high-frequency signal measurement scenarios in actual measurements and is representative. The fiducial errors of reproduced signals with different frequency are shown in Figure 5.

Figure 5.

Plot of the reproduced waveform error changes with the measured signal frequency

From Figure 5, it can be seen that when the frequency of the measured signal increases from 1kHz to 1MHz, the error of the reproduced waveform decrease and then increase. When the frequency is 100kHz, error reaches its minimum value.

In order to evaluate the performance of the measurement approach presented in this paper. It is compared with PJVS and JAWS, as shown in Table 1. PJVS has the precisest accuracy, but is can only be used to measure AC voltage with frequency below 1kHz, and it is impossible to measure the such signal with frequency above MHz. Although the JAWS system can synthesize a broadband voltage of up to 4 MHz, the influence of the low-frequency component on the accuracy of the synthetic voltage signal increases. Not only that, the JAWS system synthetic voltage amplitude is limited. In order to improve the synthetic AC signal voltage amplitude, series multiple Josephson junction array is usually needed to meet the requirements. For instance, the German federal research institute of physical technology (PTB) has ever used eight arrays containing up to 63000 Josephson junction to synthesize effective value about 1V quantum AC voltage while only 15000 Josephson junction is needed to produce 10V AC voltage by PJVS, which greatly increase the complexity of the system structure. Compared to two existing AC voltage quantum measurement methods, the method presented in this paper has advantages such as a simple system structure, convenient operation, and broadband voltage quantum traceability.

The errors of reproduced AC signals mainly depend on the accuracy of JVS system, the performance of the high-speed comparator, the timing accuracy of the multi-channel precision timer, and the reproduction error of the non-uniform discrete Fourier interpolation method. As the most accurate DC JVS currently available, the output voltage uncertainty of JVS is on the order of 10^-9. The extended uncertainty of the JVS system developed by the National Institute of Standards and Technology (NIST) in the United States under 10V DC voltage output testing is only 2.2nV (k=2). And its error can be neglected in AC voltage measurement.

The offset voltage of the AD8561 high-speed comparator chosen in this paper typically ranges from 0mV to 2mV, with a maximum of 4mV. Considering its 3000-fold amplification factor, the time error of the signal crossing the offset voltage range is almost negligible compared to the long cycle time of the measured signal from 50 kHz to 500 kHz. But when the frequency of AC voltage measurements is low, the voltage changes are relatively slow, and more time is needed to cover the offset voltage. Lower the frequency, more time is needed, and larger error can brought from this cover time. This is the cause that lower frequency makes larger reproduction error as shown in Figure 5 when frequency of measured AC voltage is less than 100kHz.

The time measurement deviation of each channel of the multi-channel picosecond level precision time timer does not exceed 10ps, and the standard deviation is less than 5ps. The gap is 10^-9 between signal period with kHz frequency and ps. Therefore, the effect brought by the timer error can be neglected when the frequency of the measured AC voltage signal is low. But it must be taken into account more as frequency of measured signal increase higher than 100kHz, especially when frequency is higher than 1 MHz because there is only 6 order between ps and the period of the measured AC voltage.

Certainly, the comparator used in the simulation of this paper is the existing devices in the device library, which have a large imbalance voltage and reach the mV level. If the newly reported high frequency comparator can be used, its imbalance voltage is ten microvolt, then the AC voltage measurement certainty proposed in this paper can be further improved to 10-6 or even 10-7 level, which is close to that of PJVS. Additionally, using a flying seconds timer is another method for measuring high-frequency AC voltage, as timer errors are the main limitation on bandwidth.