This paper describes an absolute method for calibrating commercial 1000:1 dc current transducers (DCCTs). By adding two auxiliary windings to produce 10:1 and 100:1 ratios, we use a three-step build-up method to establish the 1000:1 current ratio standard. First, we determine the 10:1 ratios of 11 DCCTs through permutation; second, we set up a two-stage composite DCCT to produce a 100:1 ratio; after switching auxiliary windings in the two-stage setup, we then derive the 1000:1 current ratio. The experimental results show that the requirements for the current source and the current meter are not stringent; their Type-B contributions to the overall uncertainties are very small. Type-A uncertainties which include factors such as the experimental environment and possible drifts of the output offsets of the DCCTs are experimentally determined. Repeated tests show that the current ratio standard has an expanded uncertainty of 0.26 x 10⁻⁶ for the 1000:1 ratio.

Traditionally, the most precise way to get the mutual inductance value is by a Campbell calculable mutual inductor. Here, an approach of measuring the mutual inductance at low frequency with compensation method is described. A multi-channel direct digital frequency synthesis source is developed to provide stable and precise phase. The mutual inductance is traced to the value of the frequency and resistance directly. The measurement uncertainty is 0.43 ppm at present and could be improved further.

A high frequency periodic signal measurement system based on equivalent sampling method is developed. A high-speed sampling voltage tracking circuit, the core component of the system, is described in detail. The circuit can transform the amplitude corresponding to different phase points of the signal undertest into the equivalent DC level through successive approximation of multiple periods. The measurement system designed in this paper completes digital sampling with high accuracy only by connecting the low-cost voltage tracking circuit to the existing commercial instruments, such as two-channel waveform generator and high-precision digital multimeter, which makes the method easy to be generalized. The special structure of the sampling tracking circuit greatly reduces the influence of random noise and time jitter on the measurement results. The experimental results show that the non-linearity error of the system is as low as 0.002%, the bandwidth can reach 200 MHz, and the uncertainty of measuring the RMS of AC voltage with peak value of ±1 V and frequency of 10 kHz, 100 kHz and 1 MHz can reach 2.8 × 10⁻⁴ V, 4.6 × 10⁻⁴ V and 2.0 × 10⁻⁴ V (k = 2), respectively.

Superconducting quantum interference devices (SQUIDs) with large input inductance and octagonal double transformer were designed and fabricated using Nb/Al-AlO_x/Nb Josephson junctions for cryogenic current comparator. A 30-turn input coil of 1.5 μH is coupled to a large octagonal transformer of 3.6 nH, the counterpart of transformer is a 1.5-turn coil of 3.0 nH coupled to a second-order gradiometric SQUID of 97 pH. The octagonal double transformer makes low-inductance SQUID easily match to the large-inductance input coil. A current sensitivity of 1.1 μA/Φ₀, a flux noise of 3.8 μΦ₀/√Hz at 4 kHz and 9.7 μΦ₀/√Hz at 1 Hz were achieved at 4.2 K. Another SQUID sensor with 10-turn input coil of 0.5 μH coupled to a large octagonal transformer of 6.0 nH, which is coupled to a first-order gradiometric SQUID of 580 pH, achieves a lower current sensitivity of 0.5 μA/Φ₀ and a flux noise of 17 μΦ₀/√Hz at 4 kHz.

When charge transport occurs under conditions such as topological protection or ballistic motion, the conductance of low-dimensional systems often exhibits quantized values in units of e ² / h , underpinning advances in quantum metrology and computing. Here we report a quantized quantity: the ratio of displacement field to magnetic field, D / B , in large-twist-angle bilayer graphene. In high magnetic fields, Landau-level crossings between the top and bottom layers produce equal-sized checkerboard patterns across the D / B – ν space. These arise from electric-field-driven interlayer charge transfer of one elementary charge per flux quantum, yielding quantized critical displacement intervals, δ D = $$\frac{e}{2{{\uppi }}{l}_{B}^{2}}$$ e 2 π l B 2 , where l _B is the magnetic length. This mechanism offers a route to magnetic sensing, as the displacement-to-magnetic-field ratio is defined solely by fundamental constants. We propose a prototype magnetometer based on this principle, potentially enabling planar mapping of magnetic fields with micrometre resolution via large-twist-angle bilayer graphene sensor arrays. Our results demonstrate that interlayer charge transfer in the quantum Hall regime gives rise to novel phenomena with potential applications in cryogenic magnetometry.

After continuous investigation on the electrical compensation method for the end effect error in the new vertical calculable cross-capacitor (VCCC), the latest optimal hollow active auxiliary electrode (OHAAE) has been developed and successfully substituted for the current geometrical nosepiece at one end of the movable guard electrode at the National Institute of Metrology, China (NIM). The critical electrical characteristics of the latest OHAAE are investigated by the model tests and eventually implemented with the least mechanical modifications to the new VCCC at NIM. The standard uncertainty of the reproduction of 1 pF capacitance unit from the new VCCC by adopting the latest OHAAE is decreased to $10.5 \times 10^{-9}$ in comparison with that of $20.0 \times 10^{-9}$ by the geometrical nosepiece.