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We tested a digital impedance bridge in a hybrid structure for comparison of a capacitor with a resistor where the impedance ratio was measured in two separate parts. The modulus of the impedance ratio was matched arbitrarily close to the input-to-output ratio, in magnitude, of a two-stage inductive voltage divider by adjusting the operating frequency of the bridge; the residual deviation between the two together with the phase factor of the impedance ratio was measured using a custom detection system based on a four-channel 24-bit digitizer. The ratio of the inductive voltage divider was calibrated, in situ , using a conventional four-arm bridge with two known capacitors. Fluctuations of the source voltages were largely removed through postprocessing of the digitized data, and the measurement results were limited by the digitizer error. We have achieved an overall bridge resolution and stability of 0.02 μF/F in 2 h for measuring a 100-pF capacitor relative to a 12 906-Ω resistor at 1233 Hz. The relative combined standard uncertainty ( k = 1) is 0.13 μF/F, dominated by the digitizer error.

The simulation and construction of a direct current (DC) and alternating current (AC) resistor, based on a silicon wafer, has been described and demonstrated. By applying the van der Pauw method and the Thompson-Lampard theorem, to within approximations accommodating the conditions of the resistor's construction, a constant resistance ratio, (π/ln2) 2 , was derived that is independent of the sample resistivity and thickness. The constant ratio, valued at approximately 20.5, can theoretically be used as a basis of comparison between two distinct calibration chains, one based on the traceability from a calculable capacitor and the other based on the quantum Hall effect. To support the calculated ratio, several sets of simulations were performed for both DC and AC cases. The DC simulation results agreed with the ratio value to within 0.035 % when using a wafer thickness of 0.53 mm. Additionally, the experimental DC and AC (1 kHz) results agreed with the calculated ratio value to within 0.23 %, with at most a 0.06 % standard uncertainty before point contact errors from device fabrication.

AC bridge techniques commonly used for precision impedance measurements have been adapted to develop an eddy current sensor for rail defect detection. By using two detection coils instead of just one as in a conventional sensor, we can balance out the large baseline signals corresponding to a normal rail. We have significantly enhanced the detection sensitivity of the eddy current method by detecting and demodulating the differential signal of the two coils induced by rail defects, using a digital lock-in amplifier algorithm. We have also explored compensating for the lift-off effect of the eddy current sensor due to vibrations by using the summing signal of the detection coils to measure the lift-off distance. The dominant component of the summing signal is a constant resulting from direct coupling from the excitation coil, which can be experimentally determined. The remainder of the summing signal, which decreases as the lift-off distance increases, is induced by the secondary eddy current. This dependence on the lift-off distance is used to calibrate the differential signal, allowing for a more accurate characterization of the defects. Simulated experiments on a sample rail have been performed using a computer controlled X-Y moving table with the X-axis mimicking the train's motion and the Y-axis mimicking the train's vibrational bumping. Experimental results demonstrate the effectiveness of the new detection method.