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Summary
This project aims to provide the world's best basis for accurate impedance measurements by tying the U.S. legal system of electrical units to the International System of Units (SI) through the realization of the SI unit of capacitance. This work also forms the foundation of NIST's measurement services for electrical impedance, ensuring a sound metrological basis for impedance measurements, both nationally and internationally, and ensuring that the claims of measurement accuracy by U.S. industries are recognized and accepted worldwide. The need continues for better representation of capacitance and also for better calibration tools at NIST with which to verify objectively claims of improved performance specifications, to achieve consistency, and to help avoid technical trade barriers.
Description
Fig. 1. Schematic of four-arm digital impedance bridge.
The primary facility for connecting the U.S. legal system of electrical units to the international system of units is the NIST calculable capacitor, with which the measurement of capacitance is effectively achieved through a measurement of length. Both the calculable capacitor and the chain of high precision measurements that transfers the SI unit to the calibration laboratories must be maintained, improved, and compared with other national metrology laboratories to ensure measurement consistency on an international level.
Over the last few decades, NIST has successfully invested in two key quantum representations of electrical quantities; both the Quantum Hall Resistance (QHR) and Josephson Voltage standards have now achieved measurement uncertainties approaching parts in 109. These quantum standards, however, represent only a few points in a multi-dimensional world of electrical measurements. The crucial link between the fundamental electrical standards and commercial electronic instrumentation is provided by precision AC measurement standards. A combination of transformer techniques and modern digital techniques has the potential to extend our expertise over a wider dynamic range.
Consistency between resistance and impedance measurement services from NIST is expected by the instrumentation industry and DOD laboratories. An improved resistance-capacitance link is also needed to realize the farad from the QHR standard. We have designed a new digital impedance bridge for the comparison of resistance with capacitance where the required precision of the source voltages is only of the order of the square root of the ultimate bridge precision. Our design is the first digital extension of the classic three-balance bridge where the auxiliary source and detector balances have been traditionally implemented using analog techniques.
The digital bridge techniques have the potential to replace the 40-year-old traceability chain based on a mechanical calculable capacitor with a new one based on the quantum SI. The digital bridge establishes traceability of impedance standards to the QHR standards that realize the SI ohm to create the foundation of NIST’s impedance measurement services.
Supporting wideband impedance measurement services also requires reference standards that can be characterized over the impedance and frequency ranges of interest. NIST has developed a system to characterize commercial 4TP capacitance standards from 1 pF to 1 nF over the frequency range from 1 kHz to 10 MHz. A bootstrapping technique using a four-arm digital bridge can extend the characterization to higher-valued capacitance standards up to 10 µF.
Major Accomplishments
- Demonstrated a digital four-arm bridge for the comparison of resistance with capacitance, achieving a combined standard uncertainty of 5 parts per billion for the comparison of a 100 kΩ resistor with a 1 nF capacitor near 1592 Hz, a critical step to derive capacitance from QHR. The achievement was described in a paper titled "A Digital Four-Arm Bridge for the Comparison of Resistance with Capacitance", which was among the top five most-read articles in the prestigious IOP journal Metrologia in October, 2024.
- Demonstrate the prototype for the United States Patent No. 12,235,303 titled “A double-balance LCR meter” for comparison of two unlike impedances. The subject invention alleviates two major sources of errors (the gain error of the amplifier and nonlinearity of the voltage detectors) that hinder commercial auto-balance LCR meters to be used as metrological tools. It alleviates the first problem (gain error) by implementing a coarse balance before the auto balance by the current amplifier. It alleviates the second problem (nonlinearity) by adding a scaling circuit to force the detected voltages approximately equal in magnitude.
- Invented a weighted lock-in detector for four-arm bridges when its two detection nodes have an arbitrary phase difference, unlike a conventional lock-in detector that requires its two input signals to have the same phase in the differential detection mode. Filed U.S. Provisional Patent Application serial number 63/759,670 “WEIGHTED LOCK-IN DETECTOR,”
- Overhauled the calibration service for the frequency dependence of 4TP air capacitors. In the past, the calibration was performed with a dual-channel vector network analyzer, requiring nine different connections to the standard with a rigid 7 mm microwave line. The new method streamlines the measurement, as each standard can be measured by simply connecting four coaxial lines between it and a four-channel vector network analyzer.
Industry Feedback
…NIST measurements of the Calculable Capacitor using Andeen-Hagerling bridges have allowed us to observe and test accuracy, principally non-linearity performance, on a scale that would otherwise be impossible…
Dr. Carl Hagerling, President
Andeen-Hagerling, Inc.