Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.


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.


Schematic of digital impedance bridge.

Schematic of 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 (RC) link is also needed to realize the farad from the QHR standard. We are currently developing a four-terminal-pair (4TP) digital bridge, employing a double-loop technique, to compare a 100 pF fused-silica capacitor, which can be directly calibrated against the calculable capacitor, with a portable 12906 Ω resistor, which has a known linear frequency dependence and can be directly calibrated against the dc QHR. Waveform synthesizers are used to excite the bridge through a 2 terminal-pair (2TP) current loop connecting the capacitor with the resistor. The voltages applied to them, after proper in-phase scaling, are measured, together with the bridge error signal, in a separate 2 TP potential loop using two identical virtual meters, created through periodic switching. In contrast to the conventional approaches of emphasizing precision and stability of the voltage sources driving the bridge, we adopt an approach of focusing on resolution and stability of the detectors. Fluctuations of source voltages are largely removed using noise cancellation techniques in post-processing of the digitized data, and the measurement results are limited by noises of the detectors.

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 four-terminal-pair capacitance standards from 1 pF to 1 nF over the frequency range from 1 kHz to 10 MHz. A bootstrapping technique using an LCR meter and an inductive voltage divider can extend the characterization to higher-valued capacitance standards up to 10 µF.

Major Accomplishments

  • Demonstrated a detector-limited 4TP digital bridge for realizing the farad from the QHR standard, using three modified Keysight 3458A multimeters for measurements of the voltage ratios, achieving 1 part in 108 Type A uncertainty in less than 15 min at 1 kHz.
  • Developed a continuously variable calculable capacitor for nonlinearity testing of the world's most accurate capacitance bridges 
  • Developed a programmable capacitance standard to provide capacitance values over six orders of magnitude from 100 aF to 100 pF with a stability of 0.1 aF
  • Served as pilot laboratory for SIM capacitance key comparison

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.

Created November 21, 2008, Updated January 27, 2021