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Australian Government: National Measurement InstituteAustralian Government: National Measurement Institute
National Measurement Institute

Impedance and Resistance Research

NMI is responsible for maintaining and disseminating Australia's standards of resistance (the ohm), capacitance (the farad) and inductance (the henry).

Research and development is currently focussed on the design and construction of a new calculable capacitor and associated measurement chain of exceptional accuracy in collaboration with the International Bureau of Weights and Measures (BIPM).

New Measurement System for Impedance Standards

The existing impedance standards measurement systems were designed and built between 30 and 40 years ago. Although modifications and additions have been made to the systems over the years, there is a need to update and extend the capabilities of the whole impedance measurement chain. A new measurement system is planned that will start at the calculable capacitor and extend to higher capacitances via a chain of Invar and fused silica capacitors using a new capacitance bridge. A link to ac resistance will be made with a new quadrature bridge and the link to inductance with a new inductance bridge. Measurements in capacitance, resistance and inductance will then be traceable to the SI units at a number of frequencies in the range 200 Hz to 2 kHz.

Calculable Capacitor

BIPM barsThe calculable capacitor currently in use at NMI was developed in the 1950s and 1960s (click here for an overview of the development of the calculable capacitor). Since the 1950s, technologies relevant to the design and construction of a calculable capacitor have advanced. NMI, in partnership with BIPM, is designing a new calculable capacitor that will take full advantage of these new technologies and, in so doing, realise the ohm with a lower uncertainty than previously achieved. NMI and BIPM are each building a capacitor to the new design.

The National Research Council of Canada (NRC) and the National Institute of Metrology, China (NIM) are also building calculable capacitors to the NMI–BIPM design. 

The most critical component of the capacitor is the set of four main electrodes, 470 mm long and 50 mm diameter, that must be accurately cylindrical to 100 nm over most of their length.  NMI has undertaken to manufacture sets of main electrodes for all four capacitors. Those for NRC and BIPM have already been completed and delivered. 


The design of the NMI calculable capacitor is described in GW Small and JR Fiander (2004) Design of a Calculable Cross-capacitor. Conference on Precision Electromagnetic Measurements CPEM2004 Conference Digest, pp 485–486. 

Capacitance Bridge

The capacitance bridge has been designed and the ratio transformers are being assembled. It will provide the 250 Vrms from 200 Hz to 2 kHz that is required for the new calculable capacitor, and will cope with the variable load of the calculable capacitor. The same bridge will be used for the build-up from 10 pF to 500 pF.

Capacitance Standards

Prototype 10 pF fixed capacitorA suite of new capacitance standards, from 10 pF to 500 pF is required. Capacitors of values 5, 10, 20 and 50 pF are being constructed from Invar. A prototype 10 pF capacitor has been constructed in stainless steel and assembled. Experience with the prototype has suggested minor improvements that have been incorporated into the final design for the Invar capacitors.

The higher value capacitors (100, 200 and 500 pF) have been constructed from 100 pF fused silica capacitance cells. To ensure that the capacitance of the fused silica capacitors is stable to 1 part in 109 during measurements, their temperature will need to be kept constant to within 0.1 mK. The temperature coefficient of capacitance of the Invar capacitors is expected to be an order of magnitude smaller than that of the fused silica capacitors. A new air bath, controlled at 20°C to better than 0.1 mK over several minutes, is being designed and constructed. The Invar and fused silica capacitors will be permanently located in the air bath.

Multiple Frequency Resistance/Capacitance Bridge

A multiple frequency resistance/capacitance bridge to relate resistors of 200 kΩ to capacitors of 500 pF had already been built for use with the original calculable capacitor. The bridge must be reworked for an uncertainty of to 1 in 109. The bridge is described in G.W. Small, J.R. Fiander and P.C. Coogan (2001) A Bridge for the Comparison of Resistance with Capacitance at Frequencies from 200 Hz to 2 kHz. Metrologia 38, 363–368.


For many years the NMI reference phase generator/lock-in amplifier combination (Small and Leslie, 1986) has been used to advantage in the calculable capacitance bridge and inductive divider calibration facility. A new equivalent generator/detector system is being developed with the advantage of optional external synchronisation to a frequency standard at 5 or 10 MHz.

The generator/detector will be operable in two modes — a precision mode for critical applications such as the quad bridge where spectral purity and harmonic rejection are essential criteria, and a general purpose mode for less critical applications such as capacitance and inductance bridges. The precision version will generate a limited set of frequencies, including 10n/16π kHz for n = 1, 2, ..., 10 (approximately 200 Hz to 2 kHz), 1233.1593.. Hz and 1541.4293.. Hz. The general purpose version will generate frequencies from 40 Hz to 10 kHz with 0.01 Hz resolution. 

Features of the generator/detector include an external reference signal for a lock-in amplifier, sweep and bright-up signals for the Harvey double-bar oscilloscope display (Harvey, 1963), a 16-channel multiplexing analog-to-digital converter intended for reading resistively-encoded switch positions, in-phase and quadrature synchronous detectors and an internal analog-to-digital converter of 5-digit linearity at the output of detector channel A. The detector includes an rms-voltage mode in channel A, with 10% equivalent noise bandwidth. All generator/detector functions are programmable via the IEEE-488 bus and from the front panel, via keypad and LCD display.

IK Harvey (1963) Phase Sensitive AC Bridge Balance Indicator. J. Sci. Instrum. 40, 114–116

GW Small and KE Leslie (1986) Synthesising Signal Generator for Use with Lock-in Amplifiers in Audio Frequency Measurements. IEEE Trans. Instrum. Meas. 35(3), 249–255

Cryogenic Current Comparator

A relatively simple cryogenic current comparator has been constructed to relate dc QHR values to decade resistance values and to compare decade values of resistances in the range of 1 Ω to 10 kΩ. The cryogenic current comparator is currently being tested.