INSTITUTE OF PHYSICS PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY Meas. Sci. Technol. 15 (2004) 969–972 PII: S0957-0233(04)73771-6 Resonance frequency of four- terminal-pair air-dielectric capacitance standards and closing the metrological impedance triangle Shakil A Awan 1 , Luca Callegaro 2,3 and Bryan P Kibble 1 1 Centre for Electromagnetic and Time Metrology, National Physical Laboratory, Queens Road, Teddington, Middlesex TW11 0LW, UK 2 Instituto Elettrotecnico Nazionale Galileo Ferraris, Strada delle Cacce, Torino, Italy Received 16 December 2003, in final form 17 February 2004 Published 20 April 2004 Online at stacks.iop.org/MST/15/969 (DOI: 10.1088/0957-0233/15/5/027) Abstract A new technique for determining the resonance frequency (f 0 ) of four-terminal-pair air-dielectric capacitance standards is discussed. The resonance frequency is determined by measuring four parameters of the capacitance standards over a range of frequencies near f 0 . These parameters are the two-terminal-pair impedance coefficients as defined in an impedance matrix. From a knowledge of the four-terminal-pair resonance frequency of the standards it is possible to calculate their frequency dependence for f ≪ f 0 using a simple electrical model. For air-dielectric capacitance standards it is also possible to determine their dissipation factor from the −3 dB width of the measured resonance curve. Ultimately, the validity of the technique described here would need to be verified by establishing closure of a proposed ‘metrological impedance triangle’ (MIT). This would involve measuring the frequency dependence of a four-terminal-pair air-dielectric capacitance and a calculable resistance standard in a 10:1 bridge between a range of frequencies, for example 1.592 kHz and 1.592 MHz. The same standards are then compared in a quadrature bridge operating at the upper frequency of 1.592 MHz to enable closure of the MIT. Accurate closure of the MIT would be an important test for the validity of a number of high-frequency techniques and calculations for the first time. Keywords: coaxial bridges, frequency dependence, impedance standards, quantum Hall effect, impedance analysers 1. Introduction Coaxial bridge techniques are in widespread use in many national metrology institutes for accurate (better than 1 ppm) impedance measurements at frequencies up to 20 kHz [1, 2]. However, at present, using similar techniques at high frequencies, up to 10 MHz, the accuracies that can be achieved are at least four orders of magnitude lower [3, 4]. One of the main limiting factors has been the lack of reference 3 Guest researcher from IEN between January–March 2002. standards with well-known frequency dependence up to the higher frequencies. A simple technique is described here which is found to be sufficiently accurate for determining the frequency dependence of four-terminal-pair (4TP) capacitance standards. A key feature of the technique is that it avoids the use of any four-terminal-pair LCR meters or impedance analysers for determining the resonance frequency of the reference standards, which has not been the case up to now [5]. Attempts have been made previously to determine the resonance frequency of 4TP capacitance standards using a ‘grid-dip’ meter [6, 7]. However, this method has been found 0957-0233/04/050969+04$30.00 © 2004 IOP Publishing Ltd Printed in the UK 969