282 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 50, NO. 2, APRIL 2001 A New Four Terminal-Pair Bridge for Traceable Impedance Measurements at Frequencies up to 1 MHz Shakil A. Awan, Bryan P. Kibble, Ian. A. Robinson, and Stephen P. Giblin Abstract—A new four terminal-pair bridge has been devel- oped and used for traceable measurement of capacitance and resistance at frequencies up to 1 MHz. The apparent capacitance of a gas-filled 100-pF standard agrees with calculated values to better than 200 F/F at 1 MHz. This is an order of magnitude improvement on existing capabilities at NPL. The frequency dependence of the dissipation factor of capacitance standards is discussed, and the capacitance and dissipation factor of ceramic NPO-dielectric standards has also been measured. The frequency dependence measurements of the calculable coaxial 100- and 1-k resistance standards are also presented. Index Terms—Capacitance, coaxial bridge, frequency depen- dence, high frequency, resistance, traceability. I. INTRODUCTION O VER the last few years, many instruments, such as LCR meters and network analyzers that claim to be able to measure impedance to better than 0.5% for frequencies up to tens of megahertz, have become commercially available This in- troduces a new requirement for traceability of impedance mea- surements above 10 kHz. To bridge the gap between 10 kHz and 1 MHz, decade value capacitance and resistance standards, a high-frequency inductive voltage divider (IVD), isolation trans- formers, a combining network [1], and a permuting capacitors device (PCD) [2] have been constructed and a high-frequency four terminal-pair bridge assembled. The PCD calibrates the high-frequency IVDs that form the ratio-arms of the bridge. A four terminal-pair bridge for characterizing high-frequency impedance standards is an alternative method to those described in [3] and [4]. The three main sources of error in a bridge system are caused by the high-frequency IVDs, cables, and the impedance standards themselves. These errors must all be investigated in order to produce an uncertainty budget. The standards are designed with minimal parasitic impedances, as these dominate their frequency dependence [5]. The error contribution of the IVD voltage ratios can be eliminated by calibration against the PCD and that from cables by applying a calculated cor- rection [1]. The PCD is made from 11 nominally equal 50-pF NPO-dielectric capacitors mounted on a printed circuit board. Manuscript received May 14, 2000; revised November 3, 2000. This work was supported within the Technical Programme of the National Measurement System Policy Unit of the Department of Trade and Industry of the U.K. The authors are with the Centre for Electromagnetic and Time Metrology, National Physical Laboratory, Teddington, U.K. Publisher Item Identifier S 0018-9456(01)02692-4. The “electrical” arrangement of the capacitors is such that ten of the capacitors can be connected in parallel so that with the remaining capacitor, a ratio is established. The mean of the 11 permutations yields the IVD ratio deviation from nom- inal . There are several benefits from using capacitors having ceramic NPO as the dielectric. These include a small temperature coefficient of approximately /K, which is a dissipation factor of only , and negli- gible capacitance hysteresis from temperature cycling. Their minimal residual self-inductance due to their small physical dimensions ( mm mm mm) makes them suitable for high-frequency use [5]. The NPO-dielectric capacitors and the circuit board design were critical in achieving a device that can calibrate IVDs to better than 10 V/V (95% confidence level) at 1 MHz [2]. II. HIGH-FREQUENCY BRIDGE CIRCUIT The high-frequency four terminal-pair bridge is shown in Fig. 1. The main impedance standards and are defined as four terminal-pair components. The high potential ports of the impedance standards are connected symmetrically with identical cables to the ratio windings of the in-phase and quadrature balance IVDs (shown as IVD1 and IVD2, respec- tively). The defining condition of zero current in the potential leads is determined by extrapolation of the results obtained from altering the cable lengths. The combining network at the low potential ports consists of variable impedances and (whose ratio is similar to that of and ). The combining network eliminates the effect of the potential drop caused by current flow through the series impedance and shunt admittance of the cable joining the low current ports. The low current ports of the standards are connected by a 500- resistor , which can be shorted by a switch . The switch is opened when the combining network is being balanced. The high current ports of the impedance standards are connected to the magnetizing windings of IVD1 and IVD2, respectively. The two-stage construction [1] of the in-phase and quadrature IVDs helps to minimize loading on the ratio-arms of the bridge. The defining point “O” in the bridge maintains zero current flow through to the shield by the Wagner balance . Quadrature balance of the bridge is achieved by injecting a small current via an impedance connected to the output of IVD2, as shown in Fig. 1. When and are resistance standards, is a specially constructed 5-pF capacitor with a negligible 0018–9456/01$10.00 © 2001 British Crown Copyright