IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 54, NO. 2, APRIL 2005 649 Characterization of a High-Resolution Analog-to-Digital Converter With a Josephson AC Voltage Source Waldemar G. Kürten Ihlenfeld, Enrico Mohns, Ralf Behr, Jonathan M. Williams, Pravin Patel, Günther Ramm, and Hans Bachmair Abstract—A Josephson ac voltage source was employed to characterize the dynamic behavior of a high-resolution 28-bit (8.5-digit) integrating analog-to-digital converter of a digital sam- pling voltmeter (DSV), which is widely used in ac metrology at the Physikalisch-Technische Bundesanstalt. Extensive measurements were carried out to validate previous mathematical models of the DSV when sampling ac signals. The characterization method is based on the discrete Fourier transform applied on sampled data of the ADC and on the known Josephson plateau values for quantifying the ratio of ac quantities and the nonlinearities of the DSV. The method shown allows considerable improvement of the accuracy of sampling techniques at low frequencies (dc up to some kilohertz) to be attained. Index Terms—Analog-to-digital conversion (ADC), discrete Fourier transform (DFT), electric variables measurement, Josephson arrays, synchronous detection. I. INTRODUCTION A NALOG-TO-DIGITAL converters (ADCs) became common in ac metrology more than 30 years ago. Despite many developments in sampling techniques, a significant and rather recent proposal was made [1], suggesting the use of reg- ularly spaced samples [2] of two ac voltage signals generated synchronously with the internal clock of a high-resolution ADC (DSV). Since then, much effort at the Physikalisch–Technische Bundesanstalt (PTB) has been concentrated on validating un- certainty evaluation models [3] based mainly on comparisons with PTB primary thermal converters (the standards for ac/dc transfer measurements). Although the theoretical predictions hitherto agreed with experimental results under sinusoidal conditions, further inves- tigations on the dynamic behavior of the high-resolution 28-bit ADC in the PTB system [3], [4] remained essential for assuring the traceability of ac power in the nonsinusoidal regime by considering nonlinearities of the ADC. Thorough investigations were carried out with an ac voltage source employing a dig- ital-to-analog converter (DAC) based on Josephson arrays [5], [6]. This source was operating synchronously with the ADC under test (DSV) as described next. Manuscript received July 2, 2004; revised October 25, 2004. W. G. Kürten Ihlenfeld, E. Mohns, R. Behr, G. Ramm, and H. Bachmair are with the Physikalisch-Technische Bundesanstalt (PTB), 38116 Braunschweig, Germany (e-mail: Guilherme.Ihlenfeld@ ptb.de). J. M. Williams and P. Patel are with the National Physical Laboratory (NPL), Middlesex, TW11 0LW, U.K. (e-mail: Jonathan.Williams@npl.co.uk). Digital Object Identifier 10.1109/TIM.2004.843064 Fig. 1. Block diagram of the system with the ac source represented by a Josephson array biased by a dc current source at the left [5] (controlled by its own computer, PC 1), and the DSV at the right. The quantized ac signal is coherent with the clock frequency of the DSV, which is triggered by the signal at each period of . and represent the internal reference and full-scale values, respectively (see text for further details). II. DESCRIPTION OF THE MEASUREMENT SYSTEM As depicted in Fig. 1, a Josephson ac source (on the left) syn- thesizes an ac signal (in this case a step-approximated triangle waveform coherent with the DSV clock ), which is optionally amplified (by A2) and sampled on its quantized plateaus over a time-frame that encompasses an integer number of periods of . Leakage on the spectral lines after a discrete Fourier trans- form (DFT) or fast Fourier transform (FFT) on the sampled data (collected and processed by PC2) is thus prevented [2]–[4]. The DSV contains the ADC with its control unit for timing (for setting the sampling and aperture times and respectively), the analog low-pass input filter (LPF with cutoff frequency ) and the signal conditioning amplifier A1 that embodies the ADC’s imperfections [gain errors with and its nonlinearities resulting the ADC input signal ] [2]–[4]. Many methods and procedures for characterizing ADCs have been reported [7], [8]. Those based on the DFT/FFT on sampled data are more compatible with the PTB system and were thus preferred [9], [10]. The step-approximated triangle waveform with quantized steps contains multitones [11] (odd harmonics). Since the PTB sampling system is primarily used for the determination 0018-9456/$20.00 © 2005 IEEE