1254 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 49, NO. 6, DECEMBER 2000 Error Analysis of an Optical Current Transducer Operating with a Digital Signal Processing System Pawel Niewczas, Andrew Cruden, W. Craig Michie, Member, IEEE, W. Iain Madden, Member, IEEE, and James R. McDonald, Member, IEEE Abstract—This paper analyzes errors associated with the analog-to-digital (A/D) conversion process of a digital signal processing unit (DSP) within the operation of an optical current transducer (OCT). Quantization of the analog current mea- surement signal leads to measurement errors which are a direct consequence of the uncertainty with which an N-bit resolution A/D assigns a binary word for a given analog input value. This paper presents comprehensive simulations of the performance of different current sensors monitored by the DSP unit and discusses aspects of compatibility between the sensor dynamic range and the resolution of an A/D conversion process. Recommendations are given on how to match the OCT to the given A/D parameters, and vice versa, in order to meet specified accuracy requirements. Index Terms—Analog–digital conversion, current measurement, digital systems, Faraday effect, magneto-optic transducer. I. INTRODUCTION T HE USE of optical current transducers (OCTs) within the power industry brings potential benefits over conventional current transformers (CTs) such as inherent high-voltage isola- tion, immunity to electromagnetic interference, enhancement in signal bandwidth and dynamic range, ease of integration into future digital control and protection systems, and reduced costs [1], [5], [6]. However, the electricity supply industry requires extremely high performance specifications [2] for both metering and protection applications, and these are not easily met with optical transducers. Measurement errors within the OCT can be attributed mainly to thermal influences, vibration-induced noise, detection of low-level optical signals, and nonlinearity of the sensor response characteristic at higher current levels. Pro- totype temperature and vibration compensation schemes have been successfully developed and are reported in detail elsewhere [1], [3], [4]. These techniques, as reported, require further re- finement in order to fully satisfy the stringent accuracy require- ments demanded of the current sensors. The OCT devices being considered within this paper are in an advanced stage of development, and efforts are underway to integrate all the compensation methods within a robust and flexible system. Vibration and temperature compensation tech- niques have been implemented using a DSP unit to perform the necessary processing. The DSP also enables greater use to be made of the OCT dynamic range by performing the transforma- tion between the OCT output and the applied current. The flex- ibility which the DSP unit brings to the measurement process is Manuscript received May 26, 1999; revised August 10, 2000. The authors are with Rolls-Royce University Technology Centre in Power Engineering, University of Strathclyde, Glasgow G1 1XW, U.K. Publisher Item Identifier S 0018-9456(00)09790-4. extremely beneficial. However, it also introduces a quantization error which is directly related to the analog-to-digital (A/D) res- olution. In this paper, the design requirements of the A/D con- version part of the OCT monitoring system are examined, from the point of view of the optimal choice of the sensor dynamic range (sensitivity) and the A/D resolution. The theoretical con- siderations are supported by experimental investigations. II. ERROR ASSOCIATED WITH THE ANALOG-TO-DIGITAL CONVERSION PROCESS The A/D converter used in the DSP monitoring unit consid- ered in this paper has a resolution of 16 b. The converter sam- ples the photo-receiver output signal that can change from the offset level ( several millivolts), when no optical power is being received, to the A/D maximum positive input voltage range of 10 V. The photo-receiver offset can be either positive or neg- ative, and therefore the A/D converter must work in a bipolar configuration. The maximum quantization error of the sampled analog mea- surement signal, for the case where the values are rounded up or down, is equal to [7] (1) where is the interval between the quantization levels, and can be expressed by: (2) where is the full-scale input voltage range of the N-bit reso- lution A/D converter ( V and b in the system analyzed above). The quantization error for each sample, , is normally as- sumed to be random and uniformly distributed in the interval with zero mean [7]. In this case, the quantization noise power, or variance, is given by (3) where, is the probability of value occurring for each sample. The square root of the above result, i.e., ( ), represents the standard deviation and is equivalent to the rms value of the quantization noise in the measurement bandwidth (dc to half the Nyquist frequency), or the measurement uncertainty. On the other hand, assuming that the current varies sinusoidally with an angular frequency (which is within the 0018–9456/00$10.00 © 2000 IEEE