Instrumentation and Measurement Technology Conference - IMTC 2007 Warsaw, Poland, May 1-3, 2007 System Identification Approach Applied to Drift Estimation. Frans VerbeystL2 Rik Pintelon, Yves Rolaint, Johan Schoukenst and Tracy S. Clement3 'Department ELEC, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium, rik.pintelon@vub.ac.be 2NMDG Engineering, C. Van Kerckhovenstraat 110, B-2880 Bomem, Belgium, frans.verbeyst(nmdg.be 3National Institute of Standards and Technology, Boulder, CO 80305 USA, clementt(boulder.nist.gov Abstract - A system identification approach is applied to estimate the time base drift introduced by a high-frequency sampling oscilloscope. First, a new least squares estimator is proposed to estimate the delay of a set of repeated measurements in the presence of additive andjitter noise. Next, the effect of both additive andjitter noise is studied in the frequency domain using simulations. Special attention is devoted to the covariance matrix of the experiments, which is used to construct a weighted least squares estimator that minimizes the uncertainty of the estimated delays. Comparative results with respect to other state-of-the-art methods are shown. Finally, the enhanced method is applied to estimate the drift observed in repeated impulse response measurements of an opto- electrical converter using an Agilent 83480A sampling oscilloscope in combination with a 83484A 50 GHz electrical plug-in. Keywords - large-signal network analysis, sampling oscilloscopes, system identification, time base drift, time base jitter I. INTRODUCTION In order for large-signal network analyzers [1],[2] to accurately measure the voltage and current at both ports of a high-frequency nonlinear device, additional calibration is required compared to classical vector network analyzers. On top of the relative calibration, an absolute power and phase calibration are needed: the amplitude and phase at one frequency must be related to those at other frequencies. The power calibration is performed using a calibrated power sensor. The phase calibration is performed using an harmonic phase reference, which is essentially a pulse generator. This one is calibrated using a high-frequency sampling oscilloscope, which itself requires calibration because it suffers from both time base errors and voltage resolution errors. The non-ideal amplitude and phase characteristic of the scope is estimated using either a nose-to-nose calibration technique [3],[4] or by measuring the impulse response of a photodiode which is calibrated using an electro-optic sampling (EOS) system [5]. Both techniques require that one properly deals with the time base errors. One of these time base errors is referred to as time base drift. When collecting a large number of repeated measurement records of the impulse response of a linear time- invariant system using a high-frequency sampling oscilloscope, it was found that the successive measurements slightly shift over time, within the acquisition window. As such it is essential to compensate for this drift before averaging. This paper describes a system identification approach to estimate the time base drift introduced by a high-frequency sampling oscilloscope in the presence of additive noise and jitter. The estimations are performed in the frequency domain. The initial method uses the first measurement record as a reference signal during the alignment of successive measurements. This paper however focusses on a new least squares estimator, which uses the aligned average as a reference signal instead of the first measurement. The resulting "enhanced LS" estimator clearly outperforms the initial estimator when the additive noise is dominant. Next, special attention is devoted to the covariance matrix of the disturbing noise. The use of this matrix allows one to come up with a good estimate of the uncertainty on the estimated delays that describe the time base drift. Using the covariance matrix, a weighted version of the "enhanced LS" estimator is implemented that minimizes the uncertainty on the estimated delays. Furthermore, it allows to compare the expected value of the cost to the actual value of the cost and as such allows to detect model errors. Comparative results with respect to other state-of-the-art methods are based on simulations performed in [6] and demonstrate the potential of the proposed estimators. Finally, the enhanced method is applied to estimate the drift during repeated measurements performed at the National Institute of Standards and Technology (NIST). The impulse response of a calibrated photodiode is measured using an Agilent 83480A sampling oscilloscope in combination with a 83484A 50 GHz electrical plug-in'. It is shown that taking the covariance matrix into account, the uncertainty on the estimated delays can be reduced by a factor of 2. II. PROPOSED APPROACH Time base drift is due to imperfections on the position of the trigger point relative to the signal and results in a time shift of the signal in the acquisition window. As a result, successive measurements correspond to delayed versions of 1. Trade names are used only to adequately specify the experimental conditions. This does not constitute an endorsement by the National Institute of Standards and Technology. Other products may perform as well or better. 1-4244-0589-0/07/$20.00 ©2007 IEEE 1