Long term stability estimation of DC electrical source from low frequency noise measurements Gino Giusi a , Graziella Scandurra a , Carmine Ciofi a and Calogero Pace b a DFMTFA and INFM, University of Messina, Salita Sperone 31, I-98166 Messina, Italy b DEIS, University of Calabria, Via Pietro Bucci 42C, I-87030 Arcavacata di Rende(CS), Italy ABSTRACT An indirect approach for estimating the long term stability of DC electrical sources from low frequency noise measurements is presented and discussed. In particular, it is demonstrated that once the unity frequency magnitude and the frequency exponent of the flicker noise component are determined, an overestimate of the variance of repeated measurements of the source output (averaged over a time interval τ ) taken ΔT seconds apart can be readily obtained. The proposed approach is validated with reference to actual experimental data. Keywords: Noise Measurements, Stability, Variance. 1. INTRODUCTION Designing high stability DC current or voltage sources such as those required in metrology applications or fundamental physics experiments for supplying magnets used for obtaining highly stable magnetic fields 1–4 is rather challenging. Accurate shielding from external electromagnetic interferences and environmental fluctuations (mainly temperature fluctuations) are mandatory if one has to achieve stability in the order of fractions of ppm over a time scale ranging from a few tens up to a few thousands of seconds. External interferences, however, are not the sole cause of undesired fluctuations at the output of DC sources, since the unavoidable noise introduced by the electronic components which make up any solid state DC current or voltage source may have a significant influence in setting the ultimate limits of the stability which can be obtained. In fact, while one can reduce (at least in principle) the influence of external interferences down to a negligible level, nothing can be done in order to reduce the effect of the noise, which therefore sets the ultimate limit to the stability which can be obtained with a given electronic design. Allan variance estimation is probably the most popular method which is used for stability estimation, particularly in the field of time metrology. 5–7 The estimation of the Allan variance for a given quantity x(t) relies in a proper elaboration of the time series y i = x(t i+1 ) - x(t i ) obtained by sampling the function x at time instants t i = iΔt. When dealing with highly stable DC sources, however, the accuracy which is required to the measurement system for providing meaningful values of y i may be very high, thus making the estimation of the stability of the source quite challenging. On the other end, the measurement of the noise spectrum superimposed to the DC value of the source can be accomplished quite easily in most cases down to a few mHz by resorting to a proper AC coupling and very low noise amplifiers. 8 If we assume that the noise superimposed to the DC value is the sole cause of the fluctuations at the output of the DC source, we can argue that the estimation of the noise power spectrum may provide enough information for judging on the stability that can be expected. Besides, several works have pointed out a strict correlation between the stability as can be measured in the time domain using Allan variance and the spectral characteristics of the quantity under investigation. 5, 9 In several cases of practical interest, we can define the stability of a DC electrical source as the variance of the results of repeated measurements of the output source (averaged over a time τ ) taken Δt seconds apart from each other. In the special case of τ =Δt this definition of stability coincides with the definition of the Allan variance in its simplest form. In this paper we demonstrate that it is in fact possible to estimate the Further author information: (Send correspondence to C. Ciofi) G. Giusi E-mail: g.giusi@ingegneria.unime.it, Telephone: +39 90 676 5648 G. Scandurra E-mail: gscandurra@ingegneria.unime.it, Telephone: +39 90 676 5648 C. Ciofi E-mail: ciofi@ingegneria.unime.it, Telephone: +39 90 676 5648 C. Pace E-mail: cpace@unical.it, Telephone: +39 984 494767 Noise in Devices and Circuits II, edited by François Danneville, Fabrizio Bonani, M. Jamal Deen, Michael E. Levinshtein Proceedings of SPIE Vol. 5470 (SPIE, Bellingham, WA, 2004) · 0277-786X/04/$15 · doi: 10.1117/12.547137 470