Errors in the Parallel Connection of a 100 : 1 Series-Parallel Buildup of Four-Terminal Resistors

This paper deals with the problem of calculating the parallel resistance of a 100: 1 series-parallel buildup of four-terminal resistors with accuracy as high as possible. A rather complex equivalent circuit has been assumed, taking into account all the causes of significant errors. Then a complete calculation has been carried out for obtaining all the error terms expressed by means of 15 relatively synthetic formulas. The method of solving the problem that has been developed is a new one and allows 1) rather simple calculations even if the network is complex, and 2) an immediate separation of the error terms from the main value (in fact, the result is given directly as the sum of a base value and a set of perturbations). The method is based on applying Cohn's theorem and using certain symmetries that have been put in evidence in the equivalent circuit. The perturbations may be considered either as corrections or as uncertainties. Very simple formulas are given for the means and the standard deviations of the errors, the perturbations being considered as uncertainties, and it being assumed that the causes of error are independent of each other and normally distributed. Anyway, these formulas may conveniently be used for initial investigation on the magnitudes of the errors before applying the more complex formulas that give the exact values of the variations. Finally, as an example, results of computations carried out on a particular buildup box are reported.