Multiple synchronous detection method for measuring non-linear and static resistance

The analyze of the stationary regime of non-linear circuits excited with periodical signals is difficult, on one hand because into the general solutions of the differential non-linear equation system the components of the stationary regime can not be separated, and on the other hand because of the different structure of the response signal and of the excitation signal. Characteristically for the non-linear element is the fact that between the input parameter and the output parameter do not exist a proportionality relation. A particular case is the non-linear resistance. This circuit element is defined by the fundamental terms of the trigonometric series of voltage and current. The characteristics of non-linear resistance are approximated by a polynomial and the paper presents a method for determining the polynomial´s coefficients to compute the non-linear and the static resistance, corresponding to a periodical current excitation applied to the non-linear resistor, by the technique of multiple synchronous detection. In the second part of the paper is presented an instrument for measurement in virtual technique the non-linear and static resistance, implemented in LabVIEW graphical programming software. The solution allows a quick and convenient measurement of these important circuit components, together with an appropriate graphical representation. The performances of this measurement technique are: easiness of design, flexibility of interconnection of signal processing software blocks, clear presentation of the results in the front panel of the instrument and, last but not least, accuracy of the measurement data software processing.