A comparison of low-frequency models of inductance standards

A number of simple inductor equivalent circuits have been tested to determine the most accurate approximation for the frequency characteristics of standard inductors at low frequencies. Using precise inductance measurements at various frequencies the elements of the circuits have been estimated. Regression analysis has been applied to the circuit equations that can be transformed to linear form. For the nonlinear case a special algorithm minimizing the sum of squares has been developed. Usually the best results are obtained when a model with stray capacitance and eddy-current influence is applied. The approximation error for some standards is less than 0.01% over the frequency range covered.