Probabilistic analysis of voltage divider ratios

Abstract

Tolerance of modern resistors typically ranges from 0.1% to 1%. From the probabilistic viewpoint, this is taken to mean that the corresponding resistance can be treated as a random variable, with an appropriate probability density function (PDF). We derive an expression for the PDF of a two-resistor voltage divider's transfer ratio, when the resistances in the divider are assigned uniform distributions. Plots of the obtained analytical expression, for various combinations of nominal resistances and tolerances of the two resistors, are compared to those produced by numerical (Monte Carlo) simulations. The asymmetrical character of the obtained resultant PDF, caused by non-linearity of the divider's circuit function, implies that the nominal, the mean and the most probable value of the divider's ratio can all differ. For normally distributed resistances in the two-resistor divider, analytical approach becomes complex, while Monte Carlo simulations readily provide the plots of voltage ratio PDFs and calculate the values of their parameters.

Keywords

• voltage divider
• tolerance
• resistors
• probability density function
• monte carlo method