Generalized description of the frequency characteristics of resistors

Abstract

The real resistor in AC current can be described as an impedance Z of components changed with frequency. The real part Rs of this impedance is not equal to the resistance R in the DC current, and there is the imaginary component Xs, both frequency dependent. A three-element equivalent circuit including the resistance R as the main parameter and the residual parameters: serial inductance L and a parallel capacitance C is the basic AC model of a real resistor. Frequency characteristics of impedance Z components of this model in relative to R values rs, xs are given. Patterns of these components in generalized form, i.e. as functions of the relative values of characteristic resistance ρ = R√C/L and characteristic frequency η = ω√CL of this equivalent circuit are determined and their frequency curves for a few values of ρ are shown. Variants of this model with four models of connections are analyzed. Relative errors δR, δX and (Formula Presented.) are also find. Few numerical examples are given and considerations are of changes of errors in the frequency band. Some conclusions are included.