Generalized Description of the Frequency Characteristics of Resistors

The real resistor in AC current can be described as an impedance Z of components changed with frequency. The real part R s of this impedance is not equal to the resistance R in the DC current, and there is the imaginary component X s, 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 r s, x s are given. Patterns of these components in generalized form, i.e. as functions of the relative values of characteristic resistance \( \rho = R\sqrt {{C \mathord{\left/ {\vphantom {C L}} \right. \kern-0pt} L}} \) and characteristic frequency \( \eta = \omega \sqrt {C\,L} \) 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 \( \delta Z\mathop = \limits^{{\text{def}}} \sqrt {\delta R^{2} + \delta X^{2} } \) are also find. Few numerical examples are given and considerations are of changes of errors in the frequency band. Some conclusions are included.