Frequency characteristics of inductance- capacitance network

The results of theoretical studies of the frequency dependencies of the capacitance C u(w) and conductivity  u(w) of inductance-capacitance network (ICN) are presented. The aim of the work was to determine the frequency at which C u(w) and  u(w) have an extremum (maximum or minimum), as well as the frequency of inversion of the sign of the capacitance where C u(w)=0. The above singular points on the frequency scale can serve as benchmarks that facilitate the construction of electrochemical equivalent circuits when processing data impedance spectroscopy. It is shown that depending on the ratio between the values of the elements included in the scheme ICN, there are 12 visually distinct species C u(w) and the  u(w). It is established that the singular points are differently located relative to each other, some or all of them may be missing. It is proposed to display the status of the ICN on the  -plane, where  and  are dimensionless parameters that depend on elements of the ICN. Equations of the boundaries separating the  -plane into 12 zones are defined. Example of the use of ICN for modeling the delay of current with respect to voltage is given.