combination of and represents the dielectric dynamics. The of the capacitor in terms R2 C2 ESR of the frequency responses is derived accordingly. For electrolytic capacitors, a rise in temperature causes a decrease in because the ESR resistance is reduced by the increased conductivity of electrolyte. The effect of temperature R1 on is described by [, ]. R1 where represents the value of at the base temperature (27 oC), is the capacitor R1b R1 Tbase T core temperature (oC), and is a temperature sensitivity factor []. F Fig. 2 ESR model of an electrolytic capacitor. Film capacitor A R-L-C series equivalent circuit that includes the equivalent inductance capacitance Lc, Cc and resistance is used to film capacitors. When the operating frequency is higher than 1 Rc kHz, the value can be modeled as a function of frequency based on []. ESR where is the base resistance, represents the frequency, and is a given value depending Rs f As on the capacitor size. is the predefined function showing the effect of frequency, which is K(f) usually given by plots in manufacturer datasheets. In this analysis, is mathematically K(f) expressed as a cubic polynomial function, as shown in (4), in which the coefficients can be k0-3 established by using least square curve fitting. In contrast with the electrolytic capacitor, the value of film capacitors increases with ESR the frequency. Its temperature-sensitivity is less than that of electrolytic capacitors [] because the of film capacitors results mainly from the tabs and contact resistances, but not from the ESR electrolyte [].
combination of R2 and C2 represents the dielectric dynamics. The ESR of the capacitor in terms of the frequency responses is derived accordingly. For electrolytic capacitors, a rise in temperature causes a decrease in ESR because the resistance R1 is reduced by the increased conductivity of electrolyte. The effect of temperature on R1 is described by [, ]. where R1b represents the value of R1 at the base temperature Tbase (27 oC), T is the capacitor core temperature (oC), and F is a temperature sensitivity factor []. Fig. 2 ESR model of an electrolytic capacitor. Film capacitor A R-L-C series equivalent circuit that includes the equivalent inductance Lc, capacitance Cc and resistance Rc is used to film capacitors. When the operating frequency is higher than 1 kHz, the ESR value can be modeled as a function of frequency based on []. where Rs is the base resistance, f represents the frequency, and As is a given value depending on the capacitor size. K(f) is the predefined function showing the effect of frequency, which is usually given by plots in manufacturer datasheets. In this analysis, K(f) is mathematically expressed as a cubic polynomial function, as shown in (4), in which the coefficients k0-3 can be established by using least square curve fitting. In contrast with the electrolytic capacitor, the ESR value of film capacitors increases with the frequency. Its temperature-sensitivity is less than that of electrolytic capacitors [] because the ESR of film capacitors results mainly from the tabs and contact resistances, but not from the electrolyte [].
IEEE_EV_PowerDensity_ver3b-pa2.docx