Spiral Capacitor Models That Consider the Capacitance and Inductance of Each Turn

Mathematical models that allow calculating the capacitance and inductance of each turn of spiral capacitor electrodes are presented. Comparison of values obtained using the proposed mathematical models and quasi-static calculation by increasing the number of turns of the spiral capacitor. Comparison demonstrated the suitability of the developed models for calculating capacity and inductance with an acceptable error rate not exceeding 0.92%. The capacitance of a real capacitor was calculated with given geometrical and electrical parameters, and an error rate was no more than 3.4%. A circuit model algorithm for spiral capacitors that takes into account the capacitance and inductance of each turn was developed. The transfer coefficients of three circuits were compared when the capacitor was connected in series between the source and the load. Comparison of frequency dependencies showed that the difference in values did not exceed 0.16%. The developed spiral capacitor models allow taking into account the compression or stretching of each turn of the spiral capacitor, caused by the changes in temperature and in the geometric dimensions of the capacitor coating.