This parallel resistance depends on the core material, working frequency, and the core flux level. The parallel resistance is added because of the losses in the magnetic core due to eddy currents, hysteresis loss.
Any real inductor can be thought of as an ideal inductor that has a resistor and a capacitor in parallel and another resistor in series. Inductors typically are built to the smallest possible dimensions to fit into small designs. At the same time, there are no ideal components in the real world. In this calculator, we considered an ideal inductor. Simplified equivalent circuit of a real inductor: R w is the resistance due to winding wire and its terminations L is the inductance of an ideal inductor R l is the resistance due to losses in the magnetic core and C w is the parasitic self-capacitance of the inductor and its terminations Equivalent Circuit of a Real Inductor Note that p/d ratio is always more than one because of the thickness of wire insulation and the minimum possible distance between two round wires lying side-by-side for a very thin insulation is the wire diameter d. Where p is the wire pitch (the distance between turns measured between wire centers) and d is the wire diameter. The Rosa’s k s, which corrects for the difference in self inductance is determined by the formula 10.4 in David Knight’s article: The Rosa’s k m value is determined by the formula 10.18 in David Knight’s article mentioned above: Where k s is a dimensionless correction coefficient for the difference between the self-inductance of a round-wire loop and that of a single-turn current sheet and k m is a dimensionless correction coefficient for the difference in the total mutual inductance of a set of round-wire loops as compared to that of a set of current-sheet loops D c is the coil diameter in cm measured between wire centers and N is the number of turns.
Where L S is the current-sheet inductance described above and An American physicist Edward Bennett Rosa (1873–1921) of the American National Bureau of Standards (NBS, now National Bureau of Standards and Technology, NIST) developed the so-called round wire corrections for the formula above in the form ( formula 10.1 in David W Knight article): It is a very good approximation for round wire coils with many closely spaced turns. The current sheet here means that the coil is wound with very thin tape wire with no gaps between adjacent turns. This formula is valid only for a solenoidal current sheet. Weaver’s article Numerical Methods for Inductance Calculation is used for calculations of inductance L S: A single-layer inductor is shown in the picture above: D c is the coil diameter, D is the coil former diameter, l is the coil length, p is the coil pitch, d is the wire without insulation diameter and d i is the wire with insulation diameter.
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