In this paper the AC winding resistance of the litz wire wound planar square coil is derived. The Biot-Savart’s law is used to derive analytical expression for the AC winding resistance. Analytical calculations are done for two planar square coils of different size. Experimental verification and comparison of the calculated and measured winding resistances are performed.
Słowa kluczowe: AC winding resistance, eddy currents, planar square coil, proximity effect, power loss, wireless power transfer
Wartykule tym, wyprowadzone zostało rownanie na rezystancj˛e uzwojenia cewek planarnych w kształcie kwadratu przewodza˛cych pra˛d przemienny. Rezystancja takich cewek nie jest stała lecz zmienia sie˛ wraz ze wzrostem czestotliwosci. Przyczyna˛ zmiany tejz˙e rezystancji jest przede wszystkim efekt zbli˙zeniowy, który powstaje podczas indukowania si ˛e pr ˛ adow wirowych w uzwojeniu. Wpływ efektu zbli˙zeniowego na rezystancje uzwojenia jest silniejszy wraz ze wzrostem czestotliwosci. Analityczne równanie na rezystancje˛ uzwojenia dla pra˛dow przemiennych takiej cewki, wyprowadzono bazuja˛c na prawie Biot-Savart’s. Experymentalna weryfikacja i porównanie teoretycznych obliczen została równiez˙ dokonana i przedstawiona w tym artykule.
Keywords: Bezprzewodowy przesył energii, efekt zblizeniowy, planarna kwadratowa cewka, pra˛dy wirowe, Rezystancja AC uzwojenia, straty mocy.
Introduction Demand of the wireless power transfer systems (WPT) for the high quality factor planar coils is significantly increasing. It can be seen that planar coils are utilized in systems like inductive heating, EV charging, robot charging, home appliances, medical appliances, and mobile device systems - . The addition of the ferrite introduces ferrite core losses and increases copper losses . The air-core inductor with advantages of even magnetic field distribution and relatively lower costs could be utilized in such a systems . Moreover in all of these systems, the low-loss planar inductors are required in order to increase the quality factor and to transfer energy with the highest possible efficiency. The WPT coils. operate at relatively low coupling factor (typical range 0.1 to 0.4), thus, there is a presence of high circulating currents that causes additional copper losses. These losses must be reduced in order to increase the WPT system efficiency thus high unloaded quality factor coils are required.Nomenclature γ = rs √ μσω - normalized radius of the strand; δ - skin depth; μ - free space magnetic permeability; σ - copper conductor conductivity; ω = 2πf - angular frequency of the conductor current; ESR - equivalent series resistnace; I - RMS value of the coil current; Ns - number of strands in the litz wire; Nt - number of the coil turns; Li, Lj - lengths of ith and jth coil sides; Pj - the power dissipated in the conductor j-th turn (one side of the coil); Rcoil - total resistance of the coil; Rdc, Rdcm - calculated and measured copper solid round wire DC resistance; Rmeas - measured AC winding resistance; Rprox, Rproxm - calculated and measured proximity effect winding resistance of the coil winding; Rskin - skin effect winding resistance of the litz wire; il(t) - sinusoidal winding conductor current; f, fcritical - operating frequency an [...]
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