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In this article, we present two methods for calculation of the inductance of toroidal core power inductors wound by rectangular cross-sectional wire, considering that the current density is inversely proportional to the circular coil radius. The first method is to simplify the helical toroidal coil into a thick-walled toroidal, and based on Grover’s toroidal inductor formula, the inductance is obtained by calculation the magnetic flux and the calculation method is simple, but the applicability is poor. The second method is to simplify the helical toroidal coil into a collection of self-closing circular coils, the calculation method is complex but has high accuracy, and the mutual inductance between the circular coils is calculated by the filament method based on the adjusted Grover’s mutual inductance of circular coils with inclined axes. We verify the adjusted Grover’s mutual inductance of filamentary circular coils with inclined axes and the mutual inductance between inclined circular coils with a rectangular cross section. Finally, we compared and analyzed the results calculated by the two methods proposed in this article and the results calculated by the finite element method.

The various advantages of toroidal inductors, which are cooler, smaller and more EMI-resistant are discussed. With toroidal inductors, there is an advantage to maintaining a single layer of windings due to which the inductor behaves closer to an ideal component of lower levels of parasitic capacitance. Multi-layer toroidal inductors involve both turn-to-turn capacitance and layer-to-layer capacitance and a very significat start/finish gap capacitance since there is no start/finish gap. This increases the total amount of parasitic capacitance by orders of magnitude.

This paper presents a micromachined implementation of embedded toroidal solenoids for high-performance on-chip inductors and transformers, which is highly demanded in radio-frequency integrated circuits (RFICs). Microfabricated on CMOS compatible silicon wafers with post-CMOS micromachining techniques, the RF toroidal components can constrain the magnetic flux into a well-defined path and away from other on-chip RF devices, thereby, being in favor of decrease in RF loss, increase in Q-factor and elimination of electromagnetic interference. By using a technical combination of an anisotropic wet etch and an isotropic dry etc., the micromachined toroidal structure can be used for the formation of metal solenoid by copper electroplating. Processed under low temperature (Max 120 °C for photoresist hard-baking), the three mask microfabrication can be compatible with CMOS IC fabrication in a post-process way. The formed toroidal inductors with 4.92 nH and 8.48 nH inductance are tested, and we obtain maximum Q-factors of 25.7 and 17.8 at 3.6 GHz and 3.1 GHz, while the self-resonant frequencies are 17.3 GHz and 7.4 GHz, respectively. On the other hand, two types of toroidal transformers are also formed and tested, resulting in satisfactory RF-performance. Therefore, the novel techniques for close-loop solenoid inductors are promising for high-performance RF ICs.

In electrical engineering a toroidal inductor is used to measure or monitor the electric currents of an AC power circuit as a function of the harmonic distortion [1,2]. A galvanically isolated current measurement is required, such that the advantages of lower losses nd measurement signals processed directly must be attained [3]. The ferrite core toroid inductors produces a reduced current accurately proporonal to the measured current. The toroidal inductor can be also commonly used for feedback control, and other applications [4].The design method of toroidal inductors have been developed by a non iterative method, which introduce an equation for estimation of the core size required as function of the wanted inductance and the maximum values specified for induction and current [5]. Another method solution consists in modeling inductors along with the equivalent circuits, calculation of the leakage inductance, core material characteristics, and geometrical configuretion for the minimization of volume inductors in order to simplify the design procedure [3]. Nevertheless, the trend for the current monitoring is driven by cost reduction, an increased functionality, and limited weight/space in some applications [3,4].This finally results in constantly increasing frequencies, which comes along with and increased bandwidth and poor stability.Based on electric and magnetic properties, like saturation magnetization, and toroidal-core losses, here is proposed the possibility of application of the grain-oriented silicon-iron cores for current monitoring, because these can reduce phase error and improve its accuracy in measurements of AC current at low frequencies (50 - 60 Hz) [6,7]. A simple method for toroidal-inductor design at minimum losses is suggested to calculate several inductors accepting a broad tolerance of the core material features.In general, the inductor design procedure described in literature makes use of numerous monograms, and the final result is achieved through several iterations. In special, toroidal inductors have been designed by several engineers with tedious methods [8-10]. For that reason, the lack of deeper understanding of the fundamental electromagnetic laws, it makes many engineers to consider the design of inductive components a difficult task.The purpose here is to explain a design method based on well-known tools by engineers [11]; presenting in a simple and easy way the relationships that exists between equivalent circuit and transfer function of a toroidal inductor. The proposed work is developed to meet the following objectives:1) To explain the relationship between equivalent circuit and magnetic parameters of a toroidal inductor;2) To develop the method based on normalized parameters;3) To demonstrate the method validation with a current-signal sensor and evaluate the EN-50160-2-2 standard as a function of single harmonic distortion (SHD) in home use loads [1].