— Embedding magnetic layer in inductors is an attractive option for increasing inductance density... more — Embedding magnetic layer in inductors is an attractive option for increasing inductance density, which is a critical issue for radiofrequency applications. In this work, a magnetostatic model for square spiral inductors incorporating a magnetic layer is developed. This analytical model provides a fast and accurate calculation of inductance for integrated inductors with embedded magnetic layers either for regular cases or a singular case. In the presented model we replaced square spiral inductors with by square rings and we shown that this replacement gives accurately alike results. The results of the presented approach have been confirmed by already published data.
This paper deals with an efficient and fast approach for determining the mutual inductance betwee... more This paper deals with an efficient and fast approach for determining the mutual inductance between coaxial circular coils of rectangular cross section in combination with thin coaxial circular coils as the thin wall solenoid, the thin disk coil and the filamentary coil. This approach is based on the filament method where conductors are approximated by the set of Maxwell's coils.
Embedding magnetic layer in inductors is an attractive option for increasing inductance density, ... more Embedding magnetic layer in inductors is an attractive option for increasing inductance density, which is a critical issue for radiofrequency applications. In this work, a magnetostatic model for square spiral inductors incorporating a magnetic layer is developed. This analytical model provides a fast and accurate calculation of inductance for integrated inductors with embedded magnetic layers either for regular cases or
Journal of Electromagnetic Waves and Applications, 2015
ABSTRACT The magnetic force exerted by an array of two coaxial thick circular coils with rectangu... more ABSTRACT The magnetic force exerted by an array of two coaxial thick circular coils with rectangular cross-sections in air is important to both electrical and mechanical engineering applications. The magnetic force is typically calculated by taking the integral over the entire space defined by the array. This calculation even for this simple array is an intractable problem and numerical methods have been extensively used. In this work, the integration was subdivided into five regions, and in four of them, an analytical formula was found. The method proposed here is based on the Green’s function of the free space that leads to the elliptical integral of the first and second kind. The formula reveals new insights into how the geometry and relative positioning of the coils within the array determines the strength of the magnetic force. The thicker the coils are and the farther apart they are, the weaker the magnetic force is, and vice versa. This new formula is simpler and practically free of truncation errors, which are commonly encountered in numerical approximations. Several examples from the literature were used to corroborate the present formulation. The results show an excellent agreement with respect to the different numerical and semi-analytical approaches used by other authors.
A new closed-form expression based on double integral computation is introduced for 3D magnetosta... more A new closed-form expression based on double integral computation is introduced for 3D magnetostatic fields of current-carrying solid conductors whose vector density satisfies the condition that its curl is zero. Such a reduced expression is derived for a toroidal conductor with radial current flow, solved analytically, and used for 3D field computation. For illustration, by applying the same reduction principle,
ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field... more ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field, force, torque, stiffness) in cylindrical magnets and coils. By using the equivalence between the amperian current model and the coulombian model of a magnet, we show that a thin coil or a cylindrical magnet axially magnetized have the same mathematical model. Consequently, we present first the analytical expressions of the magnetic field produced by either a thin coil or a ring permanent magnet whose polarization is axial, thus completing similar calculations already published in the scientific literature. Then, this paper deals with the analytical calculation of the force and the stiffness between thin coils or ring permanent magnets axially magnetized. Such configurations can also be modeled with the same mathematical approach. Finally, this paper presents an analytical model of the mutual inductance between two thin coils in air. Throughout this paper, we emphasize why the equivalence between the coulombian and the amperian current models is useful for studying thin coils or ring permanent magnets. All our analytical expressions are based on elliptic integrals but do not require further numerical treatments. These expressions can be implemented in Mathematica or Matlab and are available online. All our models have been compared to previous analytical and semianalytical models. In addition, these models have been compared to the finite-element method. The computational cost of our analytical model is very low, and we find a very good agreement between our analytical model and the other approaches presented in this paper.
This paper presents new general formulas for calculating the magnetic force between inclined circ... more This paper presents new general formulas for calculating the magnetic force between inclined circular filaments placed in any desired position. We use two approaches to calculate the magnetic force, one based on Biot-Savart law and another based on the mutual inductance between these coils. All mathematical procedures are completely described to define coil positions that lead to relatively easy method
IEEE Transactions on Applied Superconductivity, 2000
In this paper, we introduce a very fast method to compute the current distribution in helically w... more In this paper, we introduce a very fast method to compute the current distribution in helically wound thin conductors when one or many of them are arranged in a symmetrical manner to form a single-layer power cable. The method relies on two different approaches to find the magnetic vector potential due to helically wound current sheets. By invoking relevant symmetry
ABSTRACT This paper deals with an efficient approach for determining the magnetic field in system... more ABSTRACT This paper deals with an efficient approach for determining the magnetic field in systems with radial current carrying using thin sheet conductors. The obtained expressions permit to considerably reduce computational time compared to other known methods (filament method, FEM, BEM). All results are obtained in analytical form over incomplete elliptical integrals of the second and third kinds. These expressions can be usefully employed to calculate the magnetic fields in more complicated geometries and may be used to evaluate the self- and mutual-inductance coefficients in systems with thin and massive conductors. In this paper, as a comparative method regarding the accuracy and computational cost, we use the well-known filament method.
... MUTUAL INDUCTANCE CALCULATION FOR NON-COAXIAL CIRCULAR AIR COILS WITH PARALLEL AXES ... In [2... more ... MUTUAL INDUCTANCE CALCULATION FOR NON-COAXIAL CIRCULAR AIR COILS WITH PARALLEL AXES ... In [2], we presented a relatively easy approach to calculate the mutual inductance between circular coils with inclined axes in air. ...
In this paper, new expressions are presented for three-dimensional magnetic-field calculation for... more In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at
... IV. EXAMPLES To verify the validity of these expressions, let us solve the following problem.... more ... IV. EXAMPLES To verify the validity of these expressions, let us solve the following problem. The coil dimensions are as follows. Test case: mm, mm, mm, mm, mm, mm, . The first numerical integration method that will be used is the Gaussian numerical integration. ...
This paper deals with two efficient approaches for determining the mutual inductance between thin... more This paper deals with two efficient approaches for determining the mutual inductance between thin circular coils and disk coils in air. The first approach gives new expressions for calculating the mutual inductance of treated configurations. These results are expressed over the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and one term that must be solved numerically. Another approach is based on the filament method where conductors are approximated by the set of Maxwell's coils. The obtained expressions are expressed over the complete elliptical integrals of the first and second kind and permit also fast calculation of the mutual inductance for mentioned systems. These new expressions are accurate and simple for useful applications. All results obtained by the two approaches are in excellent agreement.
This paper presents an efficient method for computing the mutual inductance between two thin coax... more This paper presents an efficient method for computing the mutual inductance between two thin coaxial disk coils in air. The derived principal semi-analytical expressions involve complete elliptic integrals of the first and second kind, Heuman's Lambda function and three terms that have to be computed numerically. The presented method is compared to the filament method where both conductors are approximated by Maxwell's filamentary coils. The mutual inductance values (for a chosen case) computed by both methods are in good agreement. However, the method presented in this work exceeds by far the filament method in its precision and computational efficiency. In another example, the computed mutual inductance is validated by measurement.
— Embedding magnetic layer in inductors is an attractive option for increasing inductance density... more — Embedding magnetic layer in inductors is an attractive option for increasing inductance density, which is a critical issue for radiofrequency applications. In this work, a magnetostatic model for square spiral inductors incorporating a magnetic layer is developed. This analytical model provides a fast and accurate calculation of inductance for integrated inductors with embedded magnetic layers either for regular cases or a singular case. In the presented model we replaced square spiral inductors with by square rings and we shown that this replacement gives accurately alike results. The results of the presented approach have been confirmed by already published data.
This paper deals with an efficient and fast approach for determining the mutual inductance betwee... more This paper deals with an efficient and fast approach for determining the mutual inductance between coaxial circular coils of rectangular cross section in combination with thin coaxial circular coils as the thin wall solenoid, the thin disk coil and the filamentary coil. This approach is based on the filament method where conductors are approximated by the set of Maxwell's coils.
Embedding magnetic layer in inductors is an attractive option for increasing inductance density, ... more Embedding magnetic layer in inductors is an attractive option for increasing inductance density, which is a critical issue for radiofrequency applications. In this work, a magnetostatic model for square spiral inductors incorporating a magnetic layer is developed. This analytical model provides a fast and accurate calculation of inductance for integrated inductors with embedded magnetic layers either for regular cases or
Journal of Electromagnetic Waves and Applications, 2015
ABSTRACT The magnetic force exerted by an array of two coaxial thick circular coils with rectangu... more ABSTRACT The magnetic force exerted by an array of two coaxial thick circular coils with rectangular cross-sections in air is important to both electrical and mechanical engineering applications. The magnetic force is typically calculated by taking the integral over the entire space defined by the array. This calculation even for this simple array is an intractable problem and numerical methods have been extensively used. In this work, the integration was subdivided into five regions, and in four of them, an analytical formula was found. The method proposed here is based on the Green’s function of the free space that leads to the elliptical integral of the first and second kind. The formula reveals new insights into how the geometry and relative positioning of the coils within the array determines the strength of the magnetic force. The thicker the coils are and the farther apart they are, the weaker the magnetic force is, and vice versa. This new formula is simpler and practically free of truncation errors, which are commonly encountered in numerical approximations. Several examples from the literature were used to corroborate the present formulation. The results show an excellent agreement with respect to the different numerical and semi-analytical approaches used by other authors.
A new closed-form expression based on double integral computation is introduced for 3D magnetosta... more A new closed-form expression based on double integral computation is introduced for 3D magnetostatic fields of current-carrying solid conductors whose vector density satisfies the condition that its curl is zero. Such a reduced expression is derived for a toroidal conductor with radial current flow, solved analytically, and used for 3D field computation. For illustration, by applying the same reduction principle,
ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field... more ABSTRACT This paper presents a synthesis of analytical calculations of magnetic parameters (field, force, torque, stiffness) in cylindrical magnets and coils. By using the equivalence between the amperian current model and the coulombian model of a magnet, we show that a thin coil or a cylindrical magnet axially magnetized have the same mathematical model. Consequently, we present first the analytical expressions of the magnetic field produced by either a thin coil or a ring permanent magnet whose polarization is axial, thus completing similar calculations already published in the scientific literature. Then, this paper deals with the analytical calculation of the force and the stiffness between thin coils or ring permanent magnets axially magnetized. Such configurations can also be modeled with the same mathematical approach. Finally, this paper presents an analytical model of the mutual inductance between two thin coils in air. Throughout this paper, we emphasize why the equivalence between the coulombian and the amperian current models is useful for studying thin coils or ring permanent magnets. All our analytical expressions are based on elliptic integrals but do not require further numerical treatments. These expressions can be implemented in Mathematica or Matlab and are available online. All our models have been compared to previous analytical and semianalytical models. In addition, these models have been compared to the finite-element method. The computational cost of our analytical model is very low, and we find a very good agreement between our analytical model and the other approaches presented in this paper.
This paper presents new general formulas for calculating the magnetic force between inclined circ... more This paper presents new general formulas for calculating the magnetic force between inclined circular filaments placed in any desired position. We use two approaches to calculate the magnetic force, one based on Biot-Savart law and another based on the mutual inductance between these coils. All mathematical procedures are completely described to define coil positions that lead to relatively easy method
IEEE Transactions on Applied Superconductivity, 2000
In this paper, we introduce a very fast method to compute the current distribution in helically w... more In this paper, we introduce a very fast method to compute the current distribution in helically wound thin conductors when one or many of them are arranged in a symmetrical manner to form a single-layer power cable. The method relies on two different approaches to find the magnetic vector potential due to helically wound current sheets. By invoking relevant symmetry
ABSTRACT This paper deals with an efficient approach for determining the magnetic field in system... more ABSTRACT This paper deals with an efficient approach for determining the magnetic field in systems with radial current carrying using thin sheet conductors. The obtained expressions permit to considerably reduce computational time compared to other known methods (filament method, FEM, BEM). All results are obtained in analytical form over incomplete elliptical integrals of the second and third kinds. These expressions can be usefully employed to calculate the magnetic fields in more complicated geometries and may be used to evaluate the self- and mutual-inductance coefficients in systems with thin and massive conductors. In this paper, as a comparative method regarding the accuracy and computational cost, we use the well-known filament method.
... MUTUAL INDUCTANCE CALCULATION FOR NON-COAXIAL CIRCULAR AIR COILS WITH PARALLEL AXES ... In [2... more ... MUTUAL INDUCTANCE CALCULATION FOR NON-COAXIAL CIRCULAR AIR COILS WITH PARALLEL AXES ... In [2], we presented a relatively easy approach to calculate the mutual inductance between circular coils with inclined axes in air. ...
In this paper, new expressions are presented for three-dimensional magnetic-field calculation for... more In this paper, new expressions are presented for three-dimensional magnetic-field calculation for a massive disk currying radial currents. These expressions have been obtained in analytical form as functions of incomplete elliptical integrals (of the first, second, and third kind) and an integral to be solved numerically. This approach enables one to easily calculate the magnetic field everywhere in space at
... IV. EXAMPLES To verify the validity of these expressions, let us solve the following problem.... more ... IV. EXAMPLES To verify the validity of these expressions, let us solve the following problem. The coil dimensions are as follows. Test case: mm, mm, mm, mm, mm, mm, . The first numerical integration method that will be used is the Gaussian numerical integration. ...
This paper deals with two efficient approaches for determining the mutual inductance between thin... more This paper deals with two efficient approaches for determining the mutual inductance between thin circular coils and disk coils in air. The first approach gives new expressions for calculating the mutual inductance of treated configurations. These results are expressed over the complete elliptical integrals of the first and second kind, Heuman's Lambda function, and one term that must be solved numerically. Another approach is based on the filament method where conductors are approximated by the set of Maxwell's coils. The obtained expressions are expressed over the complete elliptical integrals of the first and second kind and permit also fast calculation of the mutual inductance for mentioned systems. These new expressions are accurate and simple for useful applications. All results obtained by the two approaches are in excellent agreement.
This paper presents an efficient method for computing the mutual inductance between two thin coax... more This paper presents an efficient method for computing the mutual inductance between two thin coaxial disk coils in air. The derived principal semi-analytical expressions involve complete elliptic integrals of the first and second kind, Heuman's Lambda function and three terms that have to be computed numerically. The presented method is compared to the filament method where both conductors are approximated by Maxwell's filamentary coils. The mutual inductance values (for a chosen case) computed by both methods are in good agreement. However, the method presented in this work exceeds by far the filament method in its precision and computational efficiency. In another example, the computed mutual inductance is validated by measurement.
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