Devices and methods for redistributing magnetic flux density

Redistributing magnetic flux density within electro-magnetic or permanent magnet devices, as described herein, causes the device to increase its utilization of its magnetic core material and thereby increase its power density (Watts/volume). The preferred embodiment uses magnetic core bias currents, synchronized to the device's magnetizing current, through uniform, longitudinally isolated, magnetic core sections. The preferred embodiment can be complemented with local core bias currents that generate magnetic flux that oppose the incident magnetizing flux in local magnetic core sections with high flux density concentrations such as core corners. An alternative embodiment longitudinally interlaces magnetically isolated core sections of equal magnetic path length and uniform areal cross section. Another alternative embodiment redirects the magnetic flux in spiral wound inductors and transformers to the circumferential direction used in toroids. All magnetic core shapes, materials, and sizes can be modified to accommodate bias currents; however, the tape wound toroidal core featured mostly in transformers and inductors, is the easiest core to modify. Examples of the types of electro-magnetic and permanent magnet devices that benefit from the appropriate application of magnetic flux density redistribution include electrical devices such as transformers, inductors, delay lines, and electromechanical devices such as motors, generators, relays, solenoids, and rail guns.

FIELD OF THE DISCLOSURE

This disclosure relates generally to magnetic devices and more specifically to electromagnetic (E-M) and permanent magnetic (PM) devices that increase their power density (PD—Watts/volume) by redistributing the magnetic flux density (B) within the device's magnetic cores.

BACKGROUND

Introduction to Practical E-M Design

The term “E-M devices” includes, but is not limited to: passive electrical devices such as transformers, inductors, and delay lines; and electromechanical devices such as motors, generators, relays, solenoids, and the “rail gun.” Some of these E-M devices also include permanent magnetic (PM) components that work synergistically with the E-M components to hold, lift, or torque magnetic susceptible material. PM components are also used to favorably change the magnetic material's magnetic saturation characteristic. Permanent magnets, PM, may also be used in magnetic devices without electro-magnetics (E-M).

All conventional E-M devices consist of a magnetizing current, IM(f), of an operating frequency (f) flowing in a conductive coil around and external to the magnetic core. The heart of all E-M devices and permanent magnetic devices is a magnetic core. The core may be made of grain oriented silicon steel, amorphous metal, ferrite, or other ferrous based materials. Some magnetic cores are a dielectric material such as plastic or air and have no ferrous enhancement of its magnetic permeability (μ) or limitations on its maximum flux density (BMx(f)).

A magnetic device determines its operational power from the steady state operating voltage (V(f)) which develops a steady state operating load current (IL(f)) through the device. The steady state power (P(f)) required by the device is the product of its operating voltage, V(f), and load current, IL(f).
P(f)=V(f)*IL(f).

Magnetic devices are usually designed so the magnetizing current, IM(f), is small and negligible with respect to the load current, IL(f). The device's maximum steady safe state power capability (PMx(f)) is the product of the device's maximum safe steady state voltage (VMx(f)) and its maximum safe steady state load current (ILx(f)).
PMx(f)=VMx(f)*ILx(f).

Power density, PD(f), at an operating frequency, f, is the maximum safe steady state power required by the E-M device divided by the device's magnetic material volume (vol).
PD(f)=PMx(f)/vol.
Maximum Current, IMx(f), and Maximum Voltage, VMx(f)

The maximum operating electrical power for all these devices is determined by either the maximum current rating of the magnetic wire forming the magnetics' coil which conducts the maximum load current, ILx(f), or the maximum operating voltage rating, VMx(f), at which the maximum flux density, BMx(r), is less than Bsat throughout all sections of the magnetic core. (BMx(r)≦Bsat) Optimal magnetics' power design, which minimizes material requirements for the magnetic core and coil, occurs when both the maximum load current, ILx(f), and the maximum voltage, VMx(f), are the device's simultaneous operating power limitations—indicates all of the coil and all of the core are efficiently used.

The magnetic core's current limitation is principally affected by the diameter of wire required for the core's coil. The product of the wire's cross sectional area (Awr) and the number (N) of required coil turns determines, to a first order, the core's minimum required window opening to accommodate the coil winding. Optimal magnetic design requires the smallest practical coil winding window opening.

All magnetic materials are characterized by their ability to accommodate the magnetic flux density, B, induced by the magnetic force field (AT, Ampere *Turn) permeating their space. This ability is known as the material's magnetic permeability (μ). A material's magnetic permeability, μ, is the product of the permeability of free space, μo, and the material's relative permeability to free space, μR. (μ=μo*μR). The permeability of free space, μo, has the value 1.26*10−6Henries per meter (H/m), while the material's relative permeability, μR, is an integer with a range of 1 to greater than a million. Ferrous based materials designed for magnetics have a relative permeability, μR, much greater than 50—usually 1,000 to 20,000. Most magnetic materials have non-linear permeabilities increasing on the order of a factor of 10, when their magnetic force field, AT, changes from a low level magnetic excitation (ATLo) to the material's maximum high level magnetic excitation (ATHi), just below the material's maximum magnetic flux density, Bsat.

Some magnetic cores with a dielectric material such as plastic or air have no ferrous enhancement on its magnetic permeability (μ). Also, they do not have the ferrous limitation of magnetic saturation, Bsat. Air and most dielectrics have a relative permeability, μR, of approximately 1.

A magnetic material's maximum magnetic flux density, Bsat, is the maximum number of magnetic flux (φMx) lines per unit cross sectional area (AC) of magnetic material that the material will support without magnetically saturating. Magnetic force fields, AT, that try to cause the magnetic material's flux density, B, to exceed Bsat will cause the magnetic material to go into magnetic saturation and essentially reduce the magnetic core's relative magnetic permeability, μR, to 1, the value of an air core. The magnetic device's maximum operating voltage, VMx(f), occurs when the operating voltage, V(f), causes the maximum magnetizing current (IMx(f)) to induce into the magnetic device the maximum magnetic flux (φMx(f)) which causes the radially distributed magnetic flux density, BMx(r), to reach Bsat, regardless of where it occurs along the device's radial cross sectional magnetic flux density distribution, BMx(r).

In the maximum magnetic material radial cross sectional flux density distribution curves, BMx(r), shown in the Figures, the following assumptions are in place. All conventional radial flux density distribution curves, BMx(r), are normalized, maximum, and simple Amperian or the summation of normalized, maximum, simple Amperian curves. A normalized flux density distribution curve means that the actual flux density distribution, B(r), is divided by the magnetic material's magnetic saturation flux density, Bsat. Maximum flux density means that the highest flux density value of the flux density distribution, BMx(r), is Bsat and occurs in conventional magnetic material at its inner most magnetic boundary, the effective radius of the inner diameter, rIDe. Amperian may be defined as the radial cross sectional maximum flux density distribution curve, BMx(r), that follows Ampere's Law and is hyperbolically shaped, radially, from the inner boundary, rIDe, to the outer boundary, the effective radius of the outer diameter, rODe, regardless of the core's shape or size. Also, the inner boundary, rIDe, completely surrounds the magnetizing current source, IM(f), inducing the magnetic force field, AT, into the magnetic material.

On the other hand, all power density, (PD), enhanced redistributed flux density curves (BBMx(r)) presented herein, are the optimal summation of radially shifted, normalized, maximum, simple Amperian curves, BMx(r).

When an E-M or PM device's PD is compared, the device is assumed to be operating in the steady state, unless otherwise noted. A device's steady state assumes a steady electrical magnetizing current, IM(f), for a fixed load after a device has been subjected to the application of a fixed voltage, V(f), at a fixed frequency, f. Operating frequency, f, has the range of zero (0) to infinity (∞). When f equals zero (f=0), the DC or time invariant condition is being considered. Thus, VDC=V(f) when f=0.

The comparative PD of E-M and PM devices in the transient state, occurs when the device's magnetizing current, IM(t), in the time domain (t) electrically responds to a voltage step function excitation, V(t). The transient state voltage, V(t), of an electro-magnetic device is defined over its actuation time, beginning at start, t=0, to finish time, t=TD.

A circular toroid will be used to generally define the inner and outer boundaries for the radial magnetic operating regions of all magnetic cores—the region is defined from the effective radius of the inner diameter, rIDe, to the effective radius of the outer diameter, rODeThe circular toroidal shape's uniform structure lends itself to easy mathematical analysis (using Ampere's Law) from which all magnetic flux distribution curves, herein, have been ideally determined. All maximum normalized flux density distribution curves, BMx(r), represent maximum operational flux density, BMx(f), at operational frequency (f). Whether the operating voltage is steady state, V(f), or transient, V(t), the flux density distribution is Amperian. The square core's magnetic flux distribution is a summation of bi-lateral Amperian cross sectional magnetic flux distributions, each being derived from an equivalent circular toroidal shape with the same inductance and material volume of the square core.

A circular toroid exhibits a precise, circular, magnetic core geometry, and as such, the magnetic flux's center for its effective radius of curvature is exactly the geometric center of the toroid. The geometry of a circular toroidal magnetic core precisely lines up with the natural circular geometry of magnetic flux lines generated by the magnetizing current, IM(f), flowing through the center of the toroid. Consequently, the effective radius of the inside diameter, rIDe, equals the geometric radius of the inside diameter (rID). Likewise, the effective radius of the toroid's outer diameter, rODe, equals the geometric radius of its outside diameter, rOD. If a device's magnetic core exhibits a uniform and constant flux density distribution, B(r), throughout its circumferential magnetic path length, le, as shown by any of its flux density distribution curves then, by the inverse of Ampere's Law's, the magnetic core is constructed with a constant radius of curvature.

For non-circular magnetic core construction geometries, such as a square core, magnetic flux density distributions must conform to Ampere's Law at all points along the core's magnetic path length, le. However, the non-circular shape of the core forces the core's magnetic flux lines to traverse long straight magnetic sections with effectively large radius of curvature (rIDes) and traverse corners with effectively much smaller radius of curvature (rIDec). (rIDes>>rIDec) The square core's straight sections are the dominant regions that determine the non circular device's toroidal shape equivalent effective radius of inner diameter, rIDe, and equivalent effective radius of outer diameter, rODe, respectively, by the inner magnetic path length periphery (lei), the outer magnetic path length periphery (leo), and the requirement that the equivalent toroidal physical size and inductance coincide with the square core's physical size and inductance.

The operational description of redistributed magnetic flux density in a magnetic core assumes that the magnetic material used in the core's cross-section from rIDe, to rODeand at any point along its magnetic path length, le, is ideal and has a constant, uniform, and isotropic relative magnetic permeability, μR, which is greater than 100. Flux density distribution curves shown herein are only a function of the core's geometry and ideal operating frequency, f.

The magnetic core's voltage limitation, VMx(f), is effected by the magnetic flux distribution within the magnetic core. Increased magnetic flux utilization within a given magnetic core material, without magnetic saturation, achieves a higher operating voltage by Faraday's Law and, therefore, higher power density (PD—Watts/volume). Presently, all the magnetic cores in conventional E-M and PM devices are designed to use simple, Amperian, radial (r), magnetic, flux density distribution, B(r), within the core. Consequently, depending on core geometry, from 10% to up to 50% or more of the core is under utilized.

The power electrical transformer was first patented by Gaulard & Gibbs in 1882 and then practically refined by William Stanley in 1886. Since then, optimizing the magnetic design of conventional coil and core electro-magnetic devices, such as transformers, inductors, delay lines, relays, solenoids, motors, and generators, has been limited to conventional electro-magnetic design techniques. Likewise, permanent magnetic device design has followed the trends set by E-M device design. Little has changed in the design of conventional E-M devices other than the introduction of better performing materials and algorithms to speed up the design process.

It is to be understood that both the foregoing general description and the following detailed description are not limiting but are intended to provide further explanation of the novelty claimed. The accompanying drawings, which are incorporated in and constitute part of this specification, are included to illustrate and provide a further understanding of the method and system described herein. Together with the description, the drawings serve to explain the principles of construction and operation.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The broad range of magnetic materials, such as grain oriented silicon steel, amorphous metals, ferrites, and powdered iron, are ferrous based. All ferrous based magnetic materials used to build magnetic cores are modifiable by the application of the power density, (PD), enhancement technologies described below. These magnetic materials are considerably non-linear, hysteretic, and parametrically distinct from each other, which makes detailing the descriptions of how each material benefits from power density enhancement needlessly complex. However, normalized flux density distribution will be used to simplify and illustrate the various PD enhancement techniques which demonstrate that the PD enhancement techniques are independent of the magnetic material to which the PD enhancements are applied.

For purposes of the Figures described below, identical element numbers are designated by identical reference numbers as follows. For the devices shown in the following figures, magnetic flux lines circumnavigate their source, their magnetizing current, IM(f). Consequently, the polar coordinate system (r,θ,z) best describes the spatial geometry of magnetic flux lines with respect to the magnetizing current, IM(f), at a spatial center115. The symbol, r, is the radial direction with the magnetizing current, IM(f), as the center115. The symbol, θ, is the circumferential direction, encircling the magnetizing current, IM(f), and usually parallel to the magnetic flux direction. The symbol, z, is the vertical direction, usually parallel to the direction of magnetizing current, IM(f).

Transformer operation is functionally characterized by the voltages on the primary and secondary windings and the currents in the primary and secondary windings. All the transformers, inductors, or cores for inductors and transformers referenced in the Figures are operated by a time changing voltage104of frequency, f, (Vp(f)), applied to a primary or inductor winding102. An E-M device without a secondary winding and no mechanical actuation is simply an inductor. A secondary voltage105(Vs(f)), develops on a secondary winding103, that is proportional to the turns ratio, N. The turns ratio is the number of turns of secondary winding (Ns) divided by the number of turns of primary winding (Np). N=Ns/Np. The diameter of the secondary wiring103may be chosen to accommodate within safety agency thermal limits a maximum secondary current117(ISx(f)). The diameter of the primary wiring102may be chosen to accommodate, within safety agency thermal limits, a maximum primary current116(IPx(f)). The primary voltage reference104, the primary current reference116and a primary winding reference102reference the primary wiring. The secondary voltage105, a secondary current reference117and the secondary winding reference103reference the secondary wiring. The maximum primary current, IPx(f), is the vector summation of the secondary current reflected into the primary, by the reciprocal of the turns ratio, N, and the maximum magnetizing current, IMx(f). IPx(f)=IMx(f)+ISx(f)/N.

The maximum magnetizing current, IMx(f), is the primary current when the primary voltage is maximum, VMx(f), after the load is removed from the secondary and ISx(f) is zero. For a low loss primary magnetic winding, the magnetizing current, IMx(f), is nearly purely inductive, which would phase lag a pure resistive secondary current component, ISx(f), by 90°. A maximum secondary current defines the primary and secondary wiring diameters, but for practical purposes is not considered in the transformer's magnetic core analysis. Only the magnetizing current, IM(f),116, defines the radial, r, time changing flux density distribution, B(f,r), at frequency, f, in the magnetic core.

Terminology that describes spatial direction with respect to specific magnetic flux direction is used without concern for the spatial position of the magnetizing current, IM(f). The term longitudinal refers to the direction that is parallel to the magnetic flux, φM, direction regardless of its spatial position or orientation. Lateral is a directional term indicating normal (perpendicular) to the longitudinal direction. A magnetic core's magnetic path length (le) is a closed loop that parallels the direction of the magnetizing flux, φM. A magnetic device's length (lt) is the difference between a magnetic device's inner boundary, rIDe, and outer boundary, rODe.

Toroid devices such as a toroidal transformer150shown inFIGS. 3A-3Binclude a window opening108. Square core devices such as an E-I inductor290shown inFIGS. 1A-1Binclude a window opening276. Capacitor enhanced magnetic devices such as a tape wrapped toroidal core450shown inFIGS. 9A-9Binclude a window opening451.

Construction Categories (4)

The construction of a device's core, regardless of the device's application, falls under one of four example core construction categories, or combinations thereof. These categories and their examples include: 1) a laminated core (LaC) such as a low profile E-I inductor290shown inFIGS. 1A and 1B, and a high profile E-I inductor310shown inFIGS. 2A and 2B; 2) a tape wound core (TWC) such as a low profile toroidal transformer150shown inFIGS. 3A and 3B, and a high profile toroidal transformer100shown inFIGS. 4A and 4B; 3) a solid block core (SBC) such as a high profile E-I inductor360shown inFIGS. 5A and 5Band a planar inductor941shown inFIG. 6; and 4) an air or dielectric core (AiC) such as an inductor940shown inFIGS. 7A and 7B, and a rail gun960shown inFIG. 8.

Laminated cores (LaC) may be used to construct E-I cores devices (a.k.a. “square core”) such as transformers, electric motors and generators (both stator and rotor), solenoids and relays. TWC construction may be used to construct circular and square toroidal transformers and inductors. Solid block core (SBC) construction may be used for toroidal or E-I shaped cores and constructed with ferrite based magnetic core material which may be used in high frequency inductors and transformers; electric motors and generators (usually the rotor); and relays. Air or dielectric core (AiC) construction may be used in a “rail gun”; very high frequency (RF) transformers and inductors; and magnetics where extremely high magnetic induction is required without exceeding the magnetic saturation limitation of ferrous core material. The four example magnetic core constructions may all be modified to improve the device's power density by optimally redistributing their core's radial maximum magnetic flux density, BMx(r).

Selecting Magnetic Core Material for Frequency of Operation

An electromagnetic device's frequency of operation determines the device's best magnetic core selection. The high profile, stacked, laminated, square core, (LaC) construction such as the inductor310shown inFIGS. 2A and 2B, and a high profile tape wound toroidal core, TWC construction such as the transformer100shown inFIGS. 4A and 4Bare the optimal construction shapes for power density when building inductors and transformers. The circular, stacked, laminated core (LaC) is the power frequency core shape that gives the optimal power density for motors and generators. Magnetic cores for relays and solenoids operating at these power frequencies may be constructed by modified square core LaC construction. For electromagnetic devices with operating frequencies greater than 20 kHz, SBC ferrite material is the optimal magnetic material for power density relative to either the TWC, or LaC square core. Air core construction is generally used for operating frequencies greater than 100 MHz. Thus, core selection for power density is determined by the frequency of the operation of the E-M device.

Magnetic Flux Redistribution Techniques (4)

Four novel magnetic core flux density redistribution methods have been developed and are reported herein. The first flux density redistribution method is referred to as the core bias current method, whereby bias current (IB(f)) is injected through the magnetic core by a voltage source of an amplitude and phase with respect to the magnetic driving voltage source, V(f), such that a portion of the maximum operational magnetic flux density, BMx(r,f), is moved from over utilized areas of the core's cross section to under utilized areas. The bias current method for core modification may be designed to inject bias currents into the core so as to magnetically redistribute flux, longitudinally, along all of the core's magnetic path length, le, or, locally, along part of the core's magnetic path length, le, such as the corners or sharp radius of curvature that the magnetic flux must traverse along the core's magnetic path length, le. Effectively, bias current, IB(f), through the core is able to redistribute magnetic flux density, BMx(r), throughout the core, because the magnetic flux generated by the bias current, IB(f), will oppose the magnetic flux generated by the device's magnetizing current, IMx(f), at the core's inner periphery, lei, and its magnetic neighborhood, and aid the magnetic flux at the core's outer periphery, leo, and its magnetic neighborhood.

The core bias current method may be implemented by one of two frequency determinate methods. One method redistributes magnetic flux density to increase the magnetic device's PD over a broad range of frequencies. The other method uses dielectric material to form capacitance, distributed either uniformly or discretely along the device's length, lt, through which displacement currents (ID(f)) cause the device to redistribute magnetic flux density at a narrow operational frequency (fo) so as to increase the device's PD.

Constructing magnetic devices with magnetic cores having distributed capacitance (Cn) provides the additional benefit of constructing a novel power transmission line wherein the propagation of a transient voltage, V(t), along the device's transmission line length, lt, requires time delay (TD). The power transmission line also forms a new electromechanical device that develops mechanical forces in its magnetic core from the induced magnetic energy faster than for the same transient operating voltage, V(t), applied to the same core without distributed capacitance.

Another benefit of integrating capacitance with the magnetizing inductance is the creation of a parallel resonant circuit, when operated at resonance frequency (fr) causes the device to electrically appear to the driving circuit like an impedance higher than the simple inductive reactance that it would be without the capacitance. The examples of the core bias current method are a self bias current, low profile, LaC inductor290shown inFIGS. 1A and 1B; a tapped bias current, high profile, LaC inductor310shown inFIGS. 2A and 2B; a tapped bias current, low profile, TWC transformer150shown inFIGS. 3A and 3B, a self bias current, high profile, TWC transformer100shown inFIGS. 4A,4B, and4C; a capacitance enhanced, displacement bias current, tape wrapped core450shown inFIGS. 9A and 9B; a capacitance enhanced, displacement bias current, tape wrapped core500shown inFIGS. 10A and 10B; a capacitance enhanced, displacement bias current, tape wrapped core530shown inFIGS. 11A and 11B; and a capacitance enhanced, displacement bias current, tape wrapped core570shown inFIGS. 12A and 12B.

The second flux density redistribution method is referred to as magnetic core interlacing, whereby the core's cross section is modified by longitudinally sectioning the core, into concentric, magnetically isolated core sections, that are mechanically interlaced. Ideally, the mechanical interlacing of the core material is designed such that the magnetic flux path lengths, le, of each longitudinal section are equal. If the cross sections of each magnetic section are also equal, then the cross sectional magnetic flux density, BMx(r), in each magnetic section, has the same shape for simple Amperian maximum magnetizing current, IMx(f). However, each section is physically, radially, shifted from each other, thereby, radially shifting their maximum magnetic flux density distribution (BMx(r-Δr)) which maximizes the total flux density distribution, BMx(r), in the composite interlaced core. The examples of magnetic core interlacing are SBC or LaC inductor or transformer cores850shown inFIG. 13and core870shown inFIGS. 14A and 14B.

The third flux density redistribution method is referred to as the magnetic core corner flux density remediation, whereby flux density pile-up at corners or sharp bends along the longitudinal magnetic flux path, le, are remedied. Corner bias current is one method to remediate magnetic flux density pile-up at the corners. Another method physically smoothes or radially elongates the longitudinal magnetic slit at sharp radii of curvature along the longitudinal magnetic flux path. Still another method diagonally gaps corner sections, lateral to the magnetic flux direction, to remediate corner flux density saturation. The examples of magnetic core corner flux density remediation by tapped bias current include a LaC inductor330shown inFIGS. 15A and 15B, and corner flux density remediation by self bias current in a LaC inductor350shown inFIGS. 16A and 16B; and corner flux density remediation by a corner shaping370inFIG. 17A; a corner shaping371inFIG. 17B; a corner shaping372inFIG. 17C; a corner shaping373inFIG. 17D; and a corner shaping374inFIG. 17E.

The fourth flux density redistribution method is referred to as magnetic flux density redirection, whereby the magnetic core's flux density, BMx(r), is redirected from a radial direction, r, to a circular direction, θ, around the center of the magnetic core. Flux density redirection converts a spiral winding radial flux density direction, r, to a toroidal winding circumferential flux density direction, θ. The redirection works best to reduce the circuit losses due to skin effect and load current in the winding and thereby allows the device to carry a higher current for a given size, at a safe operating temperature, and thus have a higher PD. The examples of magnetic flux density redirection are an AiC600shown inFIGS. 18A and 18B, and an AiC620shown inFIGS. 19A-19C.

Inductors and Transformers

All EM and PM devices constructed with any of the core construction categories, laminated core, tape wound core, solid block core or air/dielectric cores may improve their power density by one or more of the four aforementioned core modification techniques to redistribute their magnetic core's flux density. Inductors and transformers benefit from all four core modifications

Introduction to Magnetic Flux Redistribution

All Electro-magnetic (E-M) devices and permanent magnetic (PM) devices may have their radial maximum flux density, BMx(r), optimally redistributed in their magnetic cores. In E-M cores, the optimal redistribution of flux density increases the core's power density. In PM cores, the core's magnetization is increased by redistributing the core's radial magnetic flux density, B(r). Improving the power density in an E-M device's core corresponds directly to improving the power density in the E-M device. Similarly, in PM devices improving the magnetization of the core improves the magnetization of the device. Magnetization corresponds to the power density of the device. Thus optimally redistributing flux density, B(r), in E-M and PM cores increases the power density of all the devices using these modified cores.

Magnetic Principles of Redistributed Mag. Flux Density

Up until now a magnetic device's best maximum cross sectional magnetic flux density, BMx(r), has only been allowed to assume a simple Amperian curve between its boundaries, the effective inner diameter radius, rIDe, and the effective outer diameter radius, rODe. The Amperian curve peaks at the effective radius of the inner diameter, rIDe, to Bsat (B(rIDe)=Bsat) and hyperbolically tapers away to the effective radius of the outer diameter, rODe. These conventional Amperian curves represent the best maximum magnetic flux density distribution, BMx(r), for their respective transformers and are illustrated herein for circular toroidal transformers.FIG. 20shows a graph750having an Amperian curve751plotted on a vertical axis representing Teslas per Tesla (T/T) and a horizontal axis representing the radius of a core in inches. The Amperian curve751represents a known low profile TWC transformer with a rIDeof 1.37 inches and a rOdeof 3.91 inches.FIG. 21shows a similar graph700plotting normalized flux distribution against radius having an Amperian curve702that represents the BMx(r) for a known high profile TWC transformer operating without the benefit of a self bias current.

Magnetic flux redistribution methods work by radially dispersing the magnetic flux that develops under the peak of the magnetic core's Amperian distribution curve, BMx(r). The magnetic flux is dispersed to cross sections of the magnetic core that are under utilized so that the core's cross sectional net flux is constant and Faraday's Law is satisfied for the same operating voltage, V(f). A higher maximum operating voltage, VMx(f), is then needed to reach the core's magnetic operational limit, Bsat, at any radial point along the maximum flux density distribution curve, BMx(r), thereby increasing the device's PD.

The purpose of magnetic flux density redistribution is to reshape the Amperian flux density distribution curve, BMx(r) of a device to more fully utilize the flux density region between the Amperian curve, BMx(r), and a flat line curve, Bsat,701radially bounded between rIDeand rODe, above a zero flux density reference line704as shown inFIG. 20. For example, this region can be seen in the graph750ofFIG. 20which shows the Amperian flux density distribution curve751for a low profile toroidal transformer bounded by its rIDeof 1.37 inches on the left and rOdeof 3.91 inches on its right. Also in graph750, a curve752is plotted for a low profile, core bias current enabled, toroidal transformer150shown inFIGS. 3A and 3Bwhich supports the maximum voltage, VMx(f), and maximum load current, Ilx(f), identical to the transformer represented by the curve751. However, the core bias current in transformer150enables a volume of half that of the known transformer associated with the curve751. Since both transformers support the same power level, but the transformer150has half the volume, the transformer150has a power density twice that of the known transformer.

Bias Current Magnetics

The first method for redistributing magnetic flux density from over-utilized magnetic core areas to under utilized magnetic core areas is referred to as bias current magnetics. Bias current magnetics applies, through an appropriately modified magnetic core, a maximum bias current, IBx(f), from a voltage source, VB(f), that flows through the core appropriately phase and frequency synchronized with the device's maximum magnetizing current, IMx(f), of such a magnitude, polarity, core direction and core location, so as to usefully redistribute the magnetic flux density within the core. The maximum bias current, IBx(f), generates a magnetic flux density within the core that counters the flux density generated by the maximum magnetizing current, IMx(f), in the over utilized area of the core, and aids the flux density generated by the maximum magnetizing current, IMx(f), in the under utilized area of the core.

The core's main magnetic force field, (ATM(f)) in a magnetic core is generated by the magnetizing current, IM(f), flowing in the winding window at less than the radius of the effective inner diameter, rIDe, and extends to the core's radius of the effective outer diameter, rODe. When the magnetizing current, IMx(f), is maximum, its magnetic force field, ATMx(f) is at a maximum. The bias current, IB(f), is injected through the core at radius (r1) where the core's magnetic permeability, μ, is anisotropic—maximum in the circumferential, θ, direction, but minimum in the radial direction. (i.e. μRθ>>μRr). If the permeability in the radial direction, μRr, was equal to the permeability in the circumferential direction, μRθ, then most of the magnetic flux induced by the bias current, IB(f), would encircle the bias current and would not usefully interfere with the magnetic flux caused by the magnetizing current, IM(f).

The injection of maximum bias current, IBx(f), at radial position, r1, which is greater than rIDebut less than rODe, generates a magnetic force field (AT1(f)) at the radius, r1, which extends to the radius of the effective outer diameter, rODe. Because the maximum bias current, IBx(f), is flowing in the same direction with the same phase as the maximum magnetizing current, IMx(f), the magnetic core material between radius r1and rODecontains the magnetic force field (AT2(f)) which is the summation of the maximum magnetic force field AT1(f), caused by the maximum bias current, IBx(f), and the maximum magnetic force field (ATMx(f)), caused by the maximum magnetizing current, IMx(f).

The maximum magnetic force field, AT1(f), caused by the maximum bias current, IBx(f), increases the magnetic force field, AT2(f), between r1and rODe, and, by transformer action to satisfy Faraday's Law for a constant magnetizing voltage, V(f), decreases the magnetic force field, ATMx(f), between rIDeand rODeto ATBMx(f). The magnetic force field AT2(f) readjusts to the summation of ATBMx(f) and AT1(f). The maximum bias current, IBx(f), is chosen so that the resulting maximum flux density distribution curve, BBMx(r), is Bsat at the radial positions rIDeand r1. (BBMx(rIDe)=BBMx(r1)=Bsat).

Ideally, the maximum bias current, IBMx(f), interfering constructively with the magnetizing current, IMx(f), generates a sawtooth shaped, optimally flat, maximum, flux density distribution curve, BBMx(r) which is the summation of Amperian curves started, respectively, at radial positions rIDeand r1. As succeeding bias currents are generated through the core's interior at higher radial positions, they will likewise affect the overall magnetic force field distribution, ATMx, initiated by the magnetizing current, IMx(f).

The benefit to operating an electromagnetic device with a bias current, IB(f), injected into its core interior is that a second maximum operating voltage, VMx2(f), higher than the original maximum operating voltage, VMx(f), may be sustained by the device before any part of the core's cross sectional magnetic flux density distribution curve, BBMx(r) reaches Bsat. This may be readily be seen by examining the sawtooth, maximum, flux density distribution curves, BBMx(r), generated by maximum bias current, IBx(f). The BBMx(r) curves are shown for various devices. A BBMx(r) curve713for a low profile LaC device290inFIGS. 1A-1Bis shown in a graph710ofFIG. 22. A BBMx(r) curve738for a high profile LaC device310inFIGS. 2A-2Bis shown in a graph735inFIG. 23. A BBMx(r) curve752for a low profile TWC device150shown inFIGS. 3A-3Bis shown in the graph750inFIG. 20. A BBMx(r) curve703for a high profile TWC device100inFIGS. 4A-4Cis shown in the graph700inFIG. 21. Each of the maximum, flux density distribution curves, BBMx(r), occupies more of the flux density region between maximum flux density distribution, BMx(r) and the Bsat curve701, than their respective devices without bias current would allow. The curves, BMx(r), for comparable devices without bias current, are the dashed curves shown together with the BBMx(r) curves inFIGS. 20-23. Assuming that the maximum load current, ILx(f), at VMx2(f), is the same as before the injection of IB(f), thereby requiring no change in the winding window opening and, consequently, no change in the device's volume then the electro magnetic device is operating at a higher power level for the same volume of magnetizing material, thus, increasing the power density.

Alternatively the volume of the electro-magnetic device with a maximum bias current, IBx(f), injected into its core may be reduced, whereby VMx2(f)=VMx(f) and the maximum load current, ILx(f), and winding window opening stays the same. This is done by reducing the rODefor the circular toroid or the rODefor the E-I core's toroidal equivalence while keeping the winding window opening, rIDe, the same size. The PD improvement demonstrated in the graph750ofFIG. 20, by the transformer150over the known transformer defined by the curve751demonstrates how the cross section of a device may have its rODereduced and still support the same maximum voltage, VMx(f). (VMx(f)=VMx2(f)) Various device core modifications may utilize any combinations of these two PD improvement schemes.

Corner bias currents, ICB(f), redistribute magnetic flux density, B(r), locally, in magnetically compressed areas such as sharp bends or corners. Magnetic devices constructed with LaC or E-I SBC have the sharpest corners and are candidates for corner bias current remediation of their excessive, maximum, corner flux density (BCMx(r)). The corner maximum flux density distribution, BCMx(r) of these devices tend to exceed Bsat in the radial region between the physical interior corner radius (ri) of 0.032 shown inFIG. 33and the effective radius of corner diameter, rCDe, of 0.86 inches. At radial positions greater than rCDe, up to a radial of 1.5 inches the corner magnetic flux density distribution is a simple Amperian distribution. Maximum corner bias current, ICBx(f), generates a corner magnetic flux density (BCBx(r)) that interferes with the excessive corner magnetic flux density, BCMx(r), pile-up caused by the maximum magnetizing current, IMx(f), at magnetic areas with low radius of curvature. Corner magnetic flux distribution (BBCMx(r)) requires appropriate interference between the corner maximum magnetic flux density, BCMx(r), generated by magnetizing current, IMx(f), and the corner compensating maximum magnetic flux density, BCBx(r), generated by maximum corner bias current, ICBx(f).

Maximum corner bias current, ICBx(f), generates corner maximum magnetic flux density, BCBx(r), that interferes with the corner magnetic flux density, BCMx(r), generated by the magnetizing current, IMx(f), when the magnetic material around the corner bias current passage way is isotropic such that the permeability, μθB, in the circumferential direction, θB, around the corner bias current, ICB(f), is the same as the permeability, μrB, in the radial direction, rB, around the bias current, ICB(f). The permeability, μzB, in the z direction, zB, around the bias current is arbitrary.

Both types of bias currents, longitudinal and corner, are derived from either a fixed or variable bias voltage source, VB(f), synchronized and proportional to the magnetizing voltage, V(f). Alternatively, either a fixed or variable bias current source, IB(f), synchronized and proportional to the magnetizing current, IM(f), may be used.

Anisotropic permeability is intrinsic to the tape wound toroidal core, TWC. The radially distributed tape wound layers are magnetically isolated from each other by the wound air gap and insulative layer coating between adjacent layers. In some instances, extra gapping or insulation between adjacent winding layers may be required. Thus, for the tape wound toroidal core: μRθ>>μRr. Flux density distribution in a toroidal core in the “z” direction is negligible; consequently, the requirements for permeability in the vertical or “z” direction (μRz) are arbitrary.

Laminated cores which may be used in square core transformers, motors, generators, relays, and solenoids, achieve anisotropic permeability in the laminations by magnetically sectioning the lamination in the direction parallel to the magnetic flux path, le. Likewise, solid block cores (SBC) used in square core transformers, inductors, motor and generator rotors, relays, and solenoids achieve anisotropic permeability in its SBC by magnetically sectioning the SBC in the direction parallel to the magnetic flux path, le. The sectioning is known as longitudinal sectioning and fulfills the requirement that the permeability in the circumferential direction (parallel to the flux lines), μRθ, be much greater than the permeability in the radial direction (lateral or normal to the flux lines), μRr. (μRθ>>μRr) The sectioning includes notches to accommodate the passage of bias current wiring.

Magnetic Gapping

One method to magnetically isolate longitudinal sections is by applying mechanical slits throughout the lamination's magnetic flux path length, le. Each longitudinal slit forms a thin air gap (lg) between adjacent magnetic sections, thereby, magnetically isolating laminated core sections in the radial direction while maintaining magnetic continuity throughout the magnetic path, le, in the longitudinal or θ direction. The air gap, lg, causes the radial flux lines formed by the bias current to experience a significantly reduced effective permeability (μeff) between the longitudinally slit sections. The effective permeability, μeff, is given by:
μeff=(μR*lep)/(lep+lg*μR),
where the magnetic path length, lep, is the shortest magnetic path length traversed by the flux lines surrounding the bias current—the periphery of the bias current's passage. The air gap between the core sections also provides the optimum radial position for passing the bias current conductors through the core's interior.

The effectiveness of a slit on magnetic permeability may be shown by the following example. For a magnetic lamination with a relative permeability, μR, of 15,000, and a longitudinal slit with a spacing of 0.5 mils, the dimensions of the bias current passage are 10 mils by 300 mils which produces the shortest magnetic path length, lep, around the passage perimeter of 620 mils. The effective permeability, μeff, across the slit, is 1145. Since μRθ=15,000, then for the longitudinally slit laminated square core: μRθ>>μRr≈μRz, which is desirable for implementing bias current magnetics anywhere along the slit's path length.

Mechanical Interlacing Flux Redistribution

Magnetizing flux, φM(f), is radially distributed equally in the core's longitudinally slit cross sections, when each section is mechanically interlaced so that each section's magnetic path length, le, is equal. The power density is optimally increased when the radial cross sectional areas, AC, of each longitudinally slit core section are also equal. The mechanically interlaced magnetic core is a passive flux redistribution scheme that does not require bias currents to redistribute magnetic flux density, but relies on the mechanical interlacing of equally long magnetic sections to redistribute magnetic flux density.

Displacement Current Parameters

A bias current variation that accomplishes magnetic flux density redistribution in a magnetic core is referred to as displacement current magnetics which uses capacitance distributed along the length, lt, of the magnetic core and in series with the operating magnetizing voltage, VM(fo), to develop displacement currents (ID(fo)) through the core that redistribute the core's magnetic flux density so as to increase the device's PD at optimum operating frequency, fo. The magnetic principles by which displacement current optimally redistributes magnetic flux density, BMx(r), are similar to the bias current magnetics previously described in with respect to bias current magnetics.

The distributed capacitance, Cn, electrically interacts with corresponding distributed sections of inductance (Ln) along the core's line length, lt, thereby creating a transmission line.FIG. 24shows a circuit920which is an electrical schematic representing the discrete circuit implementation of a transmission line. The discrete circuit consists of “n” sections of inductor and capacitor combinations that discretely and electrically represent a transmission line. The circuit920has a voltage source930that drives a current929into an input inductor921. The circuit920includes the first input inductor921and a capacitor section924, a second inductor922and a second capacitor section925, through an nth inductor923and an nth capacitor section926. If the inductor sections such as inductors921through923, and the capacitor sections, such as capacitors924through926, are equal along a length931of the transmission line, then the transmission line has a characteristic impedance (Zo) constant throughout a length931and a constant electromagnetic velocity of propagation (vp) along the length931. In terms of the discrete circuit parameters, the characteristic impedance, Zo, and the velocity of propagation, vp, are given by: zo=√{square root over (Ln1/Cn1)} and vp=1/√{square root over (Ln1*Cn1)}. Considering that the transmission line has the length931, then its end to end time delay, TD, is given by: TD=lt/Vp. When the transmission line is operated in its quarter wavelength frequency mode, f0.25λP, then: f0.25λ=1/4TD. Thus, displacement current magnetics has the dual benefit of creating a transmission line while improving the power density of its magnetic core.

For uniformly constructed circular toroids with uniformly inserted dielectric material both Cn and Ln are functions of the radial position, r, along the toroid's length, lt. That is: Cn(r) ∝ r, and Ln(r) ∝ 1/r. The solution to a transmission line constructed with these radially varying parameters is a Bessel function that shows mathematically that the circular toroidal based transmission line can behave like a step up or step down transformer when its load, ZL, matches the circular toroidal transmission line's characteristic output impedance, Zo(r).

The circular toroidal based transmission line behaves like a step up or step down transformer for either transient voltages, V(t), or steady state voltages, V(fo). The operational frequency (fo) is the optimal frequency within the range of the device's operational quarter wavelength frequency, f0.25λ.

Displacement Current Magnetics

Displacement current magnetics, hereafter also referred to as capacitance enhanced magnetics, include two enhancements within a magnetic core to increase the steady state power density of a device at its optimum operating frequency, fo. First, capacitance enhanced magnetics reduce the required maximum magnetization current, IMx(fo), for the same maximum operating voltage, VMx(fo). Second, the displacement currents, ID(fo) are used to favorably redistribute the device's magnetic flux density distribution curve, BMx(r), to increase the device's PD. Capacitance enhanced magnetics provides a device increased power density at an optimum operating frequency (fo). Displacement current magnetics also uses distributed capacitance to form a transmission line. The magnetic core of a displacement current magnetics device develops magnetic forces faster for a maximum transient voltage, VMx(t) then a non-distributed capacitance device.

FIG. 25is a graph780that shows various flux density distribution curves which comparatively demonstrate the power density improvements obtainable from displacement current magnetics. An Amperian curve782is the maximum magnetic flux density distribution of any known circular toroidal magnetic core with an inner diameter radius, rIDeof 0.5 inches and an outer diameter radius, rODeof 1.5 inches that provides the magnetic construction base for capacitor enhanced magnetic devices such as the external internal capacitance device450inFIGS. 9A and 9B; the external capacitance device500inFIGS. 10A and 10B; the external capacitance device530inFIGS. 11A and 11B; the external capacitance device570inFIGS. 12A and 12B; the internal capacitance device600inFIGS. 18A and 18B; and the internal capacitance device620inFIGS. 19A,19B, and19C. The curve782is the maximum Amperian flux density distribution, BBMx(r), of any toroid defined by the geometry of rIDeof 0.5 inches, because a flux density peak781, at rIDeof 0.5 inches equals the Bsat curve701. When distributed capacitance is appropriately added to the base core and the device is operated at optimum frequency, fo, then the device exhibits a nearly flat line magnetic flux density distribution curve, shown as a curve783. Comparing the curves782for a known toroid core and the curve783for the distributed capacitance core shows that the total flux, φT, in the core, represented by the area under the curves782and783, remains the same for the same maximum operating voltage, VMx(fo), applied to the device in either the absence or presence of the distributed capacitance. A curve784is the result of optimizing the power density of the device by reducing the magnetic core's strip width, wFe, such as the strip width466in the external capacitance device450inFIGS. 9A and 9B. Other examples of optimally minimized magnetic strip widths, wFe, include a strip width, wFe,506in the internal capacitance device500inFIGS. 10A and 10B; a strip width, wFe,543in the external capacitance device530inFIGS. 11A and 11B; and the strip width, wFe,579in the external capacitance device570inFIGS. 12A and 12B.

Displacement current magnetics may be applied to square core shapes as well as toroidal shapes. Both toroidal and square magnetic core shapes with appropriately distributed capacitance and inductance have unique end to end transfer functions, whereby the voltage initiated at one end of the device can be made to either increase or decrease at the other end of the device. For the case of the uniformly wound and distributed circular toroidal inductance and capacitance, a voltage impressed at the radius of inner diameter appears at the device's radius of outer diameter reduced by the device's geometry, similar to a non-isolated step down transformer. Correspondingly the current increases at the outer radius so that the electrical power at the outer radius equals the electrical power applied at the inner radius. Conversely a voltage impressed at the radius of outer diameter appears at the device's radius of inner diameter increased by the device's geometry similar to a non-isolated step up transformer. Correspondingly the current decreases at the inner radius so that the electrical power at the inner radius equals the electrical power applied at the outer radius.

A transmission line with end to end time length, TD, driven by a step function transient voltage, V(t), contains the induced transient electrical energy equally in the line's electric and magnetic fields. In the transient excitation state the line's electric field energy is contained within the line's capacitance and is equal to the magnetic field energy contained in the line's magnetic core. If the volume of the capacitance is small compared to the volume of the magnetics, which is usually the case, then for all practical purposes the transient energy power density in the device has doubled compared to the same size core without the benefit of added capacitance. Consequently, magnetic forces develop faster for an applied step function voltage, V(t), during transient time interval, TD, in an inductor modified with distributed capacitance compared to an unmodified inductor of the same inductance with the same applied step function voltage, V(t), during the same transient time interval, TD.

The transient electromechanical benefit exhibited by a transmission line applies to all transmission lines regardless of the transmission line's power level, time length, TD, size, or whether the transmission line's magnetic shape is straight or circular toroidal. The benefit arises because the distributed capacitance usefully increases and redistributes the magnetic flux density within time period, TD. A capacitance enhanced rail gun967shown inFIG. 26is a practical implementation of distributed capacitance that increases the Lorentz force propelling a projectile964down a set of muzzle rails961. Those of ordinary skill in the art will recognize that distributed capacitance in the magnetic cores of electric motors, solenoids, relays, or other like designed electromechanical devices, enable these electromechanical devices to accelerate their mechanisms faster during transition time, TD, while benefiting from increased power density in the steady state when operated at the device's optimum frequency, fo.

Redirected Magnetic Flux Density A core modification method to improve a device's PD redirects the magnetic flux density. The magnetic flux density is redirected by changing the device's winding orientation. For example, a spiral wound air core940shown inFIGS. 7A and 7Bincreases its PD by being rewound as a radial wound toroidal AiC device. Similarly, planar core transformers and inductors, such as the device941inFIG. 6, may increase power density by being reconfigured as a toroidal device with radial windings instead. Consequently, the magnetic flux density direction is redirected from radial, r, to circumferential, θ, and simplifies the magnetics'geometry by using toroidal disks instead of planar pot cores. The radial conductors on the disk are wide and short, thereby lowering the resistive losses in the winding. The result is a more efficient packaging of the electromagnetic device and consequently better electrical performance. Redirected magnetic flux density is most useful to improve the PD of planar magnetics and very high frequency air cores. The internal capacitance enhanced device600inFIGS. 18A and 18Band the internal capacitance enhanced device620inFIGS. 19A,19B and19C are the an example construction for high frequency redirected magnetic flux density. Lower frequency of operation capacitance enhanced devices such as the device450inFIGS. 9A and 9B; the device500inFIGS. 10A and 10B; the device530inFIGS. 11A and 11B; and the device570inFIGS. 12A and 12B; are alternate redirected magnetic flux density constructions.
Redistributed Magnetic Devices

A magnetic device's Amperian flux density shape may be redistributed so as to increase the power density, without effecting the core's overall size and shape, by core bias current, core interlacing, and core corner smoothing. Flux density redirection may also be used but requires changing the shape of the core. Sectioning the magnetic core longitudinally along its magnetic path length, le, so that each sub-divided cross section is uniformly wide and magnetically isolated from each other, facilitates either bias current, interlacing, or smoothing to favorably redistribute the core's magnetic flux density to improve power density.

All magnetic devices are constructed with a magnetic core—more specifically an electro-magnetic(E-M) or permanent magnet (PM) core, or combinations thereof. As explained above, the core's construction may be one of four core construction categories or combinations including a Tape Wound core (TWC); a Laminated core (LaC); a solid block core (SBC) or an air or dielectric core (AiC). All four magnetic core constructions may be modified to improve power density by optimally redistributing radial magnetic flux density (B(r)) in the core.

The following transformer or inductor or magnetic cores for transformer and inductor devices illustrate the ability to redistribute magnetic flux density within their magnetic cores, regardless of magnetic core construction, to improve the power density of the devices. Those of ordinary skill in the art will understand that the core modifications herein may be applied to other E-M or PM devices such as electric motors, electric generators, solenoids, relays, delay lines, and rail guns.

Magnetic flux density redistribution is first described for core bias currents in a TWC. The magnetic flux density redistribution will then be described using core bias currents in the LaC along the straight sections and corner sections. A description follows of passive magnetic flux density redistribution in the mechanically interlaced magnetic core. Next capacitance is distributed within the core in a series of different distribution constructions so that the capacitor's displacement currents create a frequency selective core bias current that favorably redistributes magnetic flux density. Finally, capacitance enhanced magnetics is discussed to favorably redirect magnetic flux density in magnetic cores.

Tape Wound Core (TWC)

The magnetic tape wound core (TWC) was developed to overcome the permeability loss due to the magnetic gap in a square core. An example circular magnetic tape wound core is shown as a toroidal transformer150inFIGS. 3A-3B. The TWC is typically constructed by a continuously winding fixed width, wFe, magnetic ferrous foil109having a thickness typically from 0.6 mils to 14 mils, around a circular inner hub thereby forming a circular toroidal core. A square toroidal core is constructed by winding the foil around a square hub. The circular inner hub forms a toroid winding window108with an effective inner diameter radius, rIDe, 113 inches which is the open inner diameter area of the toroidal core after the winding hub is removed. The magnetic foil109is continuously tape wound around the inner hub until the winding reaches the prescribed effective outer diameter radius, rODe. The winding window108is sized to pass the primary windings102and secondary windings103. The TWC transformers have a primary input voltage104, which is electrically connected to the primary windings102and a secondary output voltage105which is electrically developed at the secondary windings103. “Tape winding” strains the magnetic foil and, consequently, causes the foil's magnetic permeability to decrease by as much as 50% or more. The permeability can be restored by heat treating (annealing) the tape wound core.

The magnetic foil109is conductive and is coated with a very thin insulative material101that inhibits layer to layer eddy currents in the tape wound core. The thin insulative material101along with the layer to layer air gap magnetically isolates adjacent concentric magnetic foil layers thereby intrinsically contributing to a longitudinal magnetic isolation which is formed by an interface layer spacing110required for magnetic flux redistribution caused by core bias currents. The longitudinal magnetic isolation is the interface layer spacing between adjacent magnetic layers. The interface layer spacing110is the summation of the thickness of the insulative coating101and the effective air gap between the adjacent magnetic layers.

After the TWC is annealed, a thin insulator layer111is applied to cover the surface of the core to prevent the core's primary winding102and the secondary winding,103from abrading and electrically shorting to the conductive core. The primary and secondary windings102and103are usually applied by a “shuttle” winding machine. After the wires of the primary and secondary windings102and103, are applied, an optional thin insulation layer similar to insulator layer111may be wrapped around all the finished magnet wire winding.

The TWC has a closed shape that initially allowed only hand winding of the magnetic coils. Later, machines were designed to apply the windings. Special coil winding machines, called shuttle winders, were designed and built to automatically put high current magnetic wire windings on the closed toroidal cores. Without the need for lateral sectioning, as required by the lamination core, LaC, this core construction realizes the magnetic material's full magnetic permeability (μ). The toroidal TWC core is used as an alternate to square core construction of transformers and inductors.

A superior shape for conventionally designed TWC magnetics which maximally utilizes core material, is the high profile shape, where the magnetic foil's width, wFe, is set at a practical maximum to accommodate the coil winding machines. The high profile TWC shape utilizes more of the magnetic material's core for the same device power rating, relative to a low profile conventionally designed TWC of the same device power rating. Thus, an example high profile shaped TWC transformer100shown inFIGS. 4A,4B and4C is a magnetically efficient toroidal shape.

The high profile shaped TWC transformer100inFIGS. 4A,4B and4C, using the techniques described herein allows easier packaging in low profile environments such as multiple closely stacked printed circuit boards or laptop computers while maintaining the efficient magnetic utilization of the high profile TWC in the low profile shape.

Toroid, Tape Wound Core (TWC) with Core Bias Current

Tape wound core magnetics may be used to construct transformers, inductors and special solenoids and relays. These cores may be continuously wound and either left uncut, or laterally cut across the core so as to decrease the core's effective magnetic permeability, μeff, and thereby increase the maximum magnetizing current, IMx(f), required for core saturation. For either core cut construction, core bias currents may be used to favorably redistribute its magnetic flux density.

The features and benefits of core bias currents may be applied for the high profile and low profile TWC shapes. Known conventional TWCs use the high profile shape because the Amperian magnetic flux density distribution becomes flatter as the height of the profile increases. But as the conventional Amperian magnetic flux density becomes flatter with increasing core height or slit width, the core becomes more difficult to construct and undesirable to package with low profile components. In contrast, the low profile transformer has the best packaging silhouette but the most inefficient use of magnetic material. Redistributed magnetic flux density allows use of high profile power density for the low profile TWC constructed toroidal transformers.

Toroid, High Profile Tape Wound Core with Self Bias Current

The transformer100inFIGS. 4A,4B and4C includes a high profile, modified, TWC106. The TWC106includes a core self bias current that allows the core106to operate at the maximum flux density distribution as shown by the BBMx(r) curve703inFIG. 21. Referring toFIG. 4B, the TWC106is defined by a height, wFean effective radius of inner diameter, rIDe,113and an effective radius of outer diameter, rODe,114. The curve703supports about 25% more voltage, VMx(f), at the same maximum load current, ILx(f), compared to the core106operating without core bias current. The maximum flux density, BMx(f), that the core106can operate at without core bias current is shown by the curve702inFIG. 21. The power density improvement of the core106in the transformer100with core bias current over the same transformer operating without bias current is the percent areal difference between the curves703and702inFIG. 21between rIDe,113at 1.37 inches and the rOde114at 2.36 inches.

A self bias current wiring circuit121carries a self bias current122through the core106by three passages130,131and132at equally spaced radii118,119and120. The radii118,119and120are each located at the nearest convenient TWC layer interface110between the rIDe113and the rODe114. The passages130,131and132each accommodate two bias current wires of the bias current wiring121. The three bias current passages130,131and132divide the cross section width of the core106into four equal magnetic cross sections123,124,125, and126. The self bias wiring scheme is in the right half of the core106as shown in cross-section inFIG. 4B.

FIG. 4Cshows a bottom view of the self bias wiring scheme121used in the transformer100. The self bias current wiring121is wound such that the voltage induced by the time changing magnetic flux in the core106into the self bias current wiring121around the under utilized sections of core sections125and126is equal to the voltage induced into the self bias current wiring121around over utilized core sections123and124, when the flux density is equally distributed. The voltages oppose each other but null when the voltages generate a self bias current122. The self bias current122develops to support the redistributed magnetic flux density when the primary voltage104is applied to the primary wiring102. The primary voltage104is derived from a very low impedance voltage source.

The self bias current wiring121winds through the four equally wide magnetic cross sections123,124,125and126. Starting at the interior radius rIDe113, the winding121goes up and around the section123, through the passage130, and returns to the interior, winding window108at the radius rIDe113, then continues up through the interior radius113, and around the sections123and124, down through the passage131, returning again to the interior radius113. The wiring121continues to proceed up through the interior radius113and around the sections123,124, and125, down through the passage132and returns to the exterior radius, rODe,114. The wiring121continues up through the exterior radius114, around the section126, then down through the passage132, after which it returns to the exterior radius114. The winding121proceeds up the exterior radius114, around the sections125and126, down through the passage131and returns to the exterior radius114. The winding121continues to proceed up the exterior radius114around the sections124,125and126, down through the passage130where it connects to the start of the bias current winding121returning to the interior radius, rIDe113, thereby completing the winding circuit121for the self bias current122.

The maximum core bias current flux density distribution, BBMx(r) of the transformer100is shown by the curve703inFIG. 21. The radii118,119and120, are equally spaced between rIDe113and the rODe114, so that the curve703has a peak flux density points705at the radius113; a peak flux density point706at the radius118; a peak flux density point707at the radius119; and a peak flux density point708at the radius120. The peak flux density points705-708are all equal to Bsat, and touch the horizontal dashed line701, representing Bsat. The peak flux density points705,706,707and708are shown as flux vector arrows107inFIG. 4A.

Magnetic permeability, μ, in practical magnetic material is very non-linear, but maximizes when the magnetic material's maximum operating magnetic flux density distribution, BMM(r) is at or near the maximum value, BMx(r). Maximum core bias current flux density distribution, BBMx(r), operates a core's maximum flux density distribution at or near the peak value of magnetic permeability, μ. The bias current flux density distribution, BBMx(r) shown by the curve703inFIG. 21for the core106is an example of optimally using a magnetic core at its peak magnetic permeability, μ.

The maximum flux density distribution is shown by the flux vector arrows107in the magnetic sections123,124,125and126inFIG. 4A. InFIG. 4B, the flux vectors are all of equal magnitude, Bsat, and are identified as a set of vector tails128and a set of vector points127in the magnetic sections123,124,125and126. The maximum operational magnetic flux distribution, BMx(f,r), is generated by the maximum magnetizing current116flowing to the right in the primary wiring102. InFIG. 4Athe magnetic flux vectors are shown, by the “right hand rule” as directed clockwise of equal width and length, symbolizing equal maximum magnetic flux density in each magnetic section throughout the core. By the “right hand” rule, the flux vectors128are directed into the page on the left side of the center line115and the flux vectors127are directed out of the page on the right side of the center line115. InFIG. 4B, the peak magnitude of the magnetic flux density in each magnetic section123-126is Bsat and is coarsely indicated by the cross section of three flux lines, flux vector points127and the flux vector tails128in the magnetic sections123,124,125and126.

Toroid, Low Profile Tape Wound Core with Tapped Bias Current

The low profile toroidal transformer150shown inFIGS. 3A and 3Bdemonstrates improved PD, about double over a known toroidal transformer, by utilizing a tapped bias current161through a tapped bias current wiring159through a core152. A transformer core that supports the same maximum voltage, VMx(f), and maximum load current, ILx(f), at the same profile height as a height WFeof the transformer150requires its rIDeto be the same as the rIDe113of the transformer150but the core rODeof the known transformer would have to be much bigger than the rODe154of the transformer150.

The graph750inFIG. 20comparatively shows the flux density distribution curve752for the toroid transformer150inFIGS. 3A-3Bwith three core passages using the bias current161, against the flux density distribution curve751for a known toroidal transformer with the same core height as the core height wFe, of the transformer150without any bias current, but requires a larger rOde, to support the same VMx(f). The area under the curve752is equal to the area under the curve751, which, by Faraday's Law, enables both transformers to support the same VMx(f) for the same core height, wFe.

A tapped bias current wiring159is passed through a TWC152used by the transformer150. The tapped bias current wiring159starts at an appropriate tap151and continues along the primary winding102, which provides a bias voltage160(VB(f)) that drives the tapped bias current161in the bias current wiring159. The current wiring is threaded through a passage163, set at a radius156; a passage164set at a radius157; and a passage165, set at a radius158. The three bias current passages163,164and165are located, respectively, at radii156,157and158, and divide the cross section width of the core152into four equal magnetic cross sections123,124,125, and126. The bias current wiring159returns to the low side of the primary voltage104.

The maximum flux density distribution, BBMx(r), is shown by the curve752inFIG. 20. The radii156,157and158are set equally spaced between the rIDe113and the rODe154so that a sawtooth peak flux density point753at the radius113; a flux density point754at the radius156; a flux density point755at the radius157; and a flux density point756at the radius158are all equal to Bsat, and touch the horizontal dashed line701, representing Bsat.

The curve752shows the bias current flux density distribution, BBMx(r) inFIG. 20for the core152of the transformer150. The flux density distribution is an example of optimally using a magnetic core at its peak magnetic permeability, μ.

The pictorial representation of the maximum flux density distribution is shown in the low profile modified TWC152inFIG. 3Aby the flux vector arrows107in the magnetic sections123,124,125and126. InFIG. 3B, the flux vectors are all of equal magnitude, Bsat, and are identified as the vector tails128and the vector points127in the magnetic sections123,124,125and126. The maximum operational magnetic flux distribution, BMx(f,r) is generated by the maximum magnetizing current116flowing to the right in the primary wiring102. InFIG. 3A, the magnetic flux vectors are shown by the “right hand rule”, as directed clockwise of equal width and length, symbolizing equal maximum magnetic flux density in each magnetic section throughout the core. By the “right hand” rule, the flux vectors128are directed into the page on the left side of the center line115and the flux vectors127are directed out of the page on the right side of the center line115. InFIG. 3B, the peak magnitude of the magnetic flux density in each magnetic section is Bsat and is coarsely indicated by the cross section of the two flux lines in the magnetic sections123,124,125and126.

The preceding examples illustrate the PD improvements in high profile and low profile TWCs when their cores are provided with core bias currents—either self bias or tapped bias currents. Specifically, the low profile, tapped bias current TWC transformer150, safely supports the same voltage and current, (120 VAC at 4 Amps, 60 Hz in this example) as a high profile TWC transformer without bias current. The transformer150without core bias current would only safely support 85 VAC at 4 Amps, 60 Hz in this example.

Core bias currents in low profile transformer cores more fully utilize the device's magnetics and thereby require less magnetic material to construct the core. The lower the TWC profile, the higher the percentage of obtainable core PD improvement, which illustrates how core bias currents may enhance the efficient design of low profile magnetic parts. Consequently, core bias currents allow a package designer to readily design low profile parts without bulk and weight considerations required by a conventional low profile design.

The more passages that a tape wound core's cross section can accommodate, the more power density improvement that the design can realize. However, additional passages after three or four passages result in percentage improvements of 3% or less per added passage, depending on core geometry. The passages163,164and165are formed by the insertion of spacer pins129during the tape winding process. The thickness of the spacer pins129and thus the passages163,164and165allows the bias current magnet wire159to easily, but snugly, pass through the core152. The cross section of the bias current wire159may be of a different shape such as round, square, or thin ribbon, as required. The passages for tapped bias magnetics and self bias magnetics may be used interchangeably with the same core modifications as long as the passage widths accommodate the worst case bias current wiring width requirements.

An alternate tapped bias current wiring design to the tapped bias current wiring shown in transformer150inFIGS. 3A and 3Bis shown in a cross-sectional view of a transformer140inFIG. 27. The alternate wiring uses the conductive tape winding core material109which forms as the passages163,164, and165, extended at the radial points156,157and158to accommodate a set of top electrical contacts142and a set of bottom electrical contacts141that pass the bias current161through the core152. The bias current wiring159is attached to the electrical contacts142and141as shown inFIG. 27. Other than the extension of the conductive foil at the radial points156,157and158, the core152of transformer140is the same size and material as the core152of the transformer150inFIGS. 3A-3B. Similar to the transformer150, the radial points156,157and158divide the cross section of the TWC152into four sections123,124,125and126. The flux density distribution vectors128and127inFIG. 27are distributed across the core152the same as flux vectors128and127inFIG. 3B. The radial spacing in the core152of the transformer140is the same as that used for the bias current passages163,164and165in the transformer core152of the transformer150inFIG. 3B.

This alternate bias current scheme shown in the transformer140takes advantage of the relative conductive geometry of the core's foil. The conductivity between the top and bottom connections142and141is much higher than the conductivity between adjacent through the core tape winding foils109because the contact resistance between adjacent layers is very high and the geometry of the resistance along the tape winding path is also very high relative to the resistance between the top and bottom connections142and141. Consequently, most of the bias current flows through the core152between the top and bottom connections142and141, vertically through the tape winding foil109rather than horizontally between adjacent tape winding foil layers109thereby maintaining the flux density redistribution effect of the tapped bias current161in the tapped bias current wiring159.

Another alternative bias current wiring design uses either insulated or uninsulated copper strips143shown in the transformer140without spacer pins, co-wound as bias current conductors inserted at the bias current passages163,164, and165located at the appropriate radii156,157and158within the TWC152. While the cross section of the toroidal core modified for core bias current is shown divided into equal sections for best power distribution inFIGS. 3A and 3B, different radial distributions of the core's bias current passages may be considered. Besides being used for optimizing power density distribution, the radial spacing could be considered for some other core characteristic such as “soft magnetic saturation,” whereby the core eases into magnetic saturation.

Ultra Low Profile Toroidal Inductor with Self Bias Current

An ultra low profile inductor170is shown inFIGS. 28A and 28Bis constructed with a very thin core height, wFe,176but has a required cross sectional area, AC, with a very large rODerelative to the rIDe. The core height176is a thin lamination layer, LaC, which may be inlaid in printed circuit boards or in a device's molded housing. The ultra low profile inductor170may be used for toroidal transformer or inductor cores as well as low profile square core transformers and unique motor, generator, relay or solenoid constructions.

The conventional ultra low profile inductor has a magnetic core that consists of either a single thin magnetic foil, LaC, or a thin deposition of magnetic material such as Manganese Zinc (MnZn) and Nickel Zinc (NiZn) ferrite on a substrate. In general, the magnetic material in conventional electromagnetic cores is not fully utilized. As the radius of the outer diameter, rODe, increases with respect to the radius of the inner diameter, rIDe, the under-utilization of the magnetic core increases. Consequently, conventional low profile designs, and in particular conventional ultra low profile designs, have been avoided. Bias current magnetics improves the magnetic utilization of the magnetic core increasing the PD by a factor of two or better over a conventional ultra low profile transformer core design.

The ultra-low profile toroidal inductor170uses self bias current magnetics to optimize the magnetic flux distribution in the thin magnetic foil core173. The toroidal inductor170includes an inductor winding172and171and a self bias current winding182and183.FIG. 28Ashows the top view of the inductor winding172as a solid line and the bottom view of the winding171as a dashed hidden line.FIG. 28Aalso shows the top view of the self bias current winding182as a solid line and the bottom view of the self bias current winding183as a dashed hidden line. The core173is radially sectioned into five equally wide concentric magnetic foil rings109. Each ring109is identified from the inner radius rIDe113outward as foil rings123,124,125,126and186, located between the inner radius and the outer radius, rODe177. The foil rings123,124,125,126and186are physically separated and magnetically isolated from each other, by four interface gaps175, at radial points178,179,180and181so that the magnetic permeability, μ, spatial components can fulfill the bias current requirement μRθ≈μRz>>μRr, or, μRθ>>μRz≈μRr.

The thin magnetic core173may be deposited or placed either in one layer of a multi-layer printed circuit board (PCB) or deposited in one layer of integrated circuit (IC) strata. The bottom of the thin magnetic core173is layered upon an insulation material185upon which PCB or IC interconnect conductors may be placed or deposited for the primary wiring172and171and the bias current wiring182and183. A self bias current184flows through the bias current wiring182and183on the top and bottom of the inductor170. The self bias wiring182and183is threaded around each of the concentric foil rings123,124,125,126and186each having bias current wiring passages located at radii178,179,180and181as shown in the right half ofFIG. 28B.

Ultra low profile designs using thin magnetic foil offer the packaging flexibility to fold the core in halves or quarters, or more, to reduce the required mounting surface area. The foil rings,123,124,125,126and186may have one connecting strip mechanically holding them in position without effecting the modified flux density distribution. Ultra low profile ferrite depositions may also be used on surfaces with complex shapes.

The PD improvement caused by redistributed magnetic flux density increases as the height, or magnetic strip width, wFe, decreases. The core173may be reduced to a single magnetic foil or the thinnest magnetic core deposition. Bias current magnetics then optimizes the magnetic utilization of the core.

A self bias current, IBx(f),184interacts with the magnetizing current, IMx(f),116so that five peak flux density vectors189in the cross section of the core173are of equal width and hence, equal in magnitude, Bsat, and directed by the “right hand” rule applied to the magnetizing current generated in the primary winding172and171. InFIG. 28B, the cross section of the sectional flux vectors189are, by the “right hand” rule, directed into the page, the tails, on the left side of the center line115, and then directed out of the page, the points, on the right side of center line. In each magnetic section defined by the foil rings123,124,125,126and186the peak flux density, Bsat, is pictured by the cross section of magnetic flux tails188and magnetic flux points187.

FIG. 29is a graph770of flux density distribution which includes a curve771which represents the flux density distribution of the inductor170without self bias current. A curve772shows the redistributed flux density, BBMx(r), caused by the self bias current184. The radii set equally spaced at 2.33 inches, 3.29 inches, 4.25 inches and 5.21 inches between the rIDe113at 1.37 inches and the rODe,177of 6.17 inches. The curve772is a sawtooth shape with a peak flux density point773at a radius 1.37 inches, a peak flux density point774at a radius of 2.33 inches, a peak flux density point775at a radius of 3.29 inches, a peak flux density point776at a radius of 4.25 inches and a peak flux density point777at a radius of 5.21 inches. The peak flux density points773-777are all equal to Bsat, and touch the horizontal dashed line701, representing Bsat. The area difference between the curves771and772represents the PD improvement caused by the self bias current184. In this example, the area difference between the curves771and772is 105%.

The bias current flux density distribution, BBMx(r), curve772for the core173is an example of optimally using a magnetic core at its peak magnetic permeability, μ. Consequently, a non-linear magnetic permeability, μ, may increase the practical value of the power density improvement beyond 105%.

Square Core, Lamination Core (LaC) with Core Bias Current

Lamination core (LaC) magnetics may be used to construct transformers, inductors, stators and rotors in electric motors and generators, solenoids, and relays. These cores may consist of stacked precut flat magnetic sheets usually shaped into “E” and “I” sections, for inductors and transformers, that allow easy assembly of their magnetic coils, pre-wound on bobbins, onto magnetic sections—usually the center leg of the “E.” The “E” and “I” sections come together during assembly to close the magnetic path, but leave a gap at the interface of the “E” and “I” section that decreases the core's effective magnetic permeability, μeff, and thereby increases the maximum magnetizing current, IMx(f), required for core saturation.

Square core magnetics provides two opportunities to use redistributed magnetic flux density to improve power density. The first opportunity comes from redistributing the flux density in straight sections using core bias currents, similar to the techniques employed for the toroid transformer. The second opportunity redistributes the flux density at the corners of the core. Although the flux redistribution of the straight sections usefully effects the corner distribution, the corner redistribution may be independently adjusted to increase PD without effecting the flux density distribution in the straight sections. All flux density redistribution techniques are designed to increase the power density in the devices.

The following sections first describe the lamination and the lamination modifications for magnetic flux redistribution. The modified lamination sections are stacked to form laminated cores for high profile and low profile square core transformer shapes that have their magnetic flux density profiles modified, respectively, by tapped bias current and self bias current.

Square Core Transformer Construction

The core modifications used to redistribute magnetic flux density, B(r), by core bias current, IB(f), are shown for a low profile square core inductor290inFIGS. 1A and 1Band a high profile square core inductor310inFIGS. 2A and 2B. In bothFIGS. 1A-1Band2A-2B identical parts have identical reference numbers.FIGS. 30A and 30Bshow an “E-I” lamination section250constructed with magnetic material which includes an “I” shaped part266and an “E” shaped part278. The “E” part278includes a spine322, outer legs255and a center leg261. The outer legs255have a width which is the same as a width of the “I” part266and a width of the spine269. The overall length of the “E-I” section250and the length of the legs255and261varies with the finished device requirements. The width of the center leg261is typically twice the width of the outer legs255and is equally divided by a center line253. The winding window opening276has a length and a width that is equally divided by centerlines252and254. The thickness of the lamination section250in this example can vary from 0.5 mils to 25 mils or greater. Both the “E” and “I” parts266and278are coated with an insulative layer101that inhibits heat producing eddy currents from forming in adjacent stacked lamination pieces. The coplanar stacking and closure of the “E” and “I” parts266and278form a gap265between the parts266and278.

The lamination section250includes two longitudinal cut slits271and274which radially subdivide the lamination section250into three sections279,280and281of equal width. The width of section281is twice the width of either section279or280.

The modified lamination section250may be either butt stacked or overlap stacked until the stack reaches a required magnetic height for the core302used in the low profile, redistributed flux density inductor290inFIGS. 1A and 1B, or the required magnetic height for the core328used in the high profile, redistributed flux density inductor310inFIGS. 2A and 2B. The lamination longitudinal slitting271and274as shown inFIG. 2Acompletely severs the sections which then requires an auxiliary handling system for the pieces. Alternatively, the slitting process may leave each section with one magnetic material connection with adjacent sections that keeps the lamination integrity for handling the lamination pieces. The slitting process may also leave each section with two or more magnetic material connections with adjacent sections, such as the section294in the inductor290that keeps the handling integrity of the lamination pieces. A double material keeper may also be used at other points along the slits271and274.

The inductor wire winding102is usually pre-wound by a winding machine on a nonconductive bobbin. The “E” shaped lamination sections278are inserted and stacked in the center of the bobbin to complete the assembly. A core winding window opening276is formed by the closure of the “E” shaped sections278and the “I” shaped sections266and limits the total cross sectional area, AC, of the inductor winding102that may be used in the winding window276contained by the outside width and length. After the inductor winding102is applied, a thin insulative layer111may be wrapped around all the finished magnet wire winding.

It is to be understood that one longitudinal slit may be used in place of the double slits271and274on the lamination section250described above. Similar to the criteria for the number of passages in the toroid transformer core, the more slits in the laminations, the better the power density improvement. However, a simpler one slit, two wire, bias current modification may sufficiently redistribute magnetic flux density for some applications.

Square Core, High Profile Laminated Core, LaC, with Tapped Bias Current

FIGS. 2A-2Bshow a high profile inductor310having a laminated core328having a tapped bias current wiring312carrying a tapped bias current316. The tapped bias current wiring312is a single conductor winding through a notched passage327located along a longitudinal slit274spaced from a center line252or254of dual winding windows276. A tapped bias current wiring313carries a tapped bias current317through the core328by a single conductor through a notched passage326located along the longitudinal slit271, spaced from the center lines252and254of the dual winding windows276. The slit274longitudinally bisects the outer legs255and spline322of the “E” section278as well as the “I” section266. The slit271longitudinally bisects the inner half of the outer legs255and spline322of the “E” section278and the “I” section266.

The tapped bias wiring scheme is shown in the right half ofFIG. 2B. The tapped bias current wiring312starts at an appropriately selected tap151along the primary winding102which provides a bias voltage314to drive the tapped bias current316through the tapped bias current wiring circuit312. The tapped bias current wiring314starts at a tap311along the primary winding102which provides a bias voltage315to drive the tapped bias current317through the tapped bias current wiring313.

The current flux density distribution, BBMx(r), of the core328inFIGS. 2A and 2Bis shown as a curve738of a graph735inFIG. 23. The graph735uses toroidal equivalent radial distribution for its abscissa. A first abscissa point at 0.86 inches is a toroidal equivalent of the radius of equivalent inner diameter, rIDeof the core328. A second abscissa point at 1.36 inches is a toroidal equivalent of the radius of equivalent outer diameter, rODe. Abscissa spacings between the abscissa points at 0.86 inches and at 1.36 inches correspond to the spacings323,324(0.13 inches in this example) and325(0.25 inches in this example) in the inductor310inFIG. 2A. The curve738is a sawtooth shape having a peak flux density point741at a radius of 0.86 inches; a peak flux density point742at a radius of 0.99 inches; and a peak flux density point743at a radius of 1.11 inches. The peak flux density points741-743are all equal to Bsat, and touch the horizontal dashed line701, representing Bsat, showing optimal distribution.

The curve738inFIG. 23is the summation of a curve739and a curve740. The curve739is the maximum flux density imposed in the center leg261of high profile E-I inductor310inFIGS. 2A and 2Bby the magnetizing current, IMx(f), flowing in the winding window276to the left of the center leg261. The curve740is the maximum flux density imposed in the center leg261by magnetizing current flowing in the winding window276to the right of the center leg261. Bias current flux density distribution used in the inductor310is an example of optimally using a magnetic core at its peak magnetic permeability, μ.

Square Core, Low Profile Laminated Core, with Self Bias Current

The low profile transformer290has a laminated core302having a self bias current wiring291passing a self bias current292through the core302. The self bias current wiring291includes one conductor through a notched passage327located along a longitudinal slit271and two conductors through a notched passage326located along the longitudinal slit271. The slit274is spaced from the center line252of the left winding window276and the center line254of the right winding window276. The slit274is spaced beyond the spacing for the slit271. The slit274longitudinally bisects the outer legs255and spline of the “E” section278and the “I” section266. The slit271longitudinally bisects the inner half of the outer legs255and spline322of the “E” section278and the “I” section266.

The two longitudinal slits271and274uniformly divide all the cross-sectional widths of the core302into three magnetic cross sections299,300and301. The width of magnetic section299equals the width of magnetic section300. The width of magnetic section301is twice the width of magnetic sections299or300. The self bias wiring scheme is shown in the right half of the core302shown inFIG. 1B.

The self bias current wiring291is wound such that the voltage induced by the time changing magnetic flux of the core302into the self bias current wiring291around the under utilized section of the core302(section301) is equal to the voltage induced into the self bias current wiring291around the over utilized sections of the core302(section299) when the flux density is equally distributed. The voltages oppose each other but null when the voltages generate the self bias current292. The self bias current292develops to support the redistributed magnetic flux density of the core302when the primary voltage104is applied to the primary wiring102. The primary voltage104is derived from a very low impedance voltage source.

The self bias current wiring291is wound through the three magnetic cross sections299,300and301. Starting at an interior spacing270, the winding291goes up and around the sections299and300, then down through a passage327, and returns to an exterior spacing275. The winding291then goes up and around the top of the sections301and300, then down through the passage326, back to the spacing270, up and around the section299, then down through the passage326, and back to the spacing270, connecting with the start of the self bias current winding291. The passages for tapped bias magnetics and self bias magnetics may be used interchangeably with the same core modifications as long as the passage widths accommodate the worst case bias current wiring width requirements.

FIG. 22is a graph710with a curve713representing the low profile maximum core bias current flux density distribution of the core302inFIGS. 1A-1B. The graph710includes a first abscissa point at a radius of 0.97 inches that symmetrically reappears on the right side of a second abscissa point at a radius of 2.22 inches. The first abscissa point of the core302at a radius of 0.97 inches is the toroidal equivalent of the radius of equivalent inner diameter, rIDe. The abscissa point at a radius of 2.22 inches is a toroidal equivalent radius of the equivalent outer diameter, rODe. Abscissa spacings between the abscissa points correspond to transformer spacings296,297(0.31 inches in this example) and298(0.63 inches in this example) in the core302. The curve713is a sawtooth shape having a peak flux density point716at a radius of 0.97 inches; a peak flux density point717at a radius of 1.28 inches; and a peak flux density point718at a radius of 1.59 inches. The flux density points716-718are all equal to Bsat, and touch the horizontal dashed line701, representing Bsat, and, consequently, are optimally distributed.

The curve713is the summation of curves714and715. The curve714is the maximum flux density imposed in the center leg293by the magnetizing current, IMx(f), flowing in the winding window276to the left of the center leg293. The curve715is the maximum flux density imposed in the center leg293by magnetizing current flowing in the winding window276, to the right of the center leg293. Bias current flux density distribution, shown by the curve713for the core302inFIGS. 1A and 1B, is an example of optimally using a magnetic core at its peak magnetic permeability, μ.

The pictorial representation of the maximum flux density redistribution in bias current enhanced magnetic cores is shown by flux vector arrows320in the magnetic sections279,280and281in the high profile inductor310inFIG. 2Aand the low profile inductor290inFIG. 1A. Peak flux vector tails319and vector points318represent Bsat in respective magnetic cross sections279,280and281inFIG. 2Band the magnetic cross sections299,300and301inFIG. 1B. The maximum operational magnetic flux distribution, BMx(f,r), is generated by the maximum magnetizing current116flowing to the right in the primary wiring102. InFIGS. 2A and 1A, the magnetic flux vectors are shown, by the “right hand rule” as directed vertically upward through the center legs261and293. The vectors are equal width and length, symbolizing equal maximum magnetic flux density, Bsat, in each magnetic section throughout the core. By the “right hand” rule, the flux vectors319are directed into the page in the center leg261of the high profile inductor310and the center leg293of the inductor290. The flux vectors318are directed out of the page in the outer legs255in both inductors290and310. The peak magnitude of the magnetic flux density in each magnetic section279,279and281of the core328inFIG. 2Bis Bsat and is coarsely indicated by the five flux lines in the magnetic sections279,280and281. The peak magnitude of the magnetic flux density in each magnetic section299,300and301in the low profile core302inFIG. 1Bis Bsat and is coarsely indicated by the three flux lines in the magnetic sections299,300and301.

The preceding examples illustrate the PD improvements in high profile and low profile laminated cores when using core bias currents—either tapped bias or self bias currents. The lower the profile, the higher the percentage of obtainable core PD improvement. The use of core bias currents may thus allow for low profile magnetic parts. Core bias current in low profile transformer cores fully utilizes the device magnetics and thereby requires less magnetic material to construct the core than without core bias current. Consequently, core bias current allows low profile parts without the previous concern of bulk and weight that the conventional low profile design would have required.

Mechanical Interlacing Flux Redistribution

An alternate, passive, flux redistribution scheme is mechanical interlacing. An example of mechanical interlacing is shown in a magnetic core assembly850inFIG. 13. The magnetic core assembly850consists of the interlace assembling of three magnetic sub-cores,851,852and853which are fabricated from a magnetic material859.FIG. 31Aillustrates a perspective view of the sub-core851.FIG. 31Billustrates a perspective view of the sub-core852andFIG. 31Cillustrates a perspective view of the sub-core853. Each sub-core851,852and853when interlaced assembled are magnetically isolated from each other by virtue of their gap. The core assembly850is radially sub-divided into three sections, a radial section860, a radial section861and a radial section862. A portion of the sub-core851contributes to the radial section860; another portion of the sub-core851contributes to the radial section861and the rest of the sub-core851contributes to the radial section862. Likewise, a portion of the sub-core852contributes to each of the sections860,861and862. Similarly, a portion of the sub-core853contributes to each of the sections860,861and862. Each sub-core851,852and853has a constant width and constant height and therefore the cross sectional areas, Ac, are constant along magnetic path lengths867.

In each sub-core851,852and853, each radial section860,861and862connects to an adjacent radial section by a magnetically continuous top crossover855or a bottom crossover854. The purpose of the crossovers854and855is to construct sub-cores with magnetic path lengths867that are equal, but physically separate and magnetically distinct. Each sub-core851,852and853has maximum relative magnetic permeability, μR, along the magnetic path lengths867but negligible relative magnetic permeability between adjacent sections unless it is a top or bottom crossover855or854. For convenient handling, the sub-cores851,852and853may magnetically connect to each other at only one connection point without interfering with their respective magnetic flux paths. Two connection points may be used, if the first connection point magnetically saturates before the applied voltage reaches its maximum, VMx(f).

The core assembly850may be constructed by laying down the base sub-core853and then placing the sub-core852into the sub-core853. The sub-core851is then placed into the sub-core852. The assembly forms the interlaced core850in an exact rectangle with an outer length and width and a uniform height. A winding window opening856is an exact rectangle with an inner length and inner width. The width of the core850is the difference between the outer edge and the inner edge of the window856and is three times the width of the sub-core851and is constant around the winding window856.

While the core assembly850is implemented via a solid block core from ferrite molding, pressing, and firing procedures, a stackable, thin lamination may also be fabricated from interlaced sub-cores.

FIG. 32is a graph760having a curve764which represents the maximum interlaced flux density distribution, BMx(r), of the interlaced core assembly850inFIG. 13. The graph760compares the flux density of non-interlaced and interlaced core sections of the same outer and inner dimensions. A curve763is the flux density distribution of a non-interlaced SBC or LaC. The curve764is the flux density distribution of the interlaced SBC or LaC with the same outer and inner dimensions.

FIG. 32is a graph760with a curve764representing the maximum interlaced flux density distribution, BMx(r), of the interlaced core850inFIG. 13. The graph760includes a first abscissa point at1.21inches of the core850, which is a toroidal equivalent radius of inner diameter, rIDe. A second abscissa point at1.69inches of the core850is a toroidal equivalent radius of outer diameter, rOde. As shown inFIG. 32, the flux density distribution in the section860of the core850is the Amperian distribution between radius 1.21 inches and radius 1.37 inches with peak flux density point765corresponding to the radius 1.21 inches. The difference between the radii is 0.16 inches and is the width of the inner sub-core, which could be either sub-core851,852or853, depending on where the flux density cross section is taken along the magnetic path length of core850. The flux density distribution in the section861of the core850is the Amperian distribution between the radius of 1.37 inches and the radius of 1.53 inches with a peak flux density point766corresponding to the radius of 1.37 inches. The difference between the radii is 0.16 inches and is the width of the middle sub-core, which could be either sub-core851,852or853, depending on where the flux density cross section is taken along the magnetic path length of core850. The flux density distribution in the section862of the core850is the Amperian distribution between the radius of 1.53 inches and the radius of 1.69 inches with a peak flux density point767corresponding to the radius 1.53 inches. The difference between the radii is 0.16 inches and is the width of the outer sub-core, which could be either sub-core851,852or853, depending on where the flux density cross section is taken along the magnetic path length of core850. The peak flux density points765,766and767are equal to Bsat represented by the line701. The shapes of each sectional flux density distribution curve are equal to each other and are radially summed to comprise the entire flux density distribution curve764. This is because each core sub section860,861and862has the same magnetic path length867and the same cross sectional area, AC.

The maximum operating voltage for curve763is VMx1(f). The maximum operating voltage for the curve764is VMx2(f). The operating voltage, VMx2(f), is greater than operating voltage, VMx1(f), by the total flux contained between the curve764and the curve763which is 12.3% in this example. The core interlaced flux density distribution, BMx(r) curve764for the core850is an example of optimally using a magnetic core at its peak magnetic permeability, μ, compared to a simple non interlaced square core with operational maximum flux density distribution, BMx(r), curve763. Consequently, a magnetic core's non-linear magnetic permeability, μ, increases the practical value of the power density of a core such as the core beyond 12.3%.

An alternate, passive, mechanical interlaced flux redistribution scheme is demonstrated by a core assembly870shown inFIGS. 14A and 14B. The core assembly870includes the mechanical crossover of three longitudinal laminated E-I sections871,872and873. The sections871,872and873are physically and magnetically isolated from each other along their magnetic path lengths. If needed, the sections871,872and873may magnetically connect with each other at only one connection point without magnetic interference. The sections871and873cross over the section872at a top bridge875and a bottom bridge874shown inFIG. 14B. The other parts of the core assembly870are the same as those of the core250ofFIGS. 30A and 30Band thus have identical element numbers.

The flux density distribution curve for the interlace technique shown in the core assembly870is similar to the curve764inFIG. 32. Each magnetic section871,872and873has respective radial widths888,889and890which are equal widths, and approximately the same magnetic path lengths, le. The magnetic path lengths of the sections871and873will be slightly longer than the path length for section872due to the bridging. The thickness of each section871,872and873is constant along the magnetic path length. Consequently the sections871,872and873, each have similar saw tooth flux density distribution curves that are radially shifted and summed as represented by the curve764inFIG. 32.

The bridging technique shown by the core assembly870may be used to construct interlaced magnetics in PCBs and ICs by magnetic material deposition. The bridges874and875may be formed by depositing magnetic material over base magnetic sections such as section872. Longitudinal slitting may be accomplished by photo lithographic etching. Deposition and etching techniques may be used to adjust the widths and thicknesses of the sections871,872and873so as to customize uniform cross sectional area, AC, along the longitudinal magnetic path length, le.

Square Core Inductor Corner Bias Current Corner Magnetics' Limitations

Magnetic flux lines traversing sharp bends or corners, as found in a square core laminated core inductor330shown inFIGS. 15A and 15Band a square core laminated core inductor350shown inFIGS. 16A and 16Bmay create locally induced magnetic air gaps at those points along their magnetic path where the radius of curvature is very small, such as the corners. The magnetically induced gaps are created at operating voltages less than the maximum voltage, VMx(f), because Ampere's Law dictates that magnetic flux lines want to ‘bunch up’ (pile up) or increase their flux density when their radius of curvature diminishes until the flux density bunching reaches its magnetic limit, Bsat. The diminished radius of curvature at the corners, compared to the radius of curvature in the straight sections causes the corner diagonals351of the cores330and350to saturate and form air gaps before the operating voltage reaches its maximum, VMx(f). As the operating voltage, VM(f), is increased, corner saturation represented by a cross hatched section727under a curve726in a graph720begins to occur at the interior or smallest radius of corner curvature, ri, at a radius of 0.032 inches in graph720and progresses inward into the magnetic material along the corner diagonals351inFIGS. 15A & 15Band16A &16B. The magnetic saturation stops at the radial point, rCDe, at 0.86 inches that supports the Amperian maximum magnetic flux density, BMx(f), for the maximum operating voltage, VMx(f). The Amperian corner maximum flux density distribution (BMxC(r)) begins at the inner diagonal radial point, rCDe, where a maximum flux density is equal to Bsat, line701(BMxC(0.086 inches)=Bsat, line701) and hyperbolically decays to an outer diagonal radius of 1.5 inches. The consequence to the device is a reduced maximum operating voltage, VMx(f), compared to a magnetic device without sharp radius of curvature, which thereby lessens the device's relative PD.

The flux density distribution, BMxC(r), shown by the curve726is a dynamic event that only occurs at the peak of the magnetizing current, IMx(f). Corner saturation gradually increases, following the magnetizing current, IM(f), waveform until the IM(f) reaches its maximum, IMx(f), which is represented by the maximum corner flux density distribution, BMxC(r) curve726. At all times while there is available unused magnetic material at any point in the transformer's corner diagonals351as shown by the cross section726and the magnetic flux density profile of the straight section, BMx(r), approximates the magnetic density profile of the corner section, BMxC(r).

Corner Bias Current Configurations

Any E-M or PM device with a magnetic core whose magnetic flux path, le, traverses sharp bends or corners is susceptible to magnetic flux compression at the sharp bends or corners, thereby reducing the device's best PD. The corner bias current scheme shown for the square core inductor330inFIG. 15Ais shown in detail inFIG. 15B. The corner scheme inFIG. 15Bimproves the PD of the square core inductor and other devices with sharp bends or corners such as transformers, electric motors, generators, relays and solenoids.

The power density in a square core device may be improved by usefully redistributing the flux density at the inside corners to relieve magnetic flux density pile-up and premature magnetic flux density saturation at the corners.FIG. 15Ais a top view of the square core inductor330which includes a stack of lamination sections250as shown inFIGS. 30A and 30Bwithout longitudinal slits. The lamination section250contain eight corner diagonal slits337that align when stacked to form a passage for either tapped or self bias current wiring. For example,FIG. 15Ashows a tapped bias current wiring331carrying a bias current333through the corner diagonal slits337.

A tapped bias current flows through the diagonal slits337to form an Amperian series of opposing magnetic flux vectors338,339and340to a series of incident Amperian magnetizing flux vectors334,335and336which are generated in the core341by the magnetizing current, IMx(f). However, on the outside of the slits337the flux density vectors338,339and340will aid the magnetizing flux density vectors334,335, and336in the under utilized magnetic material. Consequently, the net magnetizing flux, φMx(f), will traverse the corner, but is shifted radially inward along the corner diagonal351.

FIG. 33shows a graph720with a curve726showing the maximum corner flux distribution, BMxC(r), for magnetizing current, IMx(f), along the corner diagonals351without the benefit of corner bias current. The magnetic core material from the inner corner radius, ri, of 0.032 inches to the inner radius rCDe, of 0.86 inches is magnetically saturated at the peak of the magnetizing current, IMx(f), and unavailable to support magnetizing flux, φMx(f). The saturated region is represented by the cross hatching are727under the curve726. The radius724of 1.36 inches is the effective radius of the outside diameter, rODe, of the magnetic flux passing through the straight sections of inductor330inFIG. 15A. The effective corner outer diameter radius of 1.50 inches is the radial cut off point along the corner diagonal351beyond which the magnetic material is unavailable for magnetic flux passage. The radius of 1.50 inches is always greater than radius of 1.36 inches. The area under the curve726between radial points at 0.86 inches and 1.5 inches must be sufficient to pass maximum magnetizing flux φMx(f) or premature core saturation will occur at the corners and not allow the core to realize its full maximum operating voltage, VMx(f).

When the corner bias current333flows through the corner slots337, the corner diagonal magnetic flux density for the magnetizing current IMx(f) shifts as shown by the corner bias current influenced corner flux density curve732inFIG. 34.FIG. 34is a graph730which compares a dashed curve726representing a corner flux density distribution without corner bias current and the curve732. The corner bias current333shifts to the left, along the corner diagonal351, the effective inner operational magnetic of 0.86 inches in the graph730, to a radial position731, thereby shifting to the left, peak flux density point725to a peak flux density position734. The shift decreases the magnetically saturated diagonal cross sectional area733and opens up more of the magnetic material's corner diagonal flux density region for passing the maximum magnetizing flux φMx(f) at a higher maximum operating voltage, VMx(f), which raises the device's PD.

The eight corner diagonals passages337are physically separated from each other and consequently, each diagonal passage337may have its own bias current to favorably redistribute the magnetic flux density at each corner. Alternatively, if the geometry of each diagonal passage337and the magnetic material surrounding each is similar to each other, then a common corner bias current wiring scheme such as the wiring scheme331may be used, where each corner diagonal passage337is series connected with each other as shown inFIG. 15A. The tapped corner bias current scheme includes the bias current wiring331threaded through the corner slits337attached to a tap point151along the primary wiring102, generating a bias voltage332which drives a bias current333through the bias current wiring331. The bias current wiring331series connects each corner slit337and, thus, each corner to the flux redistribution corner bias current333. Alternatively, the corner bias current333may be generated by a self bias current scheme with an independent voltage source.

The corner flux density in laminations, or solid block cores, may also be redistributed by an alternate corner bias current passage located on the inside corner of the window opening. The inductor350shown inFIG. 16Aand the corner detail shown inFIG. 16Bdemonstrate this alternative corner flux density redistribution technique. The inductor350is similar to the inductor330inFIGS. 15A and 15Band thus like elements have like reference numbers. However, the inductor350includes passages352for the corner bias wiring331carrying the corner bias current333in four interior corner protrusions354in a laminated core355. The protrusions354are formed between the spine322and the outer legs255and both sides of the center leg261of the E-shaped section278. The magnetic flux density vectors353surrounding a hole352and generated by the corner bias current oppose the flux density vectors which tend to pile-up at the corners, due to the magnetizing current, IM(f),116generated in the primary wiring102. Similar to the corner bias current scheme ofFIGS. 15A and 15B, if the geometry of each corner passage352and the magnetic material surrounding each passage is similar to each other, then a common corner bias current wiring scheme331may be used, where each corner diagonal passage is series connected with each other as shown inFIG. 16A. The corner bias current may be generated by a self bias current scheme as well as a tapped bias current scheme used by the inductor350.

FIGS. 17A-17Eshow five different corner shapes that may be used to mitigate flux density saturation at the corners without resorting to corner bias currents.FIG. 17Ashows a corner section370which is conventional interior square corners272and273along the slits271and274in an E-I core such as the core302inFIGS. 1A and 1Band the core328inFIGS. 2A and 2B. The corners272and273have very small radius of curvature and consequently pile up magnetic flux lines at their corners similar to the flux pile up at the inside corner of the window opening276. However, the flux pile up is mitigated by distributing the magnetic flux over three inside corners instead of one.

FIG. 17Bshows a section371having a fixed short radius of curvature for corners375and376respectively along the slits271and274. The radius of curvature for the corners375and376is larger than the radius of curvature for the corners272and273and, consequently reduce the flux pile up at their corners.FIG. 17Cshows a section372which has a long or variable radius of curvature for corners377and378respectively along the slits271and274. The longer varying radius of curvature for the corners377and378lessen the flux pile up at their corners compared to corners375and376.FIG. 17Dshows a section373having an elongated radius of curvature for corners379and380respectively along the slits271and274. The large elongated radius of curvature for the corners379and380lessens the flux pile up at the corners and more fully utilizes the magnetic material at the corners. Also the elongated corner enables the addition of corner holes for corner bias current modification. Combinations of corner bias current modifications and geometry modifications may be used to minimize flux pile-up in the corners.

Diagonal gapping the corners, shown as a corner diagonal slit351in a corner section374shown inFIG. 17Eis normal to the magnetic flux direction and may be used as an alternate to the traditional lateral gapping used to interface the “E” and “I” magnetic material sections. Diagonal gapping keeps the corner magnetic material from saturating at its most vulnerable point, the short radius of curvature at the corner, while allowing a conventional magnetic winding bobbin to be applied to the core. The diagonal cut (corner gap) introduces air as the magnetic medium which has no magnetic saturation limit at the sharp radius of curvature. The flux density at the corner in the gap lacks the magnetic saturation limit which would ordinarily shift the operating magnetic flux density outward along the corner diagonal from the interior of the corner.FIG. 17Eshows the minimization or elimination of flux density saturation at the interior of the corner and optimal redistribution of the operating flux density along the corner diagonal.

Construction of Square Core & Toroidal SBC Magnetics

Another major group of magnetic materials that may benefit from redistributed magnetic flux density are the solid block magnetic materials such as sintered ferrites, both Manganese Zinc (MnZn) and Nickel Zinc (NiZn), and sintered powdered iron. The maximum flux density, Bsat, of a solid block core, such as ferrite or powdered iron, is significantly less than Bsat of tape wound toroidal cores consisting of either silicon steel or an amorphous magnetic metal such as Metglas. Ferrite materials and powdered iron may be used as magnetic cores in devices that need to operate at frequencies higher than may be efficiently supported by silicon steel or amorphous magnetic metal. Alternatively, ferrite materials may have their chemistry altered so they can be better used as permanent magnets. Solid block core magnetics are usually used to construct high frequency transformers and inductors; permanent magnetic stators and rotors in electric motors, generators, solenoids and relays.

Solid block ferrite cores are manufactured by molding, pressing and firing ferrite powder. The molding procedure used to fabricate solid block ferrite cores readily lends itself to manufacturing complex solid core geometries. Ferrite solid block cores may be fabricated in different shapes such as round and square toroidal cores, E-I cores, pot cores, U-I cores, and planar cores. The square cores consist of one piece molded “E” and “I” sections that allow easy assembly of their magnetic coils, pre-wound on bobbins, onto their magnetic sections—usually the center leg of the “E.” The “E” and “I” sections come together during assembly to close the magnetic path, but leave a gap at their interface that decreases the core's effective magnetic permeability, stei and thereby increase the maximum magnetizing current, IMx(f), required for core saturation.

E-I SBC magnetics have two opportunities to use redistributed magnetic flux density to improve power density. The first opportunity is redistributing the flux density in the straight sections using core bias currents, similar to the techniques employed for the E-I LaC inductor. The second opportunity is redistributing the flux density at the corners. Although the flux redistribution of the straight section usefully effects the corner distribution, the corner redistribution may be independently adjusted to increase PD without effecting the flux density distribution in the straight sections. All flux density redistribution techniques are designed to increase the power density in the SBC devices.

All of the solid block magnetics cores have maximum magnetic permeability, μ, in all polar coordinate directions. That is: μRθ≈μRz≈μRr. For all redistributed magnetic flux density designs, the material permeability must have these polar requirements: μRθ≈μRz>>μRr. This permeability requirement is exactly the same as intrinsically found in laminated core, LaC, devices. (Optionally, μRθ>>μRz≈μRr.) Further, an E-I solid block core (SBC) by toroidal equivalence, has the same effective radius of inner diameter, rIDe, and the same effective radius of outer diameter, rODe, as a laminated core, (LaC) with the same dimensions. An SBC shape has the same hyperbolic flux density distribution curve as the flux density distribution corresponding to either a toroidal tape wound core, TWC, or an E-I laminated core device. Consequently, the same flux density redistribution techniques described for toroidal TWC and E-I LaC devices also improve the PD of correspondingly shaped SBC devices.

The following sections describe the square core device's construction “building block,” the molded “E” and “I” core sections. Then the required core modifications for magnetic flux redistribution are presented. The modified cores are then ready to have their magnetic flux density profiles modified by either tapped bias current, self bias current, or corner bias current or shaping. The features and benefits for magnetic flux redistribution in the square core SBC inductor are described.

SBC Transformer Construction

The core modifications used to redistribute magnetic flux density, B(r), by core bias current, IB(f), are shown for a high profile E-I SBC inductor360inFIGS. 5A and 5B. The size, dimensions, and wiring used for the SBC inductor360are the same as used for the high profile LaC inductor310inFIGS. 2A and 2B. Consequently, the same part numbers used forFIGS. 2A and 2Bare used to identify similar parts inFIGS. 5A and 5B.

The building blocks of the square core SBC device are the molded solid “E” section278and the solid “I” section266constructed with SBC magnetic material. The “E” section278consists of a spine322, outer legs255and a center leg261. The width of the outer legs255is the same as the width of the “I” section266and the width of the spine322. The length of the E-I sections278and266and the length of the legs255may vary with finished device requirement. The width of the center leg261is typically twice the width of the outer legs255and is equally divided by a center line253. The winding window openings276have a length and width that is equally divided by the centerlines252and254. Closure of the “E” and “I” sections278and266form a magnetic core362with an interface gap265between the sections278and266.

The “E” and “I” core sections278and266contain longitudinal cut slits271and274which radially subdivide the “E” and “I” sections278and266into three solid sub-sections279,280and281. The widths of the sub-sections279and280are equal. The width of the sub-section281is twice the width of either sub-sections279and280.

The “E” and “I” core sections278and266are molded to a required magnetic height for the core362. The “E” and “I” core sectioning as shown inFIG. 5Acompletely separates the sections278and266which requires an auxiliary handling system for the sections. Alternatively the sectioning may leave each section278and266with one magnetic material connection with adjacent sections that keeps the solid core integrity for handling the core sub-sections279,280and281. Alternatively, the sectioning may leave each section278and266with two or more magnetic material connections with adjacent sections, such as a connection294inFIG. 1A, that keeps the handling integrity of the solid core pieces. A double material keeper section may also be used at other points along the slits271and274.

The inductor wire winding102is usually pre-wound by a winding machine on a nonconductive bobbin. The solid core sub-sections279,280and281are inserted and stacked in the center of the bobbin to complete the assembly. The core winding window opening276is formed by the closure of the “E” section278and the “I” section266and limits the total cross sectional area, AC, of the inductor winding102that may be used in a given winding window contained by the outside width and length. After the inductor winding102is applied, a thin insulative layer III may be wrapped around all the finished magnet wire winding.

It is to be understood that one longitudinal slit may be used in place of the double slits on the SBC “E” section278and “I” section266. Similar to the criteria for the number of passages in the toroid TWC transformer, the more passages that are in the SBC, the more power density increases. However, a simpler one slit, two wire, bias current modification may sufficiently redistribute magnetic flux density for certain applications.

Square Core, High Profile Solid Block Core, with Tapped Bias Current

The tapped bias current wiring312carries a tapped bias current316through the core362inFIGS. 5A and 5Bby a single conductor through a notched passage327located along the longitudinal slit274, spaced from the center lines252or254of the winding windows276. The tapped bias current wiring313carries a tapped bias current317through the core362by a single conductor through a notched passage326located along the longitudinal slit271. The slit271is spaced from the center lines252or254of the winding windows276. The slit274longitudinally bisects the outer legs255, the spine322and the “I” section266. The slit271longitudinally bisects the inner half of the outer legs255, the spine322and the “I” section266.

The tapped bias wiring scheme is shown in the right half of the core362inFIG. 5B. The tapped bias current wiring312starts at a tap151along the primary winding102which provides a bias voltage, VB(f),314to drive the tapped bias current316through the tapped bias current wiring circuit312. The wiring is threaded through the notched passages327located along the slit274.

The tapped bias current wiring313starts at a tap311along the inductor winding102which provides a bias voltage, VB(f),315to drive the tapped bias current317through the tapped bias current wiring313. The wiring313is threaded through the notched passages326located along the slit271.

The maximum core bias current flux density distribution, BBMx(r), of the high profile inductor360is the same as the maximum core bias current flux density distribution, BBMx(r), for the high profile inductor310inFIGS. 2A and 2Band is shown by the curve738inFIG. 23.

The bias current flux density distribution, BBMx(r) represented by the curve738inFIG. 23for the core362used in the inductor360is an example of optimally using a magnetic core at its peak magnetic permeability, μ.

Capacitance Enhanced Magnetic Core Construction

Uniformly distributing capacitance, Cn, along a length, μ, of a magnetic core causes the core's inductance, L, to subdivide into distributed inductances, Ln, and commingle with the distributed capacitance, Cn, so as to form a transmission line. A magnetic core used to construct a transmission line may also optimally redistribute the magnetic flux density from over utilized areas of the core cross section to under utilized areas of the cross section. The redistribution is similar to the magnetic flux density redistribution caused by a large number of frequency sensitive small bias currents flowing through the core. The magnetic flux density redistribution is optimized when the capacitance distribution across the device is optimized and the device is operated at its optimum frequency, fo.

A transmission line where the values of the distributed capacitance, Cn, and the distributed inductance, Ln, are independently adjustable is referred to as a heterogeneous transmission line. A transmission line where the values of the distributed capacitance, Cn, and the distributed inductance, Ln, are dependent on each other is referred to as a homogeneous transmission line. Capacitance enhanced magnetic device450shown inFIGS. 9A and 9B; device500shown inFIGS. 10A and 10B; device530shown inFIGS. 11A and 11B; and device570shown inFIGS. 12A and 12Bare unique heterogeneous transmission lines used to construct magnetic cores usually used for transformers or inductors. Magnetic devices such as a device600shown inFIGS. 18A and 18B; and a device620shown inFIGS. 19A-19Care homogeneous transmission lines used to construct magnetic cores usually used for transformers or inductors.

The devices450,500,530,570,600and620may replace spiral wound inductors and transformers such as a device941inFIG. 6and a device940inFIGS. 7A and 7B. For high frequency operating devices, the devices570,600, and620are alternatives to spiral wound magnetics.

The devices450and500inFIGS. 9A and 9BandFIGS. 10A and 10Brespectively are transmission lines which use straight linear conductors such as a top conductor454and a bottom conductor453, electrically connected at input terminals461and462by wires452, to an input voltage456. These transmission lines are terminated at terminals463and464by a short circuit wire conductor455carrying a short circuit termination current470.

The straight linear conductors454and453may be replaced with planar disks. If planar disks are used, then the wire conductors452and455may be used to access or terminate the transmission line as long as an E-M mechanism for quickly gathering or dispersing charges is in place at the connection terminals461,462,463and464used by the conductive disks.

A technique for quickly gathering or dispersing charges at the device's connection terminals is to have a slight conductive overhang such as the overhang531inFIG. 11A, at the input terminals461and462and a slight conductive overhang532at the output terminals463and464whereby an air dielectric transmission line is formed at the edge of the planar conductor. The transmission lines530,570,600, and620inFIGS. 11B,12B,18B and19C respectively, use conductive planar top disks534,572,602,628,630and638and conductive planar bottom disks533,571,601,627,629and637for their transmission line conductors between their input and output connection terminals. Each conductive planar disk inFIGS. 11B,12B,18B and19C has the overhang531at its input terminals461and462and an overhang532at the output terminals463and464. The overhangs531and532provide local transmission lines along the conductive edge of the planar disks by which charges can quickly gather or disperse. These edge transmission lines have an air dielectric and a velocity of E-M wave propagation, vpair. The transmission line between the input and output conductors has a velocity of E-M wave propagation, vpdev, determined by the magnetic and dielectric media between the conductors. Successful gathering and dispersing of charges at the overhangs531and532requires vpairto be much greater than vpdev. Foil wiring best serve the device's electrical connection requirements when vpair≈Vpdev.

A capacitance enhanced magnetic device450is shown inFIGS. 9A and 9B. The capacitance enhanced magnetic device450includes a tape wound magnetic core457constructed to electrically connect a number, n, of discrete, external, capacitors471,472, and473, to through-the-core insulated conductors475,476and477, appropriately distributed along the radial cross sectional length of the tape wound core457. The core457is constructed of a conductive magnetic tape109. The cross sectional length, lt, of the TWC457is the difference between the radius of the outer diameter, rODe,468and the radius of the inner diameter, rIDe,467. This construction requires the magnetic core457to be annealed first and then the capacitors471,472and473are electrically attached to the conductors475,476and477. Since most dielectric materials, except mica and ceramic, do not survive the annealing temperatures, using capacitors external to the magnetic core457is a preferred capacitance in enhanced magnetics construction.

The number of sections, n, is determined by the number of capacitors required for the design. A series of through-the-core conductors475,476,477divide the magnetic core457into n inductive sections458,459,460discretely distributed along the radial length, lt, of the core457. When the n capacitors471,472,473are electrically connected to the conductors475,476,477a like number of discrete, sequential, inductive-capacitive filter sections are formed. The filter sections are radially connected by a top and bottom radial conductor454and453forming a discretely implemented transmission line, which can also be used as the core of a toroidal transformer or inductor.

Referring toFIG. 9B, the core457is co-wound with insulated tabbed conductors475,476,477which are inserted radially, inline, and through the magnetic TWC457. The conductors475,476,477are insulated from the conductive magnetic TWC457with a thin dielectric474. The bottom radial conductor453is electrically connected to the bottom of all the tabbed conductors475,476,477. The conductive magnetic TWC457is insulated from the bottom radial conductor453by a thin dielectric465. The top or tabbed ends of the feed through conductors475,476,477electrically connect, respectively, to one end of the discrete capacitors471,472,473. The other ends of the discrete capacitors471,472,473all are electrically connected to the top radial conductor454. A short circuit termination wire455is attached at two transmission line terminals463and464located at a rODe,468of the core457. The transmission line terminals461and462are located at a rIDe,467of the inner diameter and provide the input connection points for a current wire452conducting an input current469driven by an input voltage456.

The device450has a top wire conductor454and bottom wire conductor453. Alternatively, either or both conductors453and454could be replaced by conductive disks, plates or wedges.

Another example capacitance enhanced magnetic device500is shown inFIGS. 10A and 10B. The capacitance enhanced magnetic device500has an offset co-wound core501having a conductive tape wound magnetics109co-wound with a copper or aluminum foil which forms multiple electrical contacts511,512,513and a thin dielectric that forms the device's distributed capacitances (C1-Cn)507,508,509. If the magnetics requires annealing, then the dielectric layer forming the capacitors507,508,509may be constructed of mica to withstand the annealing temperature.

FIG. 10Bis a cross-section of the device500showing a repetitive sequential grouping of the multiple magnetics layers502,503,504, the conductor layers511,512,513and the dielectric layers507,508,509along the radial cross sectional length, lt, of the tape wound core501. Each grouping is mechanically referred to as a “wad” which is a discrete inductor-capacitor filter. In a “wad” the magnetics layers502,503,504form the n discrete inductors, and the discrete capacitor consists of the n thin dielectric layers507,508,509whose plates are formed with the conductive magnetic layers, and the conductive foils511,512,513. The number, n, of cross-sectional repetitive inductive and capacitive sections is the cross-sectional length, lt, divided by the thickness of one “wad.” (n=lt/(“wad” thickness). The cross sectional length, lt, shown inFIG. 10Bis the difference between the rODe468and the rIDe467. In the construction shown inFIG. 10B, the thickness of a “wad” is the summation of two layers of magnetic foil in the core501, two layers of thickness of a dielectric such as the dielectric layer507and one layer of a conductor such as the conductor511. When the inductor-capacitor filter sections are radially connected by an upper and a lower radial conductor453and454, a discretely implemented, n-section, transmission line is formed that has an equivalent circuit920ofFIG. 24.

The magnetic layers502,503,504are offset to make electrical contact with the upper radial conductor454. The dielectric layers507,508,509have an upper offset to cover the upper end of the conductors511,512,513to prevent them from shorting to the conductive magnetic layers502,503,504. Likewise, the dielectric layers507,508,509each have a lower offset which covers the lower end of the conductors511,512,513to prevent them from shorting to the conductive magnetic layers502,503,504. Before the radial conductors454and453are attached, the co-wound assembly is vacuum impregnated with a non-conductive potting compound505contained by dielectric potting cups510to provide mechanical stability for the assembly of the device500. A short circuit termination wire455is attached at a pair of transmission line terminals463and464located at the rODe468. A second pair of transmission line terminals461and462is located at the rIDe467to provide the input connection points for the wires452conducting the input current469driven by an input voltage456. Either or both the top wire conductor454and the bottom wire conductor453may be replaced by conductive disks, plates or wedges.

FIG. 11A-11Bshow another example capacitance enhanced magnetic device530which is constructed by layering a conductive tape wound magnetic core535with a pancake dielectric549and upper and lower conductive disks534and533. An anisotropic conductive interface material548electrically connects the magnetic core535to the upper conductive disk534and electrically connects the lower side of magnetic core535to the lower conductive disk533. The tape wound magnetic core535is first annealed, then a low temperature dielectric layer549that forms the capacitance is added. An anisotropic conductive interface548joins the conductive magnetics535with the dielectric layer549and the upper and lower conductive disks534and533. The anisotropic conductive interface548is maximally conductive in the vertical direction and minimally conductive in the radial direction. Loctite products3441or3447are anisotropic conductive adhesives that may be used.

FIGS. 12A-12Bshow another example capacitance enhanced magnetic device570that is constructed by layering a conductive magnetic foil disk core573with a pancake dielectric584and upper and lower conductive disks572and571. An anisotropic conductive interface material548electrically connects the foil magnetic core573to the upper conductive disk572and electrically connects the lower side of magnetic core573to the lower conductive disk571. The magnetic disk core573is annealed, then cut to shape or alternatively, cut to shape and then annealed; and then the low temperature dielectric layer584that forms the capacitance dielectric is added. Alternatively, more than one thin magnetic foil disk such as the foil disk core573may be stacked on each other to form the magnetic core.

The single foil magnetic core573is shown inFIG. 12Bwith its facial surface greatly exaggerated to illustrate the surface roughness of electrically interfacing to the magnetic core573. A compliant anisotropic conductive interface548joins the conductive magnetic disk573with the dielectric layer584and the upper and lower conductive disks572and571. The anisotropic conductive interface548is maximally conductive in the vertical or compressed direction, and minimally conductive in the radial direction.

A capacitance enhanced magnetic device600shown inFIGS. 18A-18Bincludes a dielectric or air core magnetic disk603upon which an upper conductive disk602and a lower conductive disk601are placed. The conductive disks602and601may be plated, sprayed, or vapor deposited on the dielectric or air core magnetic disk603. The device600is constructed similarly to the device570inFIGS. 12A-12B. However, the magnetics and dielectric material inFIGS. 18A-18Bare homogeneous instead of the discrete or heterogeneous materials used to construct the device570. Consequently, the anisotropic interface548is not needed. However, the relative permeability, μr, of the air core magnetics is one, the lowest possible relative magnetic permeability.

FIGS. 19A,19B and19C, are the top, inner periphery, and cross sectional views of a capacitance enhanced magnetic device620whose core is homogeneously constructed similar to the device600inFIGS. 18A-18B. The surface conductors in the device620are electrically divided into six wedge shaped segments621,622,623,624,625and626. Each wedge shaped segment621-626is an independent transmission line electrically interconnected in series with each other. Each transmission line is terminated at the effective radius of outer diameter, rODe,468in a short circuit shown respectively as conductors639,640,641,642,643and644.

FIG. 19Bshows a series of connecting wires645,646,647,648and649interconnecting the segmented sections621-626to each other and an input voltage456. A wire452connects the input voltage456to the top conducting segment628and a wire645connects the bottom conducting segment627to the adjacent top conducting segment630. A wire646connects the bottom conducting segment629to the adjacent top conducting segment632and a wire647connects the bottom conducting segment631to the adjacent top conducting segment634. A wire648connects the bottom conducting segment633to the adjacent top conducting segment636, a wire649connects the bottom conducting segment635to the adjacent top conducting segment638, and the wire452connects the bottom conducting segment637to the input voltage456.

Capacitance Enhanced Magnetic Core Operation

Adding distributed capacitance, Cn, to a magnetic core may redistribute the magnetic flux density from over utilized areas of the core's cross section to under utilized areas of the core's cross section, thereby improving the magnetic device's power density. The capacitance enhanced devices450,500,530,570,600and620have capacitance optimally and radially distributed along their magnetics from the common radius of the inner diameter467to the common radius of outer diameter468. In a circular toroidal core, the magnetic flux density redistribution is optimized when the radial capacitance distribution, Cn(r), is proportional to the radial length, r, (Cn(r) ∝ r), the device is operated at its optimum frequency, fo, and the radial inductance distribution (Ln(r)), is inversely proportional to the radial length, r, (Ln(r) ∝ 1/r). Magnetic devices constructed in this manner intrinsically form a power transmission line.

Besides having magnetic flux density optimally redistributed when operated in the steady state, at frequency, fo, a capacitance enhanced magnetic device exhibits a higher steady state operating impedance and faster developing transient magnetic forces. The transient magnetic forces within the capacitance enhanced magnetic device caused by transient voltage, V(t), increase faster than equivalent magnetic devices without distributed capacitance, thereby accelerating the starting operation of electromechanical devices such as electric motors, solenoids, relays and rail guns.

Distributed maximum displacement currents (IDx(fo)) redistribute the magnetic flux density. Similar to the core bias currents, IBx(f), the distributed capacitance, Cn(r), maximum displacement currents, IDx(fo), appropriately counteract the flux density of the maximum magnetizing current, IMx(fo), in areas of the core that have excess flux density and, in turn, generate flux density in areas of the core that benefit from increased flux density. The displacement currents, IDx(fo), are frequency dependent and thus the optimum flux density redistribution is frequency dependent having an optimum operating frequency, f0, near but less than the calculated linear quarter wavelength frequency, f0.25 λP.

Displacement currents478,479,480are shown in the external capacitance device450inFIGS. 9A and 9B. Displacement currents514,515,516are shown in the internal capacitance device500ofFIGS. 10A and 10B. Displacement currents550,551,552and553are shown in the external capacitance device530inFIGS. 11A and 11B. Displacement currents585,586,587and588are shown in the external capacitance device570inFIGS. 12A and 12B. Displacement currents604,605,606and607are shown in the homogeneous capacitance device600inFIGS. 18A and 18B. Displacement currents656,657,658and659are shown in the homogeneous capacitance device620inFIGS. 19A-19C.

The device450inFIGS. 9A and 9Bis an example to show capacitance enhanced magnetic flux density redistribution by the discretely distributed displacement currents478,479and480that flow through each of the external discretely distributed capacitors471,472,473and generate circumferential magnetic flux lines illustrated inFIG. 9Bby points481,482,483and tails484,485,486. The displacement current, IDx(fo), generated flux lines are in phase with the magnetic flux generated by the inductive magnetizing current, IMx(f0)469thereby redistributing magnetic flux density similar to the bias current described in the section on bias current magnetics. However, with capacitance enhanced magnetics, displacement currents penetrate through the core457through nearly infinitesimally distributed points along the toroidal device's radial length, lt. An optimum distribution of capacitance across the radial cross sectional length, lt, whereby the velocity of E-M wave propagation is constant throughout is required to achieve the maximum power density. Because of the optimum operating frequency's proximity to the device's quarter wave frequency, f0.25λP, the magnetizing current, IM(fo),469at the optimum operating frequency, fo, is less than the magnetizing current required for the same inductance, without distributed capacitance, operated at the same voltage and frequency. The reduced magnetizing current, IM(fo) of the capacitance enhanced magnetics device further improves the power density of the circular toroidal device as well as does the redistributed magnetic flux density caused by the displacement currents, IDx(fo).

The capacitance enhanced magnetic devices450,500,530and570are circular toroidal shaped transmission lines consisting of circular toroidal shaped, high permeability, μ, distributed magnetics that uniquely and independently integrate into their structure toroidal shaped distributed capacitance. The capacitance enhanced magnetic device600inFIGS. 18A and 18Band the device620inFIGS. 19A-19Care circular toroidal shaped transmission lines consisting of circular toroidal shaped, dielectric or air core permeability, μ, distributed magnetics that uniquely and codependently integrate into their structure toroidal shaped distributed capacitance. In the toroidal transmission line, the distributed capacitance, capacitance per unit radial length, Cn(r), varies directly with the radius of the toroidal shaped transmission line, while the distributed inductance, inductance per unit radial length, Ln(r), varies inversely with the radius. If these circular toroidal transmission lines are operated at their optimum frequency, fo, as 4-terminal transmission lines terminated in their characteristic output impedance, Zo, then the circular toroidal geometry can determine transformer turns ratio, N, instead of winding turns count, thereby simplifying transformer construction. That is, turns ratio, N, defined earlier as, Vp(f)/Vs(f)=N, and ISx(f)/IPx(f)=N, may now be determined by the toroidal transmission line's ratio of radii, radius of inner diameter, rID, divided by radius of outer diameter, rOD. N is proportional to rID/rOD. (N ∝ rID/rOD)

In the magnetic device450inFIGS. 9A and 9B, the input components921and924of the transmission line equivalent circuit920inFIG. 24are formed in the following manner. The magnetic core for the input distributed inductance921is formed by the first two inner layers of the TWC magnetics458on the input side of the vertical conductor475. The conductive current loop required to define the distributed inductance921consists of the input voltage456connected by the input wires452to the top radial wire454which connects via the capacitor471(capacitor924) to the vertical conductor475which connects to the longitudinal bottom conductor453and returns to the input voltage456via the input wires452. The vertical conductor475carries the displacement current, ID1(f),478through the core457similar to the magnetic core bias current described in the toroidal and square core transformers.

The magnetic core for the second input distributed inductance922inFIG. 24is formed by four successive layers of magnetic strips459between the vertical conductors475and476inFIGS. 9A-9B. The conductive current loop required to define the second input distributed inductance922consists of the top radial wire454, which connects via the capacitor471to the vertical conductor475, which connects to the longitudinal bottom conductor453which forward connects to the vertical conductor476, which returns to the top radial conductor454by the capacitor472(capacitor925). The vertical conductor476carries the displacement current, ID2(f),479through the core457similar to the magnetic core bias current described in the toroidal and square core transformers. The electrical pattern repeats until the end of the line at the radius of the outer diameter, rODe468.

The direction of the flux vectors481,482,483and484,485,486is determined by the “right hand” rule for magnetizing current flowing up in the input conductor, and then to the left as longitudinal current in the top conductor454. The flux vectors481,482,483and484,485,486are out of the page on the left side of the center line115and into the page on the right side of center line115.

The curve782inFIG. 25is the flux density distribution, BMx(r), of the magnetic core457without the benefit of distributed capacitance. The displacement currents of the external discrete distributed capacitors471,472,473set up discrete magnetic force fields, ATDxn(f), along the radial length, lt, between the radii467and468in the device450. Because of the 180° phase shift with respect to the magnetizing current force fields, ATMx(f), the currents cause the redistribution of magnetic flux density throughout the core457. The discrete capacitors471,472,473added to the core457change the core's flux density distribution, when operated at optimum frequency, fo, to the curve783inFIG. 25which allows a reduction in the toroidal strip width by 30%, thereby increasing the device's power density by 42%. The maximum flux density distribution for the reduced strip width is the curve784inFIG. 25. The non-linearity of the magnetic material, as discussed for TWC and LaC, may increase the power density gain well beyond 42%.

The magnetic device500inFIGS. 10A and 10Boperates in a similar manner to the device450ofFIGS. 9A and 9B, except the distributed capacitance is discretely implemented internally within the magnetic core501. As explained above, the corresponding equivalent inductors921,922and923and capacitors922,924, and926are constructed in “wads” of a section of magnetic material forming the core of the distributed inductance, Ln, and a section of dielectric material, integrated with the magnetics, forming the corresponding distributed capacitance, Cn.

The equivalent of the circuit capacitor924inFIG. 24for the device500inFIG. 10Bis a parallel combination capacitor formed by the two dielectric layers507sandwiched between two common connected conductive plates, the magnetic core material layers502and one conductive foil511. Similarly, the equivalent circuit capacitor925is a parallel combination capacitor formed by two dielectric layers508sandwiched between two common connected conductive plates, the magnetic core material layer503and one conductive foil512. Multiple discrete capacitors are continuously formed along transmission line500until the last capacitor is formed at the end of the line at radius468by two dielectric layers509sandwiched between the last two common connected conductive plates, the magnetic core material504and the conductive foil513.

The magnetic core for the input distributed inductance921is formed by the first two inner layers of the TWC magnetics502, one layer on the input side of the vertical conductor511and the other layer on the output side of the vertical conductor511. The conductive current loop defining distributed inductance921consists of the input voltage456connected by the input wires452to the top radial wire454which connects via the capacitor924to vertical conductor511which connects to the longitudinal bottom conductor453which returns to the input voltage456via the input wires452. The vertical conductor511carries the displacement current, ID1(f),514, formed by two strands of displacement current through both dielectrics507, which together form the capacitor924. The displacement current, ID1(f),514is similar to the magnetic bias current described in the toroidal and square core transformers. The displacement currents, IDn(f) generate magnetic flux vector points517,518,519and520,521,522which set up discrete magnetic force fields, ATDn(f), along the radial length of the device that by their 180° phase shift with respect to magnetizing current, IM(f) aids the redistribution of magnetic flux density throughout the core501.

The magnetic device530inFIGS. 11A and 11Boperates similar to the device450inFIGS. 9A and 9Band the device500inFIGS. 10A and 10Bby using the conductive magnetic material layers540,541,542as the vertical conductors carrying “n” channels of displacement current, IDn(f), through the core535, similar to the core bias current, IB(f), described for the toroidal and square core transformers.

The capacitance enhanced magnetic device530is a toroidal transmission line, having distributed capacitances924,925through926inFIG. 24implemented with a pancake dielectric549attached to the bottom surface of the magnetic core535by the anisotropic vertically conducting interface material548. Each layer of the TWC magnetic material535forms the core of the “nth” section of inductance in the transmission line equivalent circuit920inFIG. 24. The anisotropic conductive material548channels the displacement current through the “nth” conductive magnetic layer to the corresponding “nth” section of the dielectric in the dielectric layer549to form the pairs of distributed inductance923and distributed capacitance926.

The cross section of the transmission line530inFIGS. 11A and 11Bis subdivided into four sections536,537,538and539that show the relationship between the magnetic currents544,545,546and547and the displacement currents550,551,552and553. At an optimum operating frequency, fo, the magnetizing current550at the input at the radial position467is minimum, while the magnetizing current553at the output into a short circuit termination at the radial position468is maximum. The displacement currents550,551,552and553generate the magnetic flux vector points554,555,556and557and the magnetic flux vector tails558,559,560and561into the four magnetic cross sections536,537,538, and539. The displacement currents set up discrete magnetic force fields, ATDn(f), along the radial length that by their 180° phase shift with respect to magnetizing current, IMx(f), causes the redistribution of magnetic flux density throughout the core535. The displacement current551located about 40% along the transmission line's length, lt, is maximum, while the displacement current553located near the output radial position468is minimum. The displacement currents550and552are mid-valued and complete the displacement current distribution.

The magnetic device570inFIGS. 12A and 12Boperates in a similar manner to the device530inFIGS. 11A and 11Bexcept the device570uses the conductive circular magnetic foil to provide vertical displacement current conduction through the core573similar to the core bias current, IBx(f), described for the toroidal and square core transformers. The capacitance enhanced magnetic device570is a toroidal transmission line, having distributed capacitances924,925through926inFIG. 24implemented with a pancake dielectric549attached to the bottom surface of the magnetic core573by the anisotropic vertically conducting interface material548. The radial distribution of both the dielectric material549and the magnetic material573are continuously uniform. Consequently, the core for the distributed inductance923and the corresponding dielectric for the distributed capacitance926are infinitesimally distributed.

The cross section of transmission line570is subdivided into four sections574,575,576and577that show the trend of developing magnetic currents580,581,582and583and the displacement currents585,586,587and588. At an optimum operating frequency, fo, the magnetizing current585at the input at the radial position467is minimum, while the magnetizing current588at the output into a short circuit termination at the radial position468is maximum. The displacement currents585,586,587and588generate magnetic flux vector points589,590,591and592; and magnetic flux vector tails,593,594,595and596into the four cross sections574,575,576and577. The displacement currents set up discrete magnetic force fields, ATDn(f), along the radial length of the device that by their 180° phase shift with respect to magnetizing current, IM(f), aid the redistribution of magnetic flux density throughout the core573. The displacement current586located about 40% along the transmission line's length, lt, is maximum, while the displacement current588located near the output radial position468is minimum. The displacement currents585and587are mid-valued and complete the displacement current distribution.

The curve782inFIG. 25is the flux density distribution, BMx(r), of the magnetic cores of the devices500,530and570without the benefit of distributed capacitance. The displacement currents of the discrete internally distributed capacitors924,925through926set up discrete magnetic force fields, ATDxn(f), along the radial length, lt, between radii467and468, that, because of their 180° phase shift with respect to magnetizing current force fields, ATMx(f), causes the redistribution of magnetic flux density throughout the core. The discrete capacitors,924,925through926, added to the cores change the flux density distribution, when operated at optimum frequency, fo, to the curve783inFIG. 25allowing a reduction in the toroidal strip width by 30%, thereby increasing the device's power density by 42%. The maximum flux density distribution for the reduced strip width is shown by the curve784. The non-linearity of the magnetic material, as discussed for a TWC and a LaC, may increase the power density gain well beyond 42%.

The magnetic device600shown inFIGS. 18A and 18Boperates in a similar manner to the device570shown inFIGS. 12A and 12B. The magnetic device600includes a non-conductive dielectric core603as vertical conductors carrying a displacement current, IDx(f), through the dielectric core603similar to the core bias current, IB(f), described for the toroidal and square core transformers. The magnetic device600is a toroidal transmission line having capacitance homogeneously distributed with the pancake dielectric core603. The maximum magnetic flux density distribution, BMx(r), is optimum when operated at optimum frequency, fo. Displacement currents, IDn(f),604,605,606and607generate magnetic flux vector points608,609,610and611; and magnetic flux vector tails612,613,614and615which set up discrete magnetic force fields, ATDn(f), along the radial length of the device600that by their 180° phase shift with respect to the magnetizing current, IM(f),469aids the redistribution of magnetic flux density throughout the dielectric core603.

The magnetic device620shown inFIGS. 19A and 19Boperates in a similar manner to the device600shown inFIGS. 18A and 18B. The magnetic device620has a non-conductive dielectric core654which carries a displacement current, ID(f), through the core654, similar to the core bias current, IB(f), described for the toroidal and square core transformers. The device620is formed by cutting a device similar to the device600inFIGS. 18A and 18Binto six electrically isolated, but magnetically interconnected, wedge shaped sections621,622,623,624,625and626. Each wedge section621-626has the same velocity of wave propagation, vp, as the device600, but each wedge section621-626has six times the characteristic impedance, Zo, of the device600and presents to the input voltage650an impedance thirty six times the characteristic impedance of device600. The device620is a toroidal transmission line, whose distributed capacitance is homogeneously implemented with the pancake dielectric core654sandwiched between six wedge shaped, coplanar, top conductors628,630,632,634,636and638that physically align with six wedge shaped, coplanar, bottom conductors627,629,631,633,635and637on the opposite of the dielectric core654. The maximum magnetic flux density distribution, BMx(r), is optimum when operated at optimum frequency, fo. Displacement currents, IDn(f),656,657,658and659generate magnetic flux vector points660,661,662and663and flux vector tails664,665,666, and667which set up discrete magnetic force fields, ATDn(f), along the radial length of the device that by their 180° phase shift with respect to the magnetizing current, IM(f),655aids the redistribution of magnetic flux density throughout the core654. The flux density distribution is shown pictorially inFIG. 19Aby flux vector arrows,651,652and653.

Redirected Magnetic Flux Density Devices for Spiral Windings

Solid block core ferrite is formed in low profile modified “pot” cores, a.k.a. as “planar” cores which have a magnetic winding. An example of a low profile modified pot core is a spiral winding940shown inFIGS. 7A-7Bthat is enclosed with SBC “pot” core sections such as a top section948and a bottom section947. The top and bottom sections948and947form an inductor941shown inFIG. 6.

For very high frequency circuits, air core magnetics may be used. One common air core device is the spiral wound inductor940shown inFIGS. 7A and 7B. The spiral wound air core940has resistive limitations similar to the spiral wound inductor core941shown inFIG. 6. The spiral winding940has five turns of a spirally wound conductor width each turn spaced between a minimum inner radius945and a maximum outer radius946. A radial spacing942is the summation of the minimum inner radius945and the spiral conductor width. The spiral winding is long and narrow.

Spiral wound magnetics are used in planar “pot core” transformers and inductors such as the inductor core941shown inFIG. 6and in the air core, AiC, high frequency inductor and transformer winding circuits940shown inFIGS. 7A and 7B. The length and narrowness of the winding limits the temperature rise at the maximum current, IMx(f), that can be safely handled by the design.

The problem of performance limiting parasitic circuits may be addressed by transmission line technology. Stable parasitic components may often be exploited by creative circuit design. The intrinsic nature of transmission line technology contains and regulates its electric and magnetic fields so a stable high performance component may be obtained. Further, replacing the long narrow spiral winding with a shorter, broader, radial winding used in radial planar transmission lines improves the circuit quality, maximizes the device's inductance and helps dissipate the heat formed in the winding.

The spiral winding limitations can be overcome with a radially wound toroidal magnetic core transmission line or a radial wound air core transmission line. The radial winding forms a radially directed transmission line where the radial conductors are the transmission line's parallel conductors. The radial conductors sandwich either the TWC material535used in the device530shown inFIGS. 11A and 11Bor the magnetic foil material573used in the device570inFIGS. 12A and 12Bor a solid block core material as required. The transmission line is completed by capacitance appropriately distributed heterogeneously along the length, lt, of the transmission line as shown by the capacitance distribution in the devices450,500,530and570. Alternatively, the radial conductors may sandwich toroidal shaped dielectric material, distributed homogeneously, such as the dielectric core603used in the device600inFIGS. 18A and 18Bor the dielectric material654shown sectioned in the device620inFIGS. 19A and 19B.

The devices450,500,530,570,600and620compared to a spiral winding such as that in the device941inFIG. 6and the device940inFIGS. 7A and 7Bis that they occupy the same footprint and use transmission line construction to contain and maximize the magnetic flux which presents the highest inductance with negligible parasitic circuits.

Capacitance Enhanced Electromechanical Core Construction—Rail Gun

A rail gun960shown inFIG. 8is an example of using an air core to launch electro-magnetically accelerated projectiles with fast changing, extremely high magnetic flux density. Large transient currents965flow through the rail conductors961and a highly conductive projectile964to create a Lorentz force to accelerate the highly conductive projectile964down the rails961and out a muzzle963.

FIG. 26shows a capacitance enhanced rail gun967which is an example of a linear electro-mechanical device whose actuation force is increased by the addition of a series of distributed capacitances968,969,970. The rail gun967is similar to the conventional rail gun960inFIG. 8. A projectile964which is a conductive slider, is accelerated by Lorentz forces over the length of a barrel966. The acceleration of the slider964on a set of conductive rails961down the barrel966is analogous to the movement of a solenoid's plunger over a plunger's stroke length. Distributed capacitance along the length of the barrel966while the slider964can increase the acceleration forces applied to either the slider964during its transition time, TD, thereby quickening the device's actuation time for the applied voltage962.

Distributed discrete capacitances968,969,970are located along the length of the barrel966. The sliding conductive projectile964is launched on the conductive rails961by the application of a high power voltage pulse962to the breech end of the gun967. The projectile964is loaded at the breech and after the application of the applied voltage pulse962acts as an accelerated short circuit termination of a transmission line, traversing the transmission line length represented by the rails961and is then launched from the muzzle end963of the transmission line. Without the capacitance distribution, the electromagnetic propulsion force is simply that provided by the variable length single turn inductor whose length is determined by the position of the slider964along the rails961subjected to the voltage pulse. The distributed discrete capacitances968,969,970conduct displacement currents971that aid the rail currents965to increase the electromagnetic forces (Lorentz Forces) applied to the conductive slider964.

The projectile964accelerates while traveling along length of the barrel966when subjected to a power pulse. This is similar to an electromagnetic wave traveling in a transmission line consisting of uniform distributed inductance and capacitance as a function of position along the length of the gun barrel966. The distributed inductance and capacitance form a characteristic impedance, Zo, that allows a higher level of current, or more electrical power, to be applied to the device, in a quicker time. Thus the electro-mechanical forces in the “rail gun” build faster with distributed capacitance.

The rail gun967is similar in operation to most electro-mechanical devices where a plunger is operated by the application of electro-magnetic power to a coil surrounding the plunger or capsule containing the plunger. Power builds up faster in the electromechanical coil when capacitance is appropriately distributed throughout the coil.

Consequently, magnetic flux density redistributions in the varied conventional inductor and transformer magnetic core constructions are used as examples to illustrate the novel magnetic core construction modifications that may be employed to optimally redistribute magnetic flux density. These inductor and transformer magnetic core construction modifications can be applied to any type of magnetic core in any Electro-magnetic or permanent magnetic device of any size. Further, the core construction modifications can be applied to devices operating from single phase, three-phase, or any poly-phase power supply.

The methods and devices described above for transformers, inductors, or magnetic cores for transformers and inductors may be generally applied to other electro-magnetic and permanent magnetic devices such as motors, generators, relays, and delay lines.

It will be apparent to those skilled in the art that various modifications and variations can be made to the various magnetic flux density redistribution methods and systems, described herein, without departing from the spirit or scope of the novelty. Thus, the various magnetic flux density redistributions, described herein, are not limited by the foregoing descriptions but is intended to cover all modifications and variations that come within the scope of the spirit of the magnetic flux density redistribution schemes and the claims that follow.