COUPLED-INDUCTOR CORE FOR UNBALANCED PHASE CURRENTS

Abstract

An embodiment of a coupled-inductor core includes first and second members and first and second forms extending between the first and second members. The first form has a parameter (e.g., length) of a first value, and is operable to conduct a first magnetic flux having a first density that depends on the first value of the parameter. The second form is spaced apart from the first form, has the parameter (e.g., length) of a second value different from the first value, and is operable to conduct a second magnetic flux having a second density that depends on the second value of the parameter. Because two or more of the forms of such a core may have different values for the same parameter, the core may be suitable for use in a multiphase power supply where the currents through the phases are unbalanced.

Description

SUMMARY

This Summary is provided to introduce, in a simplified form, a selection of concepts that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

An embodiment of a coupled-inductor core includes first and second members and first and second forms extending between members. The first form has a parameter (e.g., length) of a first value, and is operable to conduct a first magnetic flux having a first density that depends on the first value of the parameter. The second form is spaced apart from the first form, has the parameter (e.g., length) of a second value different from the first value, and is operable to conduct a second magnetic flux having a second density that depends on the second value of the parameter.

Because two or more of the forms of such a core may have different values for the same parameter, the core may be suitable for use in a multiphase power supply where the currents through the phases are unequal, i.e., are unbalanced, but the windings disposed about the forms have the same number of turns. As compared to a coupled-inductor assembly—“coupled-inductor assembly” is an assembly that includes the core and the windings—having windings with different numbers of turns, a coupled-inductor assembly having windings with the same number of turns may have at least one winding with less resistance, and thus may be more energy efficient and may generate less heat.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an embodiment of a multiphase buck converter that includes a coupled-inductor assembly.

FIG. 2 is a diagram of switching signals that drive, and balanced currents that flow through, the phase paths of an embodiment of the buck converter of FIG. 1.

FIG. 3 is schematic diagram of an embodiment of a phase-current unbalancing circuit that may compose part of the power-supply controller of FIG. 1.

FIG. 4 is a perspective view of an embodiment of the coupled-inductor assembly of FIG. 1 that has at least two forms with different values for the same form parameter.

FIG. 5 is a magnetic-circuit model of an embodiment of the coupled-inductor assembly of FIG. 4.

FIG. 6 is a simplified magnetic-circuit model of an embodiment of the coupled-inductor assembly of FIG. 4 having two wound forms, a leakage form, and two windings respectively disposed about the two winding forms.

FIG. 7 is a block diagram of an embodiment of a computer system having a multiphase power supply that includes an embodiment of the coupled-inductor assembly of FIG. 4.

FIG. 8 is a perspective view of an embodiment of a portion of the coupled-inductor assembly of FIG. 4.

DETAILED DESCRIPTION

FIG. 1 is a schematic diagram of an embodiment of a multiphase buck converter 10, which includes phase paths (alternatively “phases”) 12₁-12_n and a coupled-inductor assembly 14 having magnetically coupled windings 16₁-16_n, one winding per phase. As discussed below in conjunction with FIGS. 3-6, the assembly 14 may be designed to carry unbalanced phase currents even when the windings 16 carrying these currents have the same number N of turns. This may reduce the resistance of at least one of these windings, and thus may allow the converter 10 to have an increased power efficiency and to generate less heat as compared to a buck converter that incorporates a conventional coupled-inductor assembly having windings with different numbers of turns.

In addition to the coupled-inductor assembly 14, the converter 10 includes a power-supply controller 18, high-side drive transistors 20₁-20_n, low-side drive transistors 22₁-22_n, a filter capacitor 24, and an optional filter inductor 26. A winding 16 and the high-side and low-side transistors 20 and 22 coupled to the winding compose a respective phase 12. For example, the winding 16₁ and transistors 20₁ and 22₁ compose the phase 12₁.

The controller 18 may be any type of controller suitable for use in a buck converter, is supplied by voltages VDD_controller and VSS_controller, and receives the regulated output voltage V_out, a reference voltage V_ref, and feedback signals I_FB1-I_FBn, which are respectively proportional to the phase currents i₁-i_n that flow through the respective phase windings 16₁-16_n. For example, each of these feedback signals I_FB1-I_FBn may be a respective voltage that has substantially the same signal phase as the corresponding phase current i and that has an amplitude proportional to the amplitude of the corresponding phase current, and may be generated by a series coupled resistor and capacitor (not shown in FIG. 1) coupled in electrical parallel with the corresponding winding 16.

The high-side transistors 20₁-20_n, which are each switched “on” and “off” by the controller 18, are power NMOS transistors that are respectively coupled between input voltages VIN₁-VIN_n and the windings 16₁-16_n. Alternatively, the transistors 20₁-20_n may be other than power NMOS transistors, and may be coupled to a common input voltage. Moreover, the transistors 20₁-20_n may be integrated on the same die as the controller 18, may be integrated on a same die that is separate from the die on which the controller is integrated, or may be discrete components.

Similarly, the low-side transistors 22₁-22_n, which are each switched on and off by the controller 18, are power NMOS transistors that are respectively coupled between low-side voltages VL₁-VL_n and the windings 16₁-16_n. Alternatively, the transistors 22₁-22_n may be other than power NMOS transistors, and may be coupled to a common low-side voltage such as ground. Moreover, the transistors 22₁-22_n may be integrated on the same die as the controller 18, may be integrated on a same die that is separate from the die on which the controller is integrated, may be integrated on a same die as the high-side transistors 20₁-20_n, may be integrated on respective dies with the corresponding high-side transistors 20₁-20_n (e.g., transistors 20₁ and 22₁ on a first die, transistors 20₂ and 22₂ on a second die, and so on), or may be discrete components.

The filter capacitor 24 is coupled between V_out and a voltage VSS_cap, and works in concert with the windings 16₁-16₁, and the filter inductor 26 (if present) to maintain the amplitude of the steady-state ripple voltage component of the regulated output voltage V_out within a desired range that may be on the order of hundreds of microvolts to tens of millivolts. Although only one filter capacitor 24 is shown, the converter 10 may include multiple filter capacitors coupled in electrical parallel. Furthermore, VSS_cap may be equal to VSS_controller and to VL₁-VL_n; for example, all of these voltages may equal ground.

As further discussed below, the filter inductor 26 may be omitted if the leakage inductances L_lk1-L_lkn of the windings 16₁-16_n are sufficient to perform the desired inductive filtering function. In some applications, the filter inductor 26 may be omitted to reduce the size and component count of the converter 10.

Each of the windings 16₁-16_n of the coupled-inductor assembly 14 may be modeled as a self inductance L and a resistance DCR. For purposes of discussion, only the model components of the winding 16₁ are discussed, it being understood that the model components of the other windings 16₂-16_n are similar, except for possibly their values.

The self inductance L₁ of the winding 16₁ may be modeled as two zero-resistance inductances: a magnetic-coupling inductance LC₁, and a leakage inductance L_lk1. When a phase current i₁ flows through the winding 16₁, the current generates a magnetic flux. The value of the coupling inductance LC₁ is proportional to the amount of this flux that is coupled to other windings 16₂-16_n, and the value of the leakage inductance L_lk1 is proportional to the amount of the remaining flux, which is not coupled to the other windings 16₂-16_n. In one embodiment, LC₁=LC₂= . . . =LC_n, and L_lk1=L_lk2= . . . =L_lkn, although inequality among the coupling inductances LC, the leakage inductances L_lk, or both LC and L_lk, is contemplated. Furthermore, in an embodiment, the respective magnetic-coupling coefficients between pairs of coupling inductances LC are equal (e.g., a current through LC₁ magnetically induces respective equal currents in LC₂, . . . LC_n), although unequal coupling coefficients are contemplated.

The resistance DCR₁ is the resistance of the winding 16₁ when a constant voltage V is applied across the winding and causes a constant current I to flow through the winding. That is, DCR₁=V/I.

FIG. 2 is a timing diagram of the drive signals PWM1 and PWM2 and the phase currents i₁ and i₂ during steady-state operation of an embodiment of the converter 10 of FIG. 1 having two magnetically coupled phases 16₁ and 16₂, where the phase currents i₁ and i₂ are balanced. The signals, however, may not be drawn to scale.

Because the phase currents i₁ and i₂ are balanced, the maximum A_1max of i₁ substantially equals the maximum A_2max of i₂, the minimum A_1min of i₁ substantially equals the minimum A_2min of i₂, the peak-to-peak amplitude A_1pp substantially equals the peak-to-peak amplitude A_2pp of i₂, and the average A_1avg of i₁ substantially equals the average A_2avg of i₂.

Referring to FIGS. 1-2, an embodiment of the operation of the buck converter 10 is discussed where the converter has only two phases 12₁ and 12₂. In this embodiment, the two phases 12₁ and 12₂ are switched 180° apart at a switching frequency F_sw.

While PWM1 is high (logic 1), the high-side transistor 20₁ is on and the low-side transistor 22₁ is off, and an increasing phase current i₁ flows from VIN₁, through the transistor 20₁, winding 16₁, and filter inductor 26 (if present), and to the capacitor 24 and to a load 28 that is supplied by V_out. This increasing current i₁ generates a magnetic flux that induces a corresponding increase in the current i₂ flowing through the other coupled phase 12₂.

In contrast, while PWM1 is low (logic 0), the high-side transistor 20₁ is off and the low-side transistor 22₁ is on, and the current i₁, which is now decreasing, flows from VL₁, through the transistor 22₁, winding 16₁ and filter inductor 26 (if present), and to the capacitor 24 and to the load 28. The current i₂ also decreases. The currents i₁ and i₂ continue to decrease until PWM2 goes high as discussed below.

Similarly, while PWM2 is high, the high-side transistor 20₂ is on and the low-side transistor 22₂ is off, and an increasing current i₂ flows from VIN₂, through the transistor 20₂, winding 16₂, and filter inductor 26 (if present), and to the capacitor 24 and to the load 28. This increasing current i₂ generates a magnetic flux that induces a corresponding increase in the current i₁ flowing through the phase 12₁.

In contrast, while PWM2 is low, the high-side transistor 20₂ is off and the low-side transistor 22₂ is on, and the current i₂, which is now decreasing, flows from VL₂, through the transistor 22₂, winding 16₂ and filter inductor 26 (if present), and to the capacitor 24 and to the load 28. The current i₁ also decreases. The currents i₁ and i₂ continue to decrease until PWM1 goes high again as discussed above.

The controller 18 compares V_out to V_ref, and controls the duty cycles of PWM1 and PWM2 to maintain a predetermined constant relationship between V_out and V_ref in the steady state, e.g., V_out=2V_ref for example, V_out may be the average or minimum of the output ripple component. For example, as current drawn by the load 28 increases, the controller 18 may increase the on times or otherwise alter the duty cycles of PWM1 and PWM2 to accommodate the increased load current; conversely, as the load current decreases, the controller may decrease the on times or otherwise alter the duty cycles of PWM1 and PWM2 to accommodate the decreased load current. The controller 18 may use a pulse-width-modulation (PWM) technique, a constant-on-time technique, or another technique to control the on and off times of the high-side and low-side transistors 20₁-20₂ and 22₁-22₂.

The controller 18 may also monitor the feedback signals I_FB1 and I_FB2, and adjusts the on times or otherwise adjusts the duty cycles of PWM1 and PWM2 as needed to maintain the balance between the currents i₁ and i₂. That is, the controller 18 adjusts PWM1 and PWM2 so that A_1max, A_1min, A_1pp, and A_1avg stay substantially equal to A_2max, A_2min, A_2pp, and A_2avg respectively. An embodiment of current-balancing circuitry that the controller 18 may include is disclosed in U.S. Pat. No. 6,278,263, which is incorporated by reference.

Because the currents i₁ and i₂ are balanced, the coupled-inductor assembly 14 may be symmetrical such that there is little or no chance of saturating the core (not shown in FIGS. 1-2) of the assembly. That is, the core rung about which the winding 16₁ is wound has the same parameters (e.g., dimensions, reluctance) as the rung about which the winding 16₂ is wound, and the number N₁ of turns of the winding 16₁ is the same as the number N₂ of turns of the winding 16₂. For an ideal, symmetrical assembly 14 carrying balanced currents i₁ and i₂ and having L_lk1=L_lk2=0, the net flux through the core is zero, and thus there is no danger of saturating the core. And even if the assembly 14 is not ideal such that L_lk1 and L_lk2 are non zero, the peak magnitudes of the fluxes flowing through the core may be small enough such that there is little chance of saturating the core.

But still referring to FIGS. 1-2 and as discussed below in conjunction with FIGS. 3-6, one may design the converter 10 so that two or more of the windings 16₁-16_n are able to carry a respective two or more unbalanced currents i₁-i_n. Unbalanced currents i flowing in the phases 12 may be suitable, for example, where the controller 18 may deactivate one or more of the phases 12 under less-than-full load conditions to conserve power. For example, consider a two-phase embodiment of the converter 10 that is designed to provide a steady-state average light load current of 15 Amperes (A), a steady-state average normal-load current of 30 A, and a steady-state average heavy-load current of 45 A. During light-load conditions, the controller 18 activates only the phase 12₁, and causes this phase to provide a 15 A steady-state average current i₁. Similarly, during normal-load conditions, the controller 18 activates only the phase 12₂, and causes this phase to provide a 30 A steady-state average current i₂. And during heavy-load conditions, the controller 18 activates both phases 12₁ and 12₂, and causes these phases to together provide a 45 A steady-state average current (i_avg=15 A and i_2avg=30 A). Although this example discusses only the unbalanced currents i₁ and i₂ having unequal average amplitudes A_avg1 and A_avg2, two phase currents, e.g., the currents i₁ and i₂, may be unbalanced if one or more of A_max, A_min, A_pp, and A_avg of the first current do not substantially equal a respective one or more of A_max, A_min, A_pp, and A_avg of the second current. An embodiment of a circuit for unbalancing phase currents is discussed below in conjunction with FIG. 3.

If the converter 10 is designed for two or more windings 16₁-16_n to carry unbalanced currents, then the core of the coupled-inductor assembly 14 may be designed so that no portion of the assembly's core saturates during operation of the converter.

One technique for preventing saturation of the assembly 14 core is to make the Ni products equal in each of the phases carrying unbalanced currents i; therefore, because the currents i in these phases are unequal, the number of turns N of the respective windings 16 are also unequal.

But this technique may result in one or more of the corresponding windings 16 being longer than, and thus having a greater DCR than, respective windings in a core assembly designed to carry balanced currents i.

Furthermore, because N must be an integer per Maxwell's equations, this technique constrains the unbalanced currents i to be integer multiples of one another.

Still referring to FIGS. 1-2, however, another technique for preventing saturation of the core may reduce the DCR of at least one winding 16 as compared to the previously described technique, and may allow one unbalanced current to be a non-integer multiple of another unbalanced current. In an embodiment of this other technique, portions of the core, such as the rungs about which the windings are wound, have different values of a same parameter, and each of the respective windings 16 carrying the unbalanced currents has a same number N of turns, such that one winding need not be longer than another winding as in the previously described technique. But this technique does contemplate that the respective windings carrying the unbalanced currents may have different numbers N of turns.

Reducing the DCR of one or more of the windings 16₁-16_n may reduce the amount of power (I_rms²·DCR) that the windings (and thus the coupled-inductor assembly 14) consume, and thus may reduce the amount of heat that the windings (and thus the coupled-inductor assembly) generate.

Consequently, a coupled-inductor assembly 14 allowing unbalanced phase currents and having one or more windings with reduced DCRs may allow the converter 10 to be more power efficient and to generate less heat than a converter that has unbalanced phase currents and that includes a coupled-inductor assembly with windings having different numbers of turns.

Furthermore, allowing one unbalanced current to be a non-integer multiple of another unbalanced current may increase the number of applications in which one may use a coupled-inductor power supply such as the converter 10.

Referring again to FIG. 1, alternate embodiments of the buck converter 10 are contemplated. For example, the converter 10 may be modified to generate V_out having a negative value. Furthermore, the converter 10 may include one or more magnetically uncoupled phases as described in previously incorporated U.S. patent application Ser. Nos. 12/136,014 and 12/136,023.

Further descriptions of coupled-inductor power supplies appear in the following references, which are incorporated by reference: Wong et al., Investigating Coupling Inductors In The Interleaved QSW VRM, IEEE 2000, and Park et al., Modeling And Analysis Of Multi-Interphase Transformers For Connecting Power Converters In Parallel, IEEE 1997.

FIG. 3 is a diagram of an embodiment of a current-unbalancing circuit 30, which the controller 18 of FIG. 1 may include to unbalance two or more of the phase currents i₁-i_n of the buck converter 10 of FIG. 1.

The circuit 30 includes an error amplifier 32, a phase-current summer 34, phase-current scalers 36₁-36_n, current-unbalancing summers 38₁-38_n, gain blocks 40₁-40_n, PWM summers 42₁-42_n, and PWM signal generators 44₁-44_n.

The error amplifier 32 generates a control voltage V_EA, which is proportional to the difference between the regulated output voltage V_nut (or a scaled version of V_out) and the reference voltage V_ref. V_EA may be the result of the amplifier 32 low-pass filtering the difference between V_out and V_ref.

The phase-current summer 34 adds the feedback signals I_FB1-I_FBn to generate a signal I_{LOADcalculated}, which is proportional to the actual load current I_LOAD through the load 28 (FIG. 1).

Each of the phase-current scalers 36₁-36_n scales I_{LOADcalculated} by a respective one of the values n/a₁-n/a_n according to the respective phase current to be carried by the respective winding 16, where n is the number of coupled phases 12₁-12_n and where a₁-a_n are respective balancing coefficients.

Each of the current-unbalancing summers 38₁-38_n subtracts from a respective signal I_FB1-I_FBn a scaled signal from a respective one of the scalers 36₁-36_n.

Each of the gain blocks 40₁-40_n multiplies a sum from a respective one of the summers 38₁-38_n by a respective gain value G₁-G_n to generate a respective signal ΔI₁-ΔI_n. The values G₁-G_n may be selected to give specified frequency and error-correction responses to the respective feedback loops formed in part by the summer 34, the scalers 36₁-36_n, the summers 38₁-38_n, and the gain blocks 40₁-40_n. Alternatively, the gain blocks 40₁-40_n may be omitted, which is equivalent to G₁=G₂= . . . =G_n=1.

Each of the summers 42₁-42_n subtracts a respective one of the signals ΔI₁-ΔI_n from V_EA.

Each of the PWM signal generators 44₁-44_n includes a comparator that receives on a non-inverting input node the resulting sum from a respective one of the summers 42₁-42_n, that receives on an inverting input node a respective conventional ramp signal, and that generates on an output node a respective one of the signals PWM1-PWMn. The phases of the ramp signals may be offset in a conventional manner such that the phases of PWM1-PWMn are offset, for example, by 360°/n as discussed above in conjunction with FIG. 2.

Referring to FIGS. 1 and 3, the operation of the unbalancing circuit 30 is described according to an embodiment where the converter 10 includes two phases 12₁-12₂ (n=2), and is designed to generate i₁=3·i₂. In this embodiment, i₁ represents the average current flowing through the phase 12₁ and i₂ represents the average current flowing through the phase 12₂. But in other embodiments, i₁ and i₂ may represent, e.g., the peak, minimum, or rms currents respectively flowing through the phases 12₁ and 12₂.

The “on” portions of PWM1 and PWM2 (e.g., the portions of PWM1 and PWM2 at logic 1 in FIG. 2) are proportional to V_EA. For example, if V_out decreases to less than V_ref, then V_EA tends to increase, and this increase in V_EA tends to increase the lengths of the on portions of PWM1 and PWM2. The increases in the lengths of the on portions of PWM1 and PWM2 increase the on times of the high-side transistors 20₁-20₂, and this tends to cause V_out to increase back toward V_ref. Conversely if V_out increases to more than V_ref, then V_EA tends to decrease, and this reduction in V_EA tends to decrease the lengths of the on portions of PWM1 and PWM2. The decreases in the lengths of the on portions of PWM1 and PWM2 decrease the on times of the high-side transistors 20₁-20₂, and this tends to cause V_out to decrease back toward V_ref.

As described below, the signals ΔI₁-ΔI₂ effectively and respectively adjust the signal V_EA for the phases 12₁-12₂ via the PWM summers 42₁-42_n to set i₁=3·i₂.

When

i ₁=3·i₂  (1)

then

I _FB1=3·I_FB2  (2)

n/a ₁ ·I _{LOADcalculated} =I _FB1  (3)

and

n/a ₂ ·I _{LOADcalculated} =I _FB2  (4)

Also, because n/a₁·I_{LOADcalculated}+n/a₂·I_{LOADcalculated}=I_{LOADcalculated}, then

n/a ₁ +n/a ₂=1.  (5)

Therefore, from equations (2)-(4), one may derive the following:

n/a ₁ ·I _{LOADcalculated}=3·I_FB2=3·n/a₂·I_{LOADcalculated}  (6)

and

a ₂=3a₁.  (7)

And, from equations (5) and (7) and that n=2 in this embodiment, one may derive the following:

a ₁ =a ₂ ·n/(a₂−n)  (8)

a ₁=8/3  (9)

and

a ₂=8.  (10)

Therefore, when I_FB1=3·I_FB2, I_FB1=2/(8/3)=¾·I_{LOADcalculated}, I_FB2=¼·I_{LOADcalculated}, the output of the unbalancing summer 38₁ equals zero, and the output of the unbalancing summer 38₂ equals zero, and the circuit 30 makes no adjustment to the signal V_EA from the error amplifier 32.

But suppose that I_FB1<3·I_FB2, and thus both I_FB1, and i₁ are too low.

Therefore, the difference output of the unbalancing summer 38₁ is negative and the value ΔI₁ is negative, but the inverting input of the PWM summer 42₁ effectively makes ΔI₁ positive, and thus makes the output of the PWM summer 44₁ more positive as compared to the summer output due to V_EA alone. This tends to increase the on portion of PWM1, and thus tends to increase both I_FB1, and i₁.

In contrast, when I_FB1<3·I_FB2, then I_FB2>(I_FB1)/3, and both I_FB2 and i₂ are too high.

Therefore, the difference output of the unbalancing summer 38₂ is positive and the value ΔI₂ is positive, but the inverting input of the PWM summer 42₂ effectively makes ΔI₂ negative, and thus makes the output of the PWM summer 44₂ more negative as compared to the output due to V_EA alone. This tends to decrease the on portion of PWM2, and thus tends to decrease both I_FB2 and i₂.

Consequently, when I_FB1 is too low and I_FB2 is too high, the current unbalancing circuit 30 acts to increase I_FB1 and reduce I_FB2 to the values set by the scalers 36₁-36₂, and thus acts to increase i₁ and reduce i₂ toward i₁=3·i₂. But since the current-unbalancing circuit 30 maintains I_{LOADcalculated} (and thus maintains the actual load current I_LOAD) substantially constant, the unbalancing circuit ideally does not cause V_out to drift out of regulation by causing V_out to increase or decrease relative to V_ref.

In a similar manner, the unbalancing circuit 30 acts to decrease I_FB1 and i₁ and to increase I_FB2 and i₂ to the respective values set by the scalers 36₁-36₂ when I_FB1 and i₁ are too high and I_FB2 and i₂ are too low.

And when I_FB1 and I_FB2 equal the values respectively set by the scalers 36₁ and 36₂ (and thus i₁=3·i₂), the difference signals ΔI₁=ΔI₂=0, and the signal V_EA sets the on portions of PWM1 and PWM2 as if the circuitry generating ΔI₁ and ΔI₂ were not present.

Still referring to FIGS. 1 and 3, the current-unbalancing circuit 30 may operate in a similar manner when the converter 10 includes more than two phases 12, and when the currents i through more than two of these phases are unbalanced.

Referring again to FIG. 3, alternate embodiments of the current-unbalancing circuit 30 are contemplated.

FIG. 4 is a perspective view of an embodiment of the coupled-inductor core assembly 14 of FIG. 1, where the core assembly may be designed for use when two or more of the phases 12₁-12_n of the buck converter 10 of FIG. 1 carry unbalanced currents.

In addition to the windings 16₁-16_n, the core assembly 14 includes a core 50 having winding forms 52₁-52_n and an optional leakage form 53, and members 54 and 56, which interconnect the forms. That is, using a ladder analogy, the forms 52₁-52_n are the rungs of the ladder, and the members 54 and 56 are the rails to which the rungs are connected. Spaces 58₁-58_n are located between the forms 52₁-52_n and 54.

Each winding 16₁-16_n is formed from a respective conductor 60₁-60_n, which has a respective width W₁-W_n, and each conductor 60₁-60_n is wound, in a Faraday's law sense, N₁-N_n turns about a respective form 52₁-52 extends beneath and adjacent to the remaining forms. For example, the winding 16₁ is formed from a conductor 60₁ that is wound N₁=1 turn about the form 52₁ and extends beneath and adjacent to the remaining forms 52₂-52_n. Although the conductor 60₁ is adjacent to only three sides of the form 52₁, the current i₁ through the conductor 60₁ traverses a closed loop through which the form 52₁ passes. The portions of this closed loop other than the conductor 60₁ may be formed, e.g., by a conductive trace on a circuit board on which the core assembly 14 is disposed. Therefore, N₁ is the integer number of closed loops through which the form 52₁ extends. Similarly, the winding 16₂ is formed from a conductor 60₂ that is wound N₂=1 turn about the form 52₂ and extends beneath and adjacent to the remaining forms 52₁ and 52₃-52_n, and so on. The conductors 60₁-60_n may be made from any suitable conductive material such as copper or another metal, and may, but need not be, electrically insulated from the forms 52₁-52_n.

Each form 52₁-52_n and 53 has a respective length I₁-I_n and I_lk, a respective permeability μ1-μ_n and μ_lk, and a respective cross-sectional area A₁-A_n and A_lk. Although some of these like parameters (e.g., the lengths I₁-I_n and I_lk) are shown as being equal in FIG. 4, some or all of these like parameters may have different values. Furthermore, some or all of the permeabilities μ₁-μ_n and μ_lk may be made to be different by forming the respective forms 52 from different materials. Moreover, an optional gap 62 (e.g., an air gap) may be disposed in the leakage form 53 to adjust the reluctance thereof. Alternatively, the optional gap 62 may be distributed throughout the material from which the leakage form 53 is made.

Referring to FIGS. 1 and 4, the operation of the coupled-inductor assembly 14 is generally described when a current i₁ flows through the conductor 60₁ in the direction shown, it being understood that the operation is similar when a current flows through the other conductors 60₂-60_n. For purposes of example, it is assumed that the coupled-inductor assembly 14 is mounted to a printed circuit board such that the forms 52₂-52_n do not pass inside the loop(s) composed in part by the conductor 60₁.

As the current i₁ flows through the conductive loop composed in part by the conductor 60₁, it generates a total magnetic flux φ_T. In a first-order approximation, a first portion φ₁ of the total flux φ_T flows through the form 52₁, and a second portion φ_out of the total flux φ_T flows outside of the form 52₁ such that φ_T is given by the following equation:

φ_T=φ₁+φ_out  (11)

The first flux portion φ₁ flows through the remaining forms 52₂-52_n and 53 such that the sum of the fluxes φ₂-φ_n and φ_lk flowing through each of the remaining forms equals φ₁. Because the portion of φ₁ that equals φ₂+φ₃+ . . . +φ_n flows through the forms 52₂-52_n about which the conductors 60₂-60_n are wound, this portion of φ₁ is called the coupling flux. The portion φ₂-φ_n of the coupling flux φ₁ induce respective currents to flow in the conductors 60₂-60_n. As discussed further below in conjunction with FIGS. 5-6, the specific values of the fluxes φ₁-φ_n depend on the reluctances R₁-R_n and R_lk of the forms 52₁-52_n and 53.

And the remaining flux equal to the sum φ_out+φ_lk is called the total leakage flux, because it does not induce any currents to flow in the conductors 60₂-60_n. Where φ_out<<φ_lk, then the total leakage flux may be approximated as φ_lk. As discussed further below in conjunction with FIGS. 5-6, the specific value of the flux φ_lk depends on the reluctances R₁-R_n and R_lk of the forms 52₁-52_n and 53.

Referring again to FIG. 4, each portion of the core 50 has a respective maximum flux density B above which that portion of the core will magnetically saturate.

For known reasons that are omitted for brevity, it may be desirable to run a power supply like the buck converter 10 of FIG. 1 such that no portion of the core 50 saturates when the phases 12₁-12_n carry the respective currents i₁-i_n that they are designed to carry.

An embodiment of a technique for designing the core 50 and the core-assembly 14 so that no portion of the core saturates under expected operating conditions is discussed below in conjunction with FIGS. 5-6. For reasons discussed above in conjunction with FIG. 1, this embodiment may allow N₁≠N₂≠ . . . ≠N_n.

FIG. 5 is an embodiment of an equivalent magnetic circuit 70 of the core-assembly 14 of FIG. 4. R₁-R_n and R_lk are the respective reluctances of the forms 52₁-52_n and 53 of FIG. 4, R₁₂-R_(n-1)n and R_nk are the respective reluctances of the portions of the member 54 between adjacent pairs of the forms, and R₂₁-R_n(n-1) and R_kn are the respective reluctances of the portions of the member 56 between adjacent pairs of the forms. For example, R₁₂ is the reluctance of the portion of the member 54 between the forms 52₁ and 52₂, R₂₃ is the reluctance of the portion of the member 54 between the forms 52₂ and 52₃, and so on. Similarly, R₂₁ is the reluctance of the portion of the member 56 between the forms 52₂ and 52₁, R₃₂ is the reluctance of the portion of the member 56 between the forms 52₃ and 52₂, and so on. Also, the directions of the fluxes φ₂-φ_n have been reversed relative to their directions in FIG. 4 for purposes of mathematical convention that may simplify mathematical calculations that use the circuit model 70. Furthermore, the model 70 may ignore the leakage flux φ_out if φ_out<<φ_lk, or may include the contribution of φ_out in φ_lk.

FIG. 6 is an embodiment of an equivalent magnetic circuit 80 of the core-assembly 14 of FIG. 4 for a two-phase embodiment (n=2) of the buck converter 10 of FIG. 1. In this embodiment, it is assumed that the reluctances of the members 54 and 56 are much less (for example, at least ten times less) than each of the reluctances R₁-R₂ and R_lk; therefore, the reluctances of the members 54 and 56 are approximated as zero in the magnetic circuit 80, thus further simplifying the circuit 80 as compared to the circuit 70 of FIG. 5. Furthermore, the circuit model 80 includes the contribution of φ_out (FIG. 4) in φ_lk by including in R_lk the reluctance of the path traversed by φ_out (this also assumes that φ_out is the same for i₁ and i₂). Moreover, it is assumed that the maximum flux densities of the leakage form 53 and the members 54 and 56 are large enough so that if the forms 52₁ and 52₂ do not saturate, then the leakage form and the members do not saturate. For example, this assumption may hold true where the leakage form 53 includes the gap 62 (FIG. 4) and the cross-sectional areas of the forms 54 and 56 are significantly larger than the cross-sectional areas A₁ and A₂ of the forms 52₁ and 52₂.

φ₁ and φ₂ of the model circuit 80 may be given by the following:

$\begin{array}{cc}{\varphi }_1=\frac{N_1\left(R_2+R_{\mathrm{lk}}\right)i_1-N_2R_{\mathrm{lk}}i_2}{R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}}& \left(12\right)\\ {\varphi }_2=\frac{-N_1R_{\mathrm{lk}}i_1+N_2\left(R_1+R_{\mathrm{lk}}\right)i_2}{R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}}& \left(13\right)\end{array}$

And R₁, R₂, and R_lk are given by the following:

$\begin{array}{cc}{R}_1=\frac{l_1}{{\mu }_1A_1}& \left(14\right)\\ R_2=\frac{l_2}{{\mu }_2A_2}& \left(15\right)\\ R_{\mathrm{lk}}=\frac{l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}A_{\mathrm{lk}}}& \left(16\right)\end{array}$

Furthermore, the flux densities B₁ and B₂ through the forms 52₁ and 52₂ are given by the following:

$\begin{array}{cc}{B}_1=\frac{{\varphi }_1}{A_1}& \left(17\right)\\ B_2=\frac{{\varphi }_2}{A_2}& \left(18\right)\end{array}$

Therefore, to prevent saturation of the forms 52₁ and 52₂ (and thus to prevent saturation of all portions of the core 50 in this example), one may designs the core 50 according to the following:

B ₁ <B _1max  (19)

B ₂ <B _2max  (20)

where B₁max is the maximum flux density that the form 52₁ is able to conduct without saturating, and B_2max is the maximum flux density that the form 52₂ is able to conduct without saturating. One may determine B_1max and B_2max in a conventional manner. For example, one may determine B_1max and B_2max from μ₁ and μ₂, or retrieve B_1max and B_2max from a table based on the respective materials from which the forms 52₁ and 52₂ are made.

Referring to FIGS. 4 and 6, an example procedure for designing a two-phase embodiment of the coupled-inductor assembly 14 using the circuit model 80 is described. In this example,

i ₁ =m·i ₂  (21)

where m may be any positive number.

From equations (12)-(21), one may derive the following expressions of the respective flux densities φ₁ and φ₂ in the forms 52₁ and 52₂ of the core 14, where φ₁ and φ₂ do not saturate the respective forms 52₁ and 52₂ or any other part of the core 50 in this example:

$\begin{array}{cc}{B}_1=\frac{{\varphi }_1}{A_1}=\frac{i_1}{R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}}·\hspace{1em}\left[N_1·\frac{l_2}{{\mu }_2A_1A_2}+\left(N_1-\frac{N_2}{m}\right)·\frac{l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}A_1\mathrm{Ak}}\right]<B_{1\mathrm{ma}x}& \left(22\right)\\ B_2=\frac{{\varphi }_2}{A_2}=\frac{i_1}{R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}}·\hspace{1em}\left[\frac{N_2}{m}·\frac{l_1}{{\mu }_1A_1A_2}+\left(\frac{N_2}{m}-N_1\right)·\frac{l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}A_2A_{\mathrm{lk}}}\right]<B_{2\mathrm{ma}x}& \left(23\right)\end{array}$

In this design example, the following equalities are also assumed:

μ₁=μ₂=μ  (24)

B _1max =B _2max =B _max  (25)

A ₁ =A ₂ =A _k =A  (26)

N ₁ =N ₂ =N  (27)

m=3  (28)

From equations (22)-(26), one may derive the following expressions for B₁ and B₂:

$\begin{array}{cc}{B}_1=\frac{{\varphi }_1}{A_1}=\frac{i_1N}{3A^2\left(R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}\right)}·\left[\frac{3l_2}{\mu }+\frac{2l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}}\right]<B_{\mathrm{ma}x}& \left(27\right)\\ B_2=\frac{{\varphi }_2}{A_{2}}=\frac{i_1N}{3A^2\left(R_1R_2+R_1R_{\mathrm{lk}}+R_2R_{\mathrm{lk}}\right)}·\left[\frac{l_1}{\mu }-\frac{2l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}}\right]<B_{\mathrm{ma}x}& \left(28\right)\end{array}$

Then, for a specified value for i₁, a designer may select values for A, N, μ, μ_lk, I₁, I₂, and I_1k such that equations (27) and (28) are true. Furthermore, to set B₁ equal to B₂, the designer may select the values for μ, μ_lk, I₁, I₂, and I_lk according to the following equation, which is derived from equations (27) and (28):

$\begin{array}{cc}\frac{3l_2}{\mu }+\frac{2l_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}}=\frac{l_1}{\mu }-\frac{2_{\mathrm{lk}}}{{\mu }_{\mathrm{lk}}}& \left(29\right)\end{array}$

Furthermore, in this example, although the coupled-inductor assembly 14 is designed for the windings 16₁ and 16₂ to carry unbalanced currents i₁ and i₂, the windings have the same number of turns N. Moreover, unlike the number of turns N, the variable m is not constrained to only integer values.

Appendix A includes additional mathematical expressions that are derived from the circuit model 80 of FIG. 6 and that may be useful in designing the coupled-inductor assembly 14 and a power supply such as the buck converter 10 (FIG. 1).

Still referring to FIGS. 4 and 6, other embodiments of the coupled-inductor assembly 14 and the above-described procedure for designing the assembly are contemplated. For example, the design procedure may be extrapolated to design a coupled-inductor assembly having more than two coupled phase 12, and having fewer or more than one leakage form. Furthermore, one may use the circuit model 70 of FIG. 5 to design the assembly 14 by modifying the design equations accordingly. Moreover, one may develop design equations similar to those described above to mathematically demonstrate that other portions of the core 50 (e.g., the members 54 and 56 and the leakage form 53) do not saturate in a specified application. Also, in addition to the coupled forms 52₁-52_n, the coupled-inductor assembly 14 may include uncoupled forms as discussed in U.S. patent application Ser. Nos. 12/136,014 and 12/136,023, which are incorporated by reference. Furthermore, instead of or in addition to the leakage form 53, the core assembly 14 may include a leakage plate as described in U.S. patent application Ser. No. 11/903,185, which is incorporated by reference.

FIG. 7 is a block diagram of a system 90 (here a computer system), which may incorporate a multiphase power supply 92 (such as the buck converter 10 of FIG. 1) that generates unbalanced phase currents and that includes an embodiment of the coupled-inductor assembly 14 of FIG. 4.

The system 90 includes computer circuitry 94 for performing computer functions, such as executing software to perform desired calculations and tasks. The circuitry 94 typically includes a controller, processor, or one or more other integrated circuits (ICs) 96, and the power supply 92, which provides power to the IC(s) 96. One or more input devices 98, such as a keyboard or a mouse, are coupled to the computer circuitry 94 and allow an operator (not shown) to manually input data thereto. One or more output devices 100 are coupled to the computer circuitry 94 to provide to the operator data generated by the computer circuitry. Examples of such output devices 100 include a printer and a video display unit. One or more data-storage devices 102 are coupled to the computer circuitry 94 to store data on or retrieve data from external storage media (not shown). Examples of the storage devices 102 and the corresponding storage media include drives that accept hard and floppy disks, tape cassettes, compact disk read-only memories (CD-ROMs), and digital-versatile disks (DVDs).

FIG. 8 is a view of a portion of the coupled-inductor assembly 14 of FIG. 4, according to an embodiment.

Referring to FIG. 8, an embodiment of the operation of the coupled-inductor assembly 14 is generally described when unbalanced currents i₁, i₂, and i₃—in this example, unbalanced currents means that at least one of the currents is not equal to at least one of the other currents—respectively flow through the windings 16₁, 16₂, and 16₃ in the respective directions shown, it being understood that the operation is similar when respective currents flow through other groups of one or more windings 16. For example purposes, it is assumed that the coupled-inductor assembly 14 is mounted to a printed circuit board such that the forms 52₁-52_n do not pass inside the loop(s) composed in part by windings 16 that are not associated with a respective form. For example, the form 52₁ passes inside only the loop composed in part by the winding 16₁, the form 52₂ passes inside only the loop composed in part by the winding 16₂, the form 52₃ passes inside only the loop composed in part by the winding 16₃, etc. Further for example purposes, it is assumed that there are no forms other than forms 52₁-52₃.

As the current i₁ flows through the conductive loop composed in part by the winding 16₁, it generates a total magnetic flux φ_7-1. In a first-order approximation, a first portion φ_1,1 of the total flux φ_T1 flows through the form 52₁, and a second portion φ_out1 (not shown in FIG. 8) of the total flux φ_T1 flows outside of the form 52₁ such that φ_T1 is given by the following equation:

φ_T1=φ_1,1+φ_out1  (30)

The first flux portion φ_1,1 flows through the remaining forms 52₂-52₃ such that the sum of the fluxes φ_1,2 and φ_1,3 respectively flowing through each of the remaining forms equals φ_1,1. Because the portion φ_1,1 that equals φ_1,2+φ_1,3 flows through the forms 52₂-52₃ about which the windings 16₂-16₃ are wound, this portion φ_1,1 is called the coupling flux. The portions φ_1,2 and φ_1,3 of the coupling flux φ_1,1 induce respective currents (these induced currents are not shown in FIG. 8) to flow in the conductors 60₂-60₃.

Furthermore, as the current i₂ flows through the conductive loop composed in part by the winding 16₂, it generates a total magnetic flux φ_T2. In a first-order approximation, a first portion φ_2,2 of the total flux φ_T2 flows through the form 52₂, and a second portion φ_out2 (not shown in FIG. 8) of the total flux φ_T2 flows outside of the form 52₂ such that φ_T2 is given by the following equation:

φ_T2=φ_2,2+φ_out2  (31)

The first flux portion φ_2,2 flows through the remaining forms 52₁ and 52₃ such that the sum of the fluxes φ_2,1 and φ_2,3 respectively flowing through each of the remaining forms equals φ_2,2. Because the portion φ_2,2 that equals φ_2,1+φ_2,3 flows through the forms 52₁ and 52₃ about which the windings 16₁ and 16₃ are wound, this portion φ_2,2 is called the coupling flux. The portions φ_2,1 and φ_2,3 of the coupling flux φ_2,2 induce respective currents (these induced currents are not shown in FIG. 8) to flow in the conductors 60₁ and 60₃.

Similarly, as the current i₃ flows through the conductive loop composed in part by the winding 16₃, it generates a total magnetic flux φ_T3. In a first-order approximation, a first portion φ_3,3 of the total flux φ_T3 flows through the form 52₃, and a second portion φ_out3 (not shown in FIG. 8) of the total flux φ_T3 flows outside of the form 52₃ such that φ_T3 is given by the following equation:

φ_T3=φ_3,3+φ_out3  (32)

The first flux portion φ_3,3 flows through the remaining forms 52₁ and 52₂ such that the sum of the fluxes φ_3,1 and φ_3,2 flowing through each of the remaining forms equals φ_3,3. Because the portion φ_3,3 that equals φ_3,1+φ_3,2 flows through the forms 52₁ and 52₂ about which the windings 16₁-16₂ are wound, this portion φ_3,3 is called the coupling flux. The portions φ_3,1 and φ_3,2 of the coupling flux φ_3,3 induce respective currents to flow in the conductors 60₁ and 60₂.

In the above-described example, the form 52₁ has a parameter (e.g., permeability, reluctance, or area as described above in conjunction with FIGS. 4-6) of a first value, and is configured to conduct a first magnetic flux given by the following equation:

φ_{52_1}=φ_1,1−φ_2,1−φ_3,1  (33)

Flux φ_{52_1} has a density B_{52_1} that depends on the first value of the parameter as described above in conjunction with FIG. 6.

Furthermore, as evident from equation (33), φ_{52_1} is a combination (e.g., a sum) of a second magnetic flux φ_1,1 flowing through the form 52₁ in a direction (e.g., bottom-to-top in FIG. 8) and a third magnetic flux −(φ₂+φ_3,1) simultaneously flowing through the form 52₁ in an opposite direction (e.g., top-to-bottom in FIG. 8).

Furthermore, the form 52₂ has the same parameter (e.g., permeability, reluctance, or area as described above in conjunction with FIGS. 4-6) as the form 52₁ but of a second value that is different from the first value, and is configured to conduct a fourth magnetic flux given by the following equation:

φ_{52_2}=φ_2,2−φ_1,2−φ_3,2  (34)

Flux φ_{52_2} has a density B_{52_2} that depends on the second value of the parameter as described above in conjunction with FIG. 6.

Furthermore, as evident from equation (34), φ_{52_2} is a combination (e.g., a sum) of a fifth magnetic flux φ_2,2 flowing through the form 52₂ in a direction (e.g., bottom-to-top in FIG. 8) and a sixth magnetic flux −(φ_1,2+φ_3,2) simultaneously flowing through the form 52₂ in an opposite direction (e.g., top-to-bottom in FIG. 8).

And the form 52₃ has the same parameter (e.g., permeability, reluctance, or area as described above in conjunction with FIGS. 4-6) as the forms 52₁ and 52₂ but of a third value that may be the same as, or different than, or both of the first and second values, and is configured to conduct a seventh magnetic flux given by the following equation:

φ_{52_3}=φ_3,3−φ_1,3−φ_2,3  (35)

Flux φ_{52_3} has a density B_{52_3} that depends on the third value of the parameter as described above in conjunction with FIG. 6.

Furthermore, as evident from equation (35), φ_{52_2} is a combination (e.g., a sum) of an eighth magnetic flux φ_3,3 flowing through the form 52₃ in a direction (e.g., bottom-to-top in FIG. 8) and a ninth magnetic flux −(φ_1,3+φ_2,3) simultaneously flowing through the form 52₃ in an opposite direction (e.g., top-to-bottom in FIG. 8).

From the foregoing it will be appreciated that, although specific embodiments have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. Furthermore, where an alternative is disclosed for a particular embodiment, this alternative may also apply to other embodiments even if not specifically stated.

APPENDIX A

The following are mathematical expressions for parameters of a two-phase embodiment of the coupled-inductor core assembly 14 of FIGS. 1 and 4. These expressions have been derived using the magnetic circuit model 80 of FIG. 6.

L₁=Lc₁+L_lk1 is the self inductance of the winding 16₁.

L₂=Lc₂+L_lk2 is the self inductance of the winding 16₂.

L_m=Lc₁=Lc₂ is the coupling inductance between the windings 16₁ and 16₂.

L_lk1 is the leakage inductance of the winding 16₁, and is defined in terms of the portion of the self flux L₁i₁ that flows through the leakage form 53 when i₁=1 A.

L_lk2 is the leakage inductance of the winding 16₂, and is defined in terms of the portion of the self flux L₂i₂ that flows through the leakage form 53 when i₂=1 A.

R₁ is the reluctance of the form 52₁.

R₂ is the reluctance of the form 52₂.

R_lk is the reluctance of the leakage form 53.

A₁ is the cross-sectional area of the form 52₁.

A₂ is the cross-sectional area of the form 52₂.

A_lk is the cross-sectional area of the form 53.

μ₁ is the permeability of the form 52₁.

μ₂ is the permeability of the form 52₂.

μ₃ is the permeability of the form 53.

$L_1=\frac{N_1^2\left(R_2+R_k\right)}{R_1R_2+R_1R_k+R_2R_k}$ $L_2=\frac{N_2^2\left(R_1+R_k\right)}{R_1R_2+R_1R_k+R_2R_k}$ $L_m=\frac{N_1N_2R_k}{R_1R_2+R_1R_k+R_2R_k}$ $L_{k1}=\frac{N_1^2R_2}{R_1R_2+R_1R_k+R_2R_k}$ $L_{k2}=\frac{N_2^2R_1}{R_1R_2+R_1R_k+R_2R_k}$ $R_1=\frac{l_1}{{\mu }_{m1}·A_1}$ $R_2=\frac{l_2}{{\mu }_{m2}·A_2}$ $R_k=\frac{l_k}{{\mu }_kA_k}$

Special Examples

			If core and
			winding
If Leakage rung	If core structure	If winding structure	structures are
has no air gap	is symmetrical	is symmetrical	both symmetrical
(Rk = 0)	(R1 = R2)	(N1 = N2)	(R1 = R2, N1 = N2)
$L_1=\frac{N_1^2}{R_1}$	$L_1=\frac{2N_1^2}{R_1+2R_k}$	$L_1=\frac{N_1^2\left(R_2+R_k\right)}{R_1R_2+R_1R_k+R_2R_k}$	$L_1=\frac{2N_1^2}{R_1+2R_k}$
$L_{2}=\frac{N_2^2}{R_2}$	$L_2=\frac{2N_2^2}{R_1+2R_k}$	$L_2=\frac{N_1^2\left(R_1+R_k\right)}{R_1R_2+R_1R_k+R_2R_k}$	$L_2=\frac{2N_1^2}{R_1+2R_k}$
Lm = 0	$L_m=\frac{N_1N_2R_k}{R_1^2+2R_1R_k}$	$L_m=\frac{N_1^2R_k}{R_1R_2+R_1R_k+R_2R_k}$	$L_m=\frac{N_1^2R_k}{R_1^2+2R_1R_k}$
$L_{k1}=\frac{N_1^2}{R_1}$	$L_{k1}=\frac{N_1^2}{R_1+2R_k}$	$L_{k1}=\frac{N_1^2R_2}{R_1R_2+R_1R_k+R_2R_k}$	$L_{k1}=\frac{N_1^2}{R_1+2R_k}$
$L_{k2}=\frac{N_2^2}{R_2}$	$L_{k2}=\frac{N_2^2}{R_1+2R_k}$	$L_{k2}=\frac{N_1^2R_1}{R_1R_2+R_1R_k+R_2R_k}$	$L_{k2}=\frac{N_1^2}{R_1+2R_k}$

Claims

1.-21. (canceled)

22. A method, comprising: driving a magnetizing first current through a first conductor and into an output node during a first period, the first conductor wrapped around a first form of a core, the magnetizing first current having a first magnitude and generating a first magnetic flux through the first form, the first form having a first characteristic of a first value, a density of the first magnetic flux flowing through the form depending on the characteristic; anddirecting a first portion of the first magnetic flux through a second form of the core, the first portion of the flux causing an induced second current to flow through a second conductor and into the output node, the second conductor wrapped around the second form of the core, the induced second current having a second magnitude, the second form having the characteristic of a second value that is different from the first value.

23. The method of claim 22, further comprising directing a second portion of the magnetic flux through a third form of the core about which is wrapped no current-carrying conductor.

24. The method of claim 22, further comprising directing a second portion of the magnetic flux through a third form of the core about which is wrapped no current-carrying conductor, the third form having the first characteristic of a third value.

25. The method of claim 22, further comprising directing a second portion of the magnetic flux through a third form of the core about which is wrapped no current-carrying conductor, the third form having a second characteristic of a value that is different than values of the second characteristic for the first and second forms.

26. The method of claim 22, further comprising: driving a magnetizing second current through the second conductor and into the output node during a second period, the magnetizing second current having a third magnitude and generating a second magnetic flux through the second form, a density of the second magnetic flux flowing through the second form depending on the characteristic; anddirecting a first portion of the second magnetic flux through the first form of the core, the first portion of the second flux causing an induced first current to flow through the first conductor and into the output node, the induced first current having a fourth magnitude.

27. The method of claim 26 wherein: the third magnitude is substantially equal to the first magnitude; andthe fourth magnitude is substantially equal to the second magnitude.

28. A method, comprising: driving a magnetizing first current having a first magnitude through a first winding and into an output node during a first period, the first winding having a number of turns; anddriving a magnetizing second current having a second magnitude through a second winding and into the output node during a second period, the second winding having the number of turns and being magnetically coupled to the first winding.

29. The method of claim 28 wherein: the first winding is wound about a first form of a core, the magnetizing first current generating a first magnetic flux through the first form, the first form having a characteristic of a first value, a density of the magnetic flux flowing through the form depending on the characteristic; andthe second winding is wound about a second form of the core, the magnetizing second current generating a second magnetic flux through the second form, the second form having the characteristic of a second value, a density of the magnetic flux flowing through the second form depending on the characteristic.

30. The method of claim 22 wherein the first characteristic includes a length.

31. The method of claim 22 wherein the first characteristic includes a cross-sectional area.

32. The method of claim 22 wherein the first characteristic includes a magnetic permeability.

33. The method of claim 29 wherein the characteristic includes a length.

34. The method of claim 29 wherein the characteristic includes a cross-sectional area.

35. The method of claim 29 wherein the characteristic includes a magnetic permeability.