Control of power converter based on dynamic constraint factors

Abstract

A power delivery system may include a power converter configured to electrically couple to a power source and further configured to supply electrical energy to one or more loads electrically coupled to an output of the power converter, and control circuitry configured to select a constraint factor from a plurality of different constraint factors based on at least one of an input voltage to the power converter and a power level available to the power converter, and control the power converter in accordance with the constraint factor.

Claims

1. A portable electronic device, comprising: one or more components; a battery; a power converter configured to electrically couple to and receive power from the battery and further configured to supply electrical energy to the one or more components; and control circuitry configured to: select a constraint factor from a plurality of different constraint factors based on at least one of an input voltage to the power converter and a power level available to the power converter; and control the power converter in accordance with the constraint factor.

2. The portable electronic device of claim 1, wherein the control circuitry is configured to select the constraint factor based on a voltage level available from the battery.

3. The portable electronic device of claim 2, wherein the control circuitry models the voltage level available from the battery as a time-varying voltage source in series with an equivalent resistance.

4. The portable electronic device of claim 2, wherein: a plurality of constraint regions are defined for different ranges of the voltage level available from the battery; and the control circuitry is configured to select the constraint factor based on a constraint region of the plurality of constraint regions corresponding to the voltage level available from the battery.

5. The portable electronic device of claim 4, wherein a first constraint region of the plurality of constraint regions is associated with a first constraint factor which corresponds to a battery-imposed limitation on maximum current.

6. The portable electronic device of claim 5, wherein the first constraint region commences at a critical end-of-discharge voltage for the battery.

7. The portable electronic device of claim 5, wherein the first constraint factor sets a maximum current limit for the power converter defined by: $I_{CELL-MAX}=\frac{V_{CELL-EFF}-V_{C\mathrm{ELL}-\mathrm{MIN}}}{R_0}$ where V.sub.CELL-EFF is an effective battery voltage at a given instance, V.sub.CELL-MIN is the critical end-of-discharge voltage for the battery, and R.sub.0 is an equivalent series resistance of the battery.

8. The portable electronic device of claim 4, wherein a second constraint region of the plurality of constraint regions is associated with a second constraint factor which corresponds to a power converter stability-imposed limitation on maximum current.

9. The portable electronic device of claim 8, wherein the second constraint factor sets a maximum current limit for the power converter defined by: $I_{PMAX}=\frac{V_{CELL-EFF}}{2\left(R_0+R_{TRACE}+R_{SNS}+R_{LOSS}\right)}$ where R.sub.0 is an equivalent series resistance of the battery, R.sub.TRACE is a resistance of a trace and/or connector resistance between the power source and the power converter, R.sub.SNS is a resistance of a current sense resistor, and R.sub.LOSS is a resistance modeling losses of the power converter.

10. The portable electronic device of claim 8, wherein: a first constraint region of the plurality of constraint regions is associated with a first constraint factor which corresponds to a battery-imposed limitation on maximum current; and the second constraint region commences at an intersection of the first constraint factor and the second constraint factor.

11. The portable electronic device of claim 4, wherein a third constraint region of the plurality of constraint regions is associated with a third constraint factor which corresponds to an output-power-based limitation on maximum current.

12. The portable electronic device of claim 11, wherein the third constraint factor sets a maximum current limit for the power converter defined by: $I_{C\mathrm{ELL}-\mathrm{LIM}}=I_{PMAX}-\sqrt{\frac{P_{\mathrm{MAX}}-P_{\mathrm{LIM}}}{R_0+R_{\mathrm{TRACE}}+R_{\mathrm{SNS}}+R_{\mathrm{LOSS}}}}$ where I.sub.pMAX is a maximum current limit as defined for a second constraint factor, P.sub.MAX is a maximum power delivery capability of the power converter, P.sub.LIM is an output power limit defined for the power converter, R.sub.0 is an equivalent series resistance of the battery, R.sub.TRACE is a resistance of a trace and/or connector resistance between the power source and the power converter, R.sub.SNS is a resistance of a current sense resistor, and R.sub.LOSS is a resistance modeling losses of the power converter.

13. The portable electronic device of claim 12, wherein a second constraint region of the plurality of constraint regions is associated with the second constraint factor which corresponds to a power converter stability-imposed limitation on maximum current.

14. The portable electronic device of claim 11, wherein: a second constraint region of the plurality of constraint regions is associated with a second constraint factor which corresponds to a power converter stability-imposed limitation on maximum current; and the third constraint region commences at a breakpoint between the second constraint factor and the third constraint factor.

15. The portable electronic device of claim 4, wherein a fourth constraint region of the plurality of constraint regions is associated with a fourth constraint factor which corresponds to a fixed current limit.

16. The portable electronic device of claim 4, wherein: a second constraint region of the plurality of constraint regions is associated with a second constraint factor which corresponds to a power converter stability-imposed limitation on maximum current; a third constraint region of the plurality of constraint regions is associated with a third constraint factor which corresponds to an output-power-based limitation on maximum current; and a fourth constraint region is located between the second constraint region and the third constraint region.

17. The portable electronic device of claim 4, wherein the plurality of constraint regions includes: a first constraint region associated with a first constraint factor which corresponds to a battery-imposed limitation on maximum current; a second constraint region with a second constraint factor which corresponds to a power converter stability-imposed limitation on maximum current; a third constraint region associated with a third constraint factor which corresponds to an output-power-based limitation on maximum current; and a fourth constraint region associated with a fourth constraint factor which corresponds to a fixed current limit.

18. The portable electronic device of claim 1, wherein the constraint factor defines a current limit to be drawn from the battery.

19. The portable electronic device of claim 1, wherein the one or more components comprise at least one of the following: another power converter, a processor, an audio coder/decoder, an amplifier, and a display device.

20. The portable electronic device of claim 1, wherein the battery comprises a lithium-ion battery.

21. The portable electronic device of claim 1, wherein the power converter is implemented using at least one of a boost converter, buck converter, buck-boost converter, transformer, or charge pump.

22. The portable electronic device of claim 1, wherein the portable electronic device comprises a smart phone, a tablet, or a game controller.

23. A portable electronic device comprising: one or more components; a battery; a power converter configured to electrically couple to and receive power from the battery and further configured to supply electrical energy to the one or more components; and control circuitry configured to: calculate a plurality of current limit values based on at least one of an input voltage to the power converter and a power level available to the power converter; and control the power converter based on a current limit selected as a lowest of the plurality of current limit values.

24. The portable electronic device of claim 23, wherein the one or more components comprise at least one of the following: another power converter, a processor, an audio coder/decoder, an amplifier, a display device.

25. The portable electronic device of claim 23, wherein the battery comprises a lithium-ion battery.

26. The portable electronic device of claim 23, wherein the power converter is implemented using at least one of a boost converter, buck converter, buck-boost converter, transformer, or charge pump.

27. The portable electronic device of claim 23, wherein the portable electronic device comprises a smart phone, a tablet, or a game controller.

28. A power delivery system comprising: a power converter configured to electrically couple to a power source and further configured to supply electrical energy to one or more loads electrically coupled to an output of the power converter; and control circuitry configured to: calculate a plurality of current limit values based on at least one of an input voltage to the power converter and a power level available to the power converter; and control the power converter based on a current limit selected as a lowest of the plurality of current limit values.

29. The power delivery system of claim 28, wherein the one or more loads comprise at least one of the following: another power converter, a processor, an audio coder/decoder, an amplifier, a display device.

30. The power delivery system of claim 28, wherein the power source comprises a battery.

31. The power delivery system of claim 30, wherein the battery comprises a lithium-ion battery.

32. The power delivery system of claim 28, wherein the power converter is implemented using at least one of a boost converter, buck converter, buck-boost converter, transformer, or charge pump.

33. A method comprising, in a power converter configured to electrically couple to a power source and further configured to supply electrical energy to one or more loads electrically coupled to an output of the power converter: calculating a plurality of current limit values based on at least one of an input voltage to the power converter and a power level available to the power converter; and controlling the power converter based on a current limit selected as a lowest of the plurality of current limit values.

34. The method of claim 33, wherein the one or more loads comprise at least one of the following: another power converter, a processor, an audio coder/decoder, an amplifier, a display device.

35. The method of claim 33, wherein the power source comprises a battery.

36. The method of claim 35, wherein the battery comprises a lithium-ion battery.

37. The method of claim 33, wherein the power converter is implemented using at least one of a boost converter, buck converter, buck-boost converter, transformer, or charge pump.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A more complete understanding of the present embodiments and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings, in which like reference numbers indicate like features, and wherein:

(2) FIG. 1 illustrates a block diagram of selected components of a power delivery network, in accordance with embodiments of the present disclosure;

(3) FIG. 2 illustrates an example graph of an open circuit voltage of a battery versus the battery's state of charge, in accordance with embodiments of the present disclosure;

(4) FIG. 3 illustrates a block diagram of selected components of an equivalent circuit model for a battery, in accordance with embodiments of the present disclosure;

(5) FIG. 4 illustrates an example graph of a battery voltage and a battery current versus time associated with a current step drawn from a battery, in accordance with embodiments of the present disclosure;

(6) FIG. 5 illustrates a first-order model of a battery simplified to a time-varying voltage source in series with an equivalent series resistance, in accordance with embodiments of the present disclosure;

(7) FIG. 6 illustrates an example graph of a maximum battery current versus an internal effective battery voltage for battery protection, in accordance with embodiments of the present disclosure;

(8) FIG. 7 illustrates a block diagram of selected impedances within the power delivery network shown in FIG. 1, in accordance with embodiments of the present disclosure;

(9) FIG. 8 illustrates an example graph of an output power of a power converter versus battery current drawn by the power converter, in accordance with embodiments of the present disclosure;

(10) FIG. 9 illustrates an example graph of a maximum battery current versus an internal effective battery voltage for power converter stability, in accordance with embodiments of the present disclosure;

(11) FIG. 10 illustrates an example graph of a maximum battery current versus an internal effective battery voltage for power limit considerations, in accordance with embodiments of the present disclosure; and

(12) FIG. 11 illustrates an example graph of a maximum battery current versus an internal effective battery voltage for current limit considerations, in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

(13) FIG. 1 illustrates a block diagram of selected components of a power delivery network 10, in accordance with embodiments of the present disclosure. In some embodiments, power delivery network 10 may be implemented within a portable electronic device, such as a smart phone, tablet, game controller, and/or other suitable device.

(14) As shown in FIG. 1, power delivery network 10 may include a battery 12 and a power converter 20 configured to convert a battery voltage V.sub.CELL generated by battery 12 into a supply voltage V.sub.SUPPLY used to power a plurality of downstream components 18, wherein each downstream component 18 may draw a respective current I.sub.LOAD1, I.sub.LOAD2, I.sub.LOAD3, etc., from the output of power converter 20, meaning an aggregate load current I.sub.LOAD=I.sub.LOAD1+I.sub.LOAD2+ . . . +I.sub.LOADN may be generated by power converter 20. Power converter 20 may be implemented using a boost converter, buck converter, buck-boost converter, transformer, charge pump, and/or any other suitable power converter. Downstream components 18 of power delivery network 10 may include any suitable functional circuits or devices of power delivery network 10, including without limitation other power converters, processors, audio coder/decoders, amplifiers, display devices, etc.

(15) As shown in FIG. 1, power delivery network 10 may also include control circuitry 30 for controlling operation of power converter 20, including switching and commutation of switches internal to power converter 20. In addition, as described in greater detail below, control circuitry 30 may also implement active protection mechanisms for limiting current I.sub.CELL drawn from battery 12.

(16) As of the filing date of this application, lithium-ion batteries are typically known to operate from 4.2 V down to 3.0 V, known as an open circuit voltage V.sub.OC of the battery (e.g., battery 12). As a battery discharges due to a current drawn from the battery, the state of charge of the battery may also decrease, and open circuit voltage V.sub.OC (which may be a function of state of charge) may also decrease as a result of electrochemical reactions taking place within the battery, as shown in FIG. 2. Outside the range of 3.0 V and 4.2 V for open circuit voltage V.sub.OC, the capacity, life, and safety of a lithium-ion battery may degrade. For example, at approximately 3.0 V, approximately 95% of the energy in a lithium-ion cell may be spent (i.e., state of charge is 5%), and open circuit voltage V.sub.OC would be liable to drop rapidly if further discharge were to continue. Below approximately 2.4V, metal plates of a lithium-ion battery may erode, which may cause higher internal impedance for the battery, lower capacity, and potential short circuit. Thus, to protect a battery (e.g., battery 12) from over-discharging, many portable electronic devices may prevent operation below a predetermined end-of-discharge voltage V.sub.CELL-MIN.

(17) FIG. 3 illustrates a block diagram of selected components of an equivalent circuit model for battery 12, in accordance with embodiments of the present disclosure. As shown in FIG. 3, battery 12 may be modeled as having a battery cell 32 having an open circuit voltage V.sub.OC in series with a plurality of parallel resistive-capacitive sections 34 and further in series with an equivalent series resistance 36 of battery 12, such equivalent series resistance 36 having a resistance of R.sub.0. Resistances R.sub.1, R.sub.2, . . . R.sub.N, and respective capacitances C.sub.1, C.sub.2, . . . , C.sub.N may model battery chemistry-dependent time constants τ.sub.1, τ.sub.2, . . . , τ.sub.N, that may be lumped with open circuit voltage V.sub.OC and equivalent series resistance 36. Notably, an electrical node depicted with voltage V.sub.CELL-EFF in FIG. 3 captures the time varying discharge behavior of battery 12, and battery voltage V.sub.CELL is an actual voltage seen at the output terminals of battery 12. Voltage V.sub.CELL-EFF may not be directly measurable, and thus battery voltage V.sub.CELL may be the only voltage associated with battery 12 that may be measured to evaluate battery state of health. Also of note, at a current draw of zero (e.g., I.sub.CELL=0), battery voltage V.sub.CELL may be equal to voltage V.sub.CELL-EFF which may in turn be equal to an open circuit voltage V.sub.OC at a given state of charge.

(18) FIG. 4 illustrates example graphs of battery voltage V.sub.CELL and battery current I.sub.CELL versus time associated with a current step drawn from battery 12, in accordance with embodiments of the present disclosure. As shown in FIG. 4, in response to a current step event, battery voltage V.sub.CELL may respond to the step, as the response curve for battery voltage V.sub.CELL experiences an initial instantaneous drop (e.g., due to equivalent series resistance 36) and time-dependent voltage drops due to time constants τ.sub.1, τ.sub.2, . . . , τ.sub.N. Open circuit voltage V.sub.OC and the various impedances R.sub.0, R.sub.1, R.sub.2, . . . R.sub.N, may be a function of state of charge of battery 12, thus implying that a transient response to a new, fully-charged battery could be significantly different from that of an aged, partially-discharged battery.

(19) In operation, control circuitry 30 may determine a maximum battery current I.sub.CELL that may be drawn from battery 12 at any given instant based on one or more constraints, including protection of battery 12, stability of power converter 20, and/or limitations associated with practical limitations.

(20) A first constraint that may be imposed by control circuitry 30 is battery-imposed limitations for the maximum of battery current I.sub.CELL. To illustrate application of this constraint, FIG. 5 illustrates a first-order model of battery 12 simplified to a time-varying voltage source 38 with voltage V.sub.CELL-EFF in series with equivalent series resistance 36 having a resistance value of R.sub.0, in accordance with embodiments of the present disclosure. A maximum battery current I.sub.CELL-MAX that battery 12 may be capable of delivering may be directly dependent on equivalent series resistance 36. Battery current I.sub.CELL must pass through equivalent series resistance 36, which may reduce battery voltage V.sub.CELL from voltage V.sub.CELL-EFF by an amount equal to resistance R.sub.0 multiplied by battery current I.sub.CELL (e.g., V.sub.CELL=V.sub.CELL-EFF—R.sub.0I.sub.CELL). Perhaps more significantly, battery current I.sub.CELL flowing through equivalent series resistance 36 may cause power dissipation within battery 12 that is equal to resistance R.sub.0 multiplied by the square of battery current I.sub.CELL (e.g., P=R.sub.0I.sub.CELL.sup.2). At high rates of discharge, battery current I.sub.CELL may lead to significant heating within battery 12. The requirement discussed above that battery voltage V.sub.CELL must remain above end-of-discharge voltage V.sub.CELL-MIN sets a limitation on maximum battery current I.sub.CELL-MAX, as given by:

(21) $I_{CELL-MAX}=\frac{V_{CELL-EFF}-V_{C\mathrm{ELL}-\mathrm{MIN}}}{R_0}$
Accordingly, maximum battery current I.sub.CELL-MAX may be a function of voltage V.sub.CELL-EFF, assuming only battery-imposed limitations, and may be plotted as illustrated by line CON1 shown in FIG. 6.

(22) To enforce such limitation, control circuitry 30 may implement an active protection scheme to ensure that end-of-discharge voltage V.sub.CELL-MIN is not violated, despite transient loads on power converter 20, so as to avoid damage to battery 12. For example, control circuitry 30 may be configured to monitor battery voltage V.sub.CELL at terminals of battery 12 and vary maximum battery current I.sub.CELL-MAX drawn by power converter 20 as shown by constraint CON1 in FIG. 6 in order to ensure battery 12 is not over-discharged to pushed beyond its safe operating range, in order to extend life of battery 12. However, complicating such control of maximum battery current I.sub.CELL-MAX is that the transient response of battery 12 may be a function of multiple time constants (e.g., τ.sub.1, τ.sub.2, . . . , τ.sub.N) as described above, and it may be unfeasible or uneconomical to measure such time constants for a given battery and vary maximum battery current I.sub.CELL-MAX in a feedforward manner Thus, as further described below, control circuitry 30 may implement a negative feedback control loop around power converter 20 that may monitor battery voltage V.sub.CELL and vary maximum battery current I.sub.CELL-MAX to maintain battery voltage V.sub.CELL at a desired target value.

(23) In addition to limiting current to provide for protection of battery 12 as described above, it may also be desirable to limit current to provide stability for power converter 20, in order to operate beyond a maximum power point into a region of instability of power converter 20, as described in greater detail below. To illustrate, reference is made to FIG. 7, which depicts a detailed block diagram of selected impedances within power delivery network 10 shown in FIG. 1, in accordance with embodiments of the present disclosure. As shown in FIG. 7, power delivery network 10 may be modeled with battery 12 as shown in FIG. 5 in series with a trace resistor 52, a current sense resistor 54, an impedance 56 to model equivalent losses in power converter 20, and a load 58 representing the aggregate of downstream devices 18. Trace resistor 52 may have a resistance R.sub.TRACE representing a resistance of electrical conduit between battery 12 and power converter 20 (e.g., a connector, printed circuit board trace, etc.). Sense resistor 54 may have a resistance R.sub.SNS and may be used to sense battery current I.sub.CELL based on a voltage drop across sense resistor 54 and resistance R.sub.SNS in accordance with Ohm's law. Impedance 56 may model losses inside power converter 20 with resistance R.sub.LOSS. After accounting for power losses occurring in these various impedances, power converter 20 may deliver output power P.sub.OUT to load 58, given as:
P.sub.OUT=I.sub.CELLV.sub.CELL-EFF−I.sub.CELL.sup.2R.sub.TOT
where
R.sub.TOT=R.sub.0+R.sub.TRACE+R.sub.SNS+R.sub.LOSS

(24) For a given total resistance R.sub.TOT and given voltage V.sub.CELL-EFF, there may exist a maximum power P.sub.MAX for output power P.sub.OUT of power delivery network 10 as a function of battery current I.sub.CELL that occurs at a current I.sub.PMAX, as shown in FIG. 8, where current I.sub.PMAX may be given by:

(25) $I_{PMAX}=\frac{V_{CELL-EFF}}{2R_{TOT}}$

(26) Thus, it is shown from FIG. 8 that power delivery system 10 will operate with optimum power efficiency and stability if I.sub.CELL<I.sub.PMAX, and will operate in a region of instability (negative slope of output power P.sub.OUT versus battery current I.sub.CELL) when I.sub.CELL>I.sub.PMAX. This maximum allowable current I.sub.PMAX may be plotted as shown in FIG. 9 as constraint CON2 superimposed over constraint CON1 for maximum battery current I.sub.CELL-MAX depicted in FIG. 6. Because total resistance R.sub.TOT is greater than equivalent series resistance R.sub.0, it may be evident that the slope of constraint CON1 is steeper than the slope of constraint CON2. On extrapolation, the line of constraint CON2 may intercept the horizontal axis of voltage V.sub.CELL-EFF at 0 V, which is not shown in FIG. 9, as many batteries (e.g., lithium-ion batteries) will not be allowed to drop to such magnitude.

(27) For high-efficiency power converters, impedance 56 may be negligible compared to equivalent series resistance 36, trace resistor 52, and sense resistor 54, such that total resistance R.sub.TOT may be rewritten as:
R.sub.TOT≈R.sub.0+R.sub.TRACE+R.sub.SNS

(28) As battery 12 is discharged with use, equivalent series resistance 36 may increase and voltage V.sub.CELL-EFF may decrease accordingly. Therefore, maximum allowable current I.sub.PMAX corresponding to maximum power P.sub.MAX may be a function of voltage V.sub.CELL-EFF and impedances of power delivery network 10.

(29) In addition to limiting current to provide for protection of battery 12 as described above, and in addition to limiting current to provide stability for power converter 20 as described above, it may also or alternatively be desirable to limit current based on considerations of practical implementations, as described in greater detail below.

(30) As an example, beyond a certain voltage V.sub.CELL-EFF, the maximum battery current I.sub.CELL, and therefore the maximum power delivery capability P.sub.MAX, of power converter 20 may become so large that the design of power converter 20 becomes increasingly difficult or even unfeasible. Practical limitations such as, for example, inductor saturation current and required dynamic range of current sensing circuitry in power converter 20 may dictate an upper power limit P.sub.LIM be placed on output power P.sub.OUT. Thermal considerations may also need to be taken into consideration and may drive a need to limit maximum power delivery from power converter 20.

(31) Assuming output power P.sub.OUT is limited to power limit P.sub.LIM, a power balance equation for power delivery system 10 may be written as:
I.sub.CELL.sup.2R.sub.TOT−I.sub.CELLV.sub.CELL-EFF+P.sub.LIM=0
which can be rewritten as:

(32) $I_{C\mathrm{ELL}-\mathrm{LIM}}=I_{PMAX}-\sqrt{\frac{P_{MAX}-P_{\mathrm{LIM}}}{R_{TOT}}}$

(33) This maximum allowable current I.sub.CELL-LIM may be plotted as shown in FIG. 10 as constraint CON3A superimposed over constraints CON1 and CON2 depicted in FIG. 9. A separation between two power limited regions for P.sub.MAX and P.sub.LIM are graphically shown in FIG. 10 as occurring at a breakpoint between the curves representing constraints CON2 and CON3A. In the region limited by power limit P.sub.LIM, a maximum for battery current I.sub.CELL may be set by the lower of the two values for maximum allowable current. As is shown in FIG. 10, along the curve for constraint CON3A, the maximum current for battery current I.sub.CELL may increase as voltage V.sub.CELL-EFF decreases.

(34) In addition to limiting current to provide for protection of battery 12 as described above, limiting current to provide stability for power converter 20 as described above, and limiting current for power limiting considerations, it may also or alternatively be desirable to apply a fixed current limit I.sub.FIXED based on considerations of practical implementations, as described in greater detail below. This maximum allowable current I.sub.FIXED may be plotted as shown in FIG. 11 as constraint CON3B superimposed over constraints CON1, CON2, and CON3A depicted in FIG. 10. Thus the maximum current for battery current I.sub.CELL may be set by the lowest of the four values for maximum allowable current.

(35) As used herein, when two or more elements are referred to as “coupled” to one another, such term indicates that such two or more elements are in electronic communication or mechanical communication, as applicable, whether connected indirectly or directly, with or without intervening elements.

(36) This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Similarly, where appropriate, the appended claims encompass all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Moreover, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, or component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative. Accordingly, modifications, additions, or omissions may be made to the systems, apparatuses, and methods described herein without departing from the scope of the disclosure. For example, the components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses disclosed herein may be performed by more, fewer, or other components and the methods described may include more, fewer, or other steps. Additionally, steps may be performed in any suitable order. As used in this document, “each” refers to each member of a set or each member of a subset of a set.

(37) Although exemplary embodiments are illustrated in the figures and described below, the principles of the present disclosure may be implemented using any number of techniques, whether currently known or not. The present disclosure should in no way be limited to the exemplary implementations and techniques illustrated in the drawings and described above.

(38) Unless otherwise specifically noted, articles depicted in the drawings are not necessarily drawn to scale.

(39) All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the disclosure and the concepts contributed by the inventor to furthering the art, and are construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the present disclosure have been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the disclosure.

(40) Although specific advantages have been enumerated above, various embodiments may include some, none, or all of the enumerated advantages. Additionally, other technical advantages may become readily apparent to one of ordinary skill in the art after review of the foregoing figures and description.

(41) To aid the Patent Office and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims or claim elements to invoke 35 U.S.C. § 112(f) unless the words “means for” or “step for” are explicitly used in the particular claim.