Systems and methods for dynamic range enhancement using an open-loop modulator in parallel with a closed-loop modulator
10720888 ยท 2020-07-21
Assignee
Inventors
- Ramin Zanbaghi (Austin, TX)
- Aaron J. Brennan (Austin, TX, US)
- John L. Melanson (Austin, TX)
- Mikel Ash (Austin, TX, US)
Cpc classification
H03F2200/324
ELECTRICITY
H03F3/2175
ELECTRICITY
H03F2200/432
ELECTRICITY
H03F2200/351
ELECTRICITY
H03F1/0277
ELECTRICITY
H03F2200/321
ELECTRICITY
International classification
H03F1/30
ELECTRICITY
H03F1/02
ELECTRICITY
Abstract
An integrated circuit may have two signal paths: an open-loop modulator (which may comprise a digital-input Class-D amplifier) and a closed-loop modulator (which may comprise an analog-input Class-D amplifier). A control subsystem may be capable of selecting either of the open-loop modulator or the closed-loop modulator as a selected path based on one or more characteristics (e.g., signal magnitude) of an input audio signal. For example, for higher-magnitude signals, the closed-loop modulator may be selected while the open-loop modulator may be selected for lower-magnitude signals. In some instances, when the open-loop modulator is selected as the selected path, the closed-loop modulator may power off, which may reduce power consumption. In addition, one or more techniques may be applied to reduce or eliminate user-perceptible audio artifacts caused by switching between the open-loop modulator and the closed-loop modulator, and vice versa.
Claims
1. A system comprising: an open-loop modulator configured to receive an input signal and generate an output signal based on the input signal when the open-loop modulator is selected as a selected path; a closed-loop modulator configured to receive the input signal and generate a closed-loop output signal based on the input signal when the closed-loop modulator is selected as the selected path; and a control subsystem configured to select one of the open-loop modulator and the closed-loop modulator as the selected path based on one or more characteristics of the input signal.
2. The system of claim 1, wherein the open-loop modulator comprises a digital-input Class-D amplifier.
3. The system of claim 1, wherein the closed-loop modulator comprises an analog-input Class-D amplifier.
4. The system of claim 1, wherein the open-loop modulator and the closed-loop modulator each comprise and share: a switched output stage configured to drive an output load with the output signal; and a predriver stage configured to drive one or more predriver signals to the output stage based on the input signal, wherein the output signal is a function of the one or more predriver signals.
5. The system of claim 4, wherein the predriver generates the one or more predriver signals based on a control signal which is a function of the input signal.
6. The system of claim 5, wherein the control signal is a pulse-width modulated signal.
7. The system of claim 1, wherein the input signal is a pulse-width modulated signal.
8. The system of claim 1, wherein the control subsystem is configured to power on the closed-loop modulator for a period of time prior to switching selection of the selected path from the open-loop modulator to the closed-loop modulator.
9. The system of claim 1, wherein the control subsystem is configured to select the selected path based on a magnitude of the input signal.
10. The system of claim 1, wherein the control subsystem is configured to select the selected path based on whether a magnitude of the input signal crosses a threshold value within a period of time after a zero-crossing event of the input signal.
11. The system of claim 10, wherein the control subsystem is configured to: select the closed-loop modulator as the selected path when the magnitude of the input signal crosses above the threshold value within a period of time after a zero-crossing event of the input signal; and select the open-loop modulator as the selected path when the magnitude of the input signal remains below the threshold value within a period of time after a zero-crossing event of the input signal.
12. The system of claim 1, wherein the control subsystem is configured to select the selected path based on a slew rate of the input signal at a zero-crossing event of the input signal.
13. The system of claim 12, wherein the control subsystem is configured to: select the closed-loop modulator as the selected path when a magnitude of the slew rate of the input signal is greater than a threshold slew rate at the zero-crossing; and select the open-loop modulator as the selected path when the magnitude of the slew rate of the input signal is lesser than a threshold slew rate at the zero-crossing.
14. The system of claim 1, wherein the open-loop modulator includes a digital equalization filter configured to match a transfer function of the open-loop modulator to a transfer function of the closed-loop modulator.
15. The system of claim 14, wherein the digital equalization filter may be calibrated in accordance with a calibration operation to match the transfer function of the open-loop modulator to the transfer function of the closed-loop modulator.
16. The system of claim 1, wherein the closed-loop modulator comprises a low-pass filter configured to convert an error signal equal to the difference between the analog version of the input signal and a feedback signal generated by the closed-loop modulator into a filtered error signal.
17. The system of claim 16, wherein the closed-loop modulator further comprises a feedforward path that bypasses the low-pass filter and combines the input signal with the filtered error signal.
18. The system of claim 1, wherein the controller is further configured to power off the closed-loop modulator when the open-loop modulator is the selected path.
19. The system of claim 1, wherein the open-loop modulator is a digital open-loop modulator.
20. The system of claim 1, wherein the closed-loop modulator is an analog closed-loop modulator.
21. The system of claim 1, wherein the control subsystem is configured to: select the closed-loop modulator as the selected path when the magnitude of the input signal is above a threshold value; and select the open-loop modulator as the selected path when the magnitude of the input signal is below the threshold value.
22. A method comprising: selecting one of an open-loop modulator and a closed-loop modulator based on one or more characteristics of an input signal; generating an output signal based on the input signal by the open-loop modulator when the open-loop modulator is selected as a selected path; and generating an output signal based on the input signal by the closed-loop modulator when the closed-loop modulator is selected as a selected path.
23. The method of claim 22, wherein the open-loop modulator comprises a digital-input Class-D amplifier.
24. The method of claim 22, wherein the closed-loop modulator comprises an analog-input Class-D amplifier.
25. The method of claim 22, further comprising: driving an output load with the output signal by a switched output stage shared by the open-loop modulator and the closed-loop modulator; and drive one or more predriver signals to the output stage based on the input signal by a predriver shared the open-loop modulator and the closed-loop modulator, wherein the output signal is a function of the one or more predriver signals.
26. The method of claim 25, further comprising generating the one or more predriver signals based on a control signal which is a function of the input signal.
27. The method of claim 26, wherein the control signal is a pulse-width modulated signal.
28. The method of claim 22, wherein the input signal is a pulse-width modulated signal.
29. The method of claim 22, further comprising powering on the closed-loop Class-D modulator for a period of time prior to switching selection of the selected path from the open-loop modulator to the closed-loop modulator.
30. The method of claim 22, further comprising selecting the selected path based on a magnitude of the input signal.
31. The method of claim 22, further comprising selecting the selected path based on whether a magnitude of the input signal crosses a threshold value within a period of time after a zero-crossing event of the input signal.
32. The method of claim 31, further comprising: selecting the closed-loop modulator as the selected path when the magnitude of the input signal crosses above the threshold value within a period of time after a zero-crossing event of the input signal; and selecting the open-loop modulator as the selected path when the magnitude of the input signal remains below the threshold value within a period of time after a zero-crossing event of the input signal.
33. The method of claim 22, further comprising selecting the selected path based on a slew rate of the input signal at a zero-crossing event of the input signal.
34. The method of claim 33, further comprising: selecting the closed-loop modulator as the selected path when a magnitude of the slew rate of the input signal is greater than a threshold slew rate at the zero-crossing; and selecting the open-loop modulator as the selected path when the magnitude of the slew rate of the input signal is lesser than a threshold slew rate at the zero-crossing.
35. The method of claim 22, further comprising applying a digital equalization filter within the open-loop modulator to match a transfer function of the open-loop modulator to a transfer function of the closed-loop modulator.
36. The method of claim 35, further comprising calibrating the digital equalization filter in accordance with a calibration operation to match the transfer function of the open-loop modulator to the transfer function of the closed-loop modulator.
37. The method of claim 22, further comprising converting by a low-pass filter within the closed-loop modulator an error signal equal to the difference between the analog version of the input signal and a feedback signal generated by the closed-loop modulator into a filtered error signal.
38. The method of claim 37, further comprising bypassing the low-pass filter with a feedforward path that combines the input signal with the filtered error signal.
39. The method of claim 22, further comprising powering off the closed-loop modulator when the open-loop modulator is the selected path.
40. The method of claim 22, wherein the open-loop modulator is a digital open-loop modulator.
41. The method of claim 22, wherein the closed-loop modulator is an analog closed-loop modulator.
42. The method of claim 22, comprising: selecting the closed-loop modulator as the selected path when the magnitude of the input signal is above a threshold value; and selecting the open-loop modulator as the selected path when the magnitude of the input signal is below the threshold value.
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)
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DETAILED DESCRIPTION
(9) In accordance with embodiments of the present disclosure, an integrated circuit for use in an audio device, such as a personal audio device (e.g., mobile telephone, portable music player, tablet computer, personal digital assistant, etc.), may have two parallel signal paths: an open-loop Class-D modulator (which may comprise a digital-input Class-D amplifier) and a closed-loop Class-D modulator (which may comprise an analog-input Class-D amplifier). A control subsystem may be capable of selecting either of the open-loop Class-D modulator or the closed-loop Class-D modulator as a selected path based on one or more characteristics (e.g., signal magnitude) of an input audio signal. For example, for higher-magnitude signals, the closed-loop Class-D modulator may be selected while the open-loop Class-D modulator may be selected for lower-magnitude signals. In some instances, when the open-loop Class-D modulator is selected as the selected path, the closed-loop Class-D modulator may power off, which may reduce power consumption. In addition, one or more techniques may be applied to reduce or eliminate user-perceptible audio artifacts caused by switching between the open-loop Class-D modulator and the closed-loop Class-D modulator, and vice versa.
(10) The integrated circuit described above may be used in any suitable system, device, or apparatus, including without limitation, a personal audio device.
(11)
(12) As shown in
(13) As depicted in
(14) The filtered error signal may be combined with the analog input signal to generate an error-corrected analog input signal that is communicated to analog PWM signal generator 36. Such direct analog feed forward of the analog input signal may provide for relatively fast and memory-less switching when selection is switched from open-loop modulator 22 to closed-loop modulator 24, thus potentially reducing the occurrence of user-perceptible audio artifacts.
(15) Analog PWM signal generator 36 may include any system, device, or apparatus configured to generate a periodic signal V.sub.IN_A having a pulse width which is a function of the magnitude of the error-corrected analog input signal. For example, the pulse width of periodic signal V.sub.IN_A may increase as the magnitude of the error-corrected analog input signal increases, and vice versa.
(16) Common path 26 may include adder/controller 38, predriver 40, and a switched output stage comprising a pull-up driver device 42 (which may be implemented as a p-type metal-oxide-semiconductor field effect transistor in the embodiments represented by
(17) Adder/controller 38 may comprise any system, device, or apparatus configured to add periodic signal V.sub.IN_D output by open-loop modulator 22 to periodic signal V.sub.IN_A output by closed-loop modulator 24 to generate predriver control signal V.sub.IN. In some embodiments, adder/controller 38 may comprise a select input (e.g., communicated from microcontroller core 18) that may selectively mute one of its inputs (e.g., mute either of periodic signal V.sub.IN_D and periodic signal V.sub.IN_A) based on one or more characteristics (e.g., signal magnitude) of digital audio input signal DIG_IN. For example, if the signal magnitude of digital audio input signal DIG_IN is below a threshold magnitude level, adder/controller 38 may mute its input receiving periodic signal V.sub.IN_A from closed-loop modulator 24 such that periodic signal V.sub.IN_D from open-loop modulator 22 passes to the output of adder/controller 38 as predriver control signal V.sub.IN. As another example, if the signal magnitude of digital audio input signal DIG_IN is above the threshold magnitude level, adder/controller 38 may mute its input receiving periodic signal V.sub.IN_D from open-loop modulator 22 such that periodic signal V.sub.IN_A from closed-loop modulator 24 passes to the output of adder/controller 38 as predriver control signal V.sub.IN.
(18) Predriver circuitry 40 may comprise any system, device, or apparatus configured to receive predriver control signal V.sub.IN, which may comprise a pulse-width modulated voltage signal, and apply control logic and/or buffering to such input voltage to drive a pull-up device driving signal voltage V.sub.P to the gate terminal of pull-up driver device 42 and to drive a pull-down device driving signal voltage V.sub.IN to the gate terminal of pull-down driver device 44, wherein pull-up device driving signal voltage V.sub.P and pull-down device driving signal voltage V.sub.N are each a function of predriver control signal V.sub.IN. Based on respective input voltage signals V.sub.P and V.sub.N driven to their respective gates, pull-up driver device 42 and pull-down driver device 44 may drive an output voltage V.sub.OUT to load 46 which is a function of the respective input voltage signals. Accordingly, in those embodiments represented by
(19) Load 46 may include any suitable output load. For example, load 46 may include an audio transducer (e.g., a loudspeaker, earbud speakers 8A and 8B, etc.).
(20) As also shown in
(21) In operation, for lower magnitudes of digital audio input signal DIG_IN (e.g., below a threshold magnitude), signal distribution block 20 may communicate digital audio input signal DIG_IN (or a signal similar thereto) to open-loop modulator 22 and adder/controller 38 may cause periodic signal V.sub.IN_D to pass to its output as predriver control signal V.sub.IN. In some embodiments, signal distribution block 20 may withhold a signal from closed-loop modulator 24, which may serve the purpose of powering off or reducing power consumption of closed-loop modulator 24. In some embodiments, adder/controller 38 may mute its input for receiving periodic signal V.sub.IN_A, although in embodiments in which signal distribution block 20 withholds a signal from closed-loop modulator 24, such muting may not be required. Use of open-loop modulator 22 in generating predriver control signal V.sub.IN for lower magnitudes of digital audio input signal DIG_IN may be preferable as open-loop modulator 22 may have lower distortion and a lower noise floor as compared to closed-loop modulator 24.
(22) On the other hand, for higher magnitudes of digital audio input signal DIG_IN (e.g., above a threshold magnitude), signal distribution block 20 may communicate digital audio input signal DIG_IN (or a signal similar thereto) to closed-loop modulator 24 and adder/controller 38 may cause periodic signal V.sub.IN_A to pass to its output as predriver control signal V.sub.IN. In some embodiments, signal distribution block 20 may withhold a signal from open-loop modulator 22, although in many embodiments signal distribution block 20 may nonetheless communicate digital audio input signal DIG_IN (or a signal similar thereto) to open-loop modulator 22. In some embodiments, adder/controller 38 may mute its input for receiving periodic signal V.sub.IN_D, particularly in those embodiments in which signal distribution block 20 communicates digital audio input signal DIG_IN (or a signal similar thereto) to closed-loop modulator 24. Use of closed-loop modulator 24 in generating predriver control signal V.sub.IN for higher magnitudes of digital audio input signal DIG_IN may be preferable as closed-loop modulator 24 may experience less non-linearity (particularly at higher magnitudes) as compared to open-loop modulator 22 and the higher noise floor of closed-loop modulator 24 compared to that of open-loop modulator 22 may be tolerable for higher signal magnitudes.
(23) Such use of open-loop modulator 22 and closed-loop modulator 24 may increase dynamic range of an audio IC over existing approaches, as lower magnitude signals more susceptible to noise may be processed by open-loop modulator 22 which has greater immunity to noise than closed-loop modulator 24 while higher magnitude signals which are not as susceptible to noise may be processed by closed-loop modulator 24 which may have more desirable transfer characteristics (e.g., greater linearity) at higher magnitudes than that of open-loop modulator 22.
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(25) In audio IC 9A, microcontroller core 18 may communicate digital audio input signal DIG_IN to digital PWM signal generator 30, which communicates a pulse-width modulated signal DIG_PWM to signal distribution block 20. Based on one or more characteristics of digital audio input signal DIG_IN (or a signal similar thereto), signal distribution block 20 may communicate pulse-width modulated signal DIG_PWM (or a signal similar thereto) to one or both of open-loop modulator 22A or closed-loop modulator 24A which is in parallel with open-loop modulator 22A. Any signal communicated to closed-loop modulator 24A may also be communicated to an input of adder/controller 38 as periodic signal V.sub.IN_A.
(26) As shown in
(27) As depicted in
(28) Common path 26A may comprise adder/controller 38 and a variable duty cycle controller 48. Common path 26A may also include a predriver 40, pull-up driver device 42, and pull-down driver device 44 arranged in a manner identical to that of audio IC 9.
(29) Adder/controller 38 may add periodic signal V.sub.IN_D output by open-loop modulator 22A to periodic signal V.sub.IN_A output by closed-loop modulator 24A to generate intermediate predriver control signal V.sub.IN. Variable duty cycle controller 48 may adjust the duty cycle of predriver control signal V.sub.IN based on filtered error signal CTRL in order to generate predriver control signal V.sub.IN, which may be input to predriver 40.
(30) In the topology of audio IC 9A, two channels are used to generate predriver control signal V.sub.IN. The first channel is that of open-loop modulator 22A, used for lower magnitudes of digital audio input signal DIG_IN signals (e.g., those below a threshold magnitude) in which periodic signal V.sub.IN_D may pass substantially unchanged to the output of variable duty cycle controller 48 as predriver control signal V.sub.IN. The second channel is that in which periodic signal V.sub.IN_A may pass to the input of variable duty cycle controller 48 and is modified based on filtered error signal CTRL in order to generate predriver control signal V.sub.IN.
(31) Such use of open-loop modulator 22A and closed-loop modulator 24A may increase dynamic range of an audio IC over existing approaches, as lower magnitude signals more susceptible to noise may be processed by open-loop modulator 22A which has greater immunity to noise than closed-loop modulator 24A while higher magnitude signals which are not as susceptible to noise may be processed by closed-loop modulator 24A which may have more desirable transfer characteristics (e.g., greater linearity) at higher magnitudes than that of open-loop modulator 22A.
(32)
(33) When an open-loop modulator is the selected path (e.g., when a magnitude of digital audio input signal DIG_IN is below a threshold magnitude), its parallel closed-loop modulator may be powered off or powered down, an input signal may be communicated to the open-loop modulator and not the closed-loop modulator, and the output of the open-loop modulator but not the output of the closed-loop modulator may be passed to a switched output stage for driving a load.
(34) At step 52, and while operating with the open-loop modulator as the selected path, microcontroller core 18 may monitor for a trigger for switching the selected path from the open-loop modulator to the closed-loop modulator. Such trigger may include an actual crossing from below to above a threshold magnitude of digital audio input signal DIG_IN, or an indication or prediction that such a threshold crossing is imminent. Once such a trigger occurs, method 50 may proceed to step 54. Otherwise, method 50 may remain at step 52.
(35) At step 54, in response to the trigger, the closed-loop modulator may be powered on, which may include powering on of a low-pass filter (e.g., filter 34 or 34A) of the closed-loop modulator. At step 56, the same input signal may be communicated to both the open-loop modulator and the closed-loop modulator, while adder/controller 38 may continue to mute its input from the closed-loop modulator and pass the output of the open-loop modulator to the switched output stage.
(36) At step 58, microcontroller core 18 may monitor output signal V.sub.OUT and the output of the closed-loop modulator (e.g., periodic signal V.sub.IN_A), to determine if the output of the closed-loop modulator has converged with output signal V.sub.OUT, in order to reduce audio artifacts (e.g., audible pops and clicks) from occurring by switching between the open-loop modulator and the closed-loop modulator. Once converged, method 50 may proceed to step 60. Otherwise, method 50 may remain at step 58 until convergence occurs.
(37) At step 60, adder/controller 38 may mute its input from the open-loop modulator, and pass the output of the closed-loop modulator to the switched output stage. After completion of step 60, method 50 may end.
(38) Although
(39) Method 50 may be implemented using microcontroller core 18, components thereof or any other system such as those shown in
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(41) In operation, at each zero crossing 72, microcontroller core 18 may pre-process audio data that it has received in order to look ahead a time duration of t.sub.pp to determine if digital audio input signal DIG_IN (or a derivative thereof) crosses above a threshold magnitude (e.g., either above threshold +V.sub.th or below threshold V.sub.th) within the time duration t.sub.pp. If microcontroller core 18 determines a threshold crossing 74 occurs within duration t.sub.pp after a zero crossing 72, microcontroller core 18 may select a closed-loop modulator as the selected path. Otherwise, if a threshold crossing 74 does not occur within duration t.sub.pp after a zero crossing 72, microcontroller core 18 may select an open-loop modulator as the selected path. For example, at zero crossing 72A, microcontroller core 18 may determine that digital audio input signal DIG_IN experiences threshold crossings 74A, 74B, and 74C within duration t.sub.pp and thus may select the closed-loop modulator as the selected path (and, if the open-loop modulator was selected prior to zero crossing 72A, switch from the open-loop modulator to the closed-loop modulator as the selected path at zero crossing 72A). As another example, at zero crossing 72C, microcontroller core 18 may determine that digital audio input signal DIG_IN experiences threshold crossings 74E, 74F, 74G, and 74H within duration t.sub.pp and thus may maintain selection of the closed-loop modulator as the selected path. Later, at a zero crossing 72E, microcontroller core 18 may determine that digital audio input signal DIG_IN experiences no threshold crossings within duration t.sub.pp and thus may switch selection of the selected path from the closed-loop modulator to the open-loop modulator. Subsequently, at zero crossing 72G, microcontroller core 18 may determine that digital audio input signal DIG_IN experiences threshold crossings 741, 74J, and 74K within duration t.sub.pp and thus may switch selection of the selected path from the open-loop modulator to the closed-loop modulator.
(42) In certain applications, such as audio ICs utilizing active noise cancellation, pre-processing as described above may not be desirable as the signal time delay imposed by such pre-processing may not be tolerable by the active noise cancellation circuitry. Thus, in some embodiments, rather than determine at zero crossings 72 whether to switch between selected paths, microcontroller core 18 may instead switch the selected path between the open-loop modulator and the closed-loop modulator at threshold crossings 74. Thus, at signal levels between V.sub.th and +V.sub.th, microcontroller core 18 may select the open-loop modulator as the selected path, and may otherwise select the closed-loop modulator as the selected path.
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(45) At step 92, microcontroller core 18 may cause a known direct current (DC) signal to be applied to a closed-loop modulator (e.g., closed-loop modulator 24 or 24A). Microcontroller core 18 may also cause an open-loop modulator (e.g., open-loop modulator 22 or 22A) in parallel with the closed-loop modulator to be inactive or muted so that it does not affect output signal V.sub.OUT during step 92. For example, during step 92, microcontroller core 18 may cause adder/controller 38 to mute its input for receiving the output of the open-loop modulator. At step 94, microcontroller core 18 may sense output signal V.sub.OUT and store an averaged value of output signal V.sub.OUT which is generated in response to the DC input signal applied to the closed-loop modulator.
(46) At step 96, microcontroller core 18 may cause the same known DC signal to be applied to the open-loop modulator. Microcontroller core 18 may also cause the closed-loop modulator to be inactive or muted so that it does not affect output signal V.sub.OUT during step 96. For example, during step 96, microcontroller core 18 may cause adder/controller 38 to mute its input for receiving the output of the closed-loop modulator.
(47) At step 98, microcontroller core 18 may cause modification of response d(z) of the digital equalization filter. Such modification may comprise modifying one or more filter parameters of the digital equalization filter (e.g., filter coefficients, poles, zeroes, etc.). At step 99, microcontroller core 18 may sense output signal V.sub.OUT generated in response to the DC signal applied to the open-loop modulator and compare an average of output signal V.sub.OUT generated in response to the DC signal applied to the open-loop modulator to the value stored at step 94. If the two values approximately match (e.g., within an allowable tolerance or error), the digital equalization filter may be fully calibrated and method 90 may end. Otherwise if the two values do not approximately match, method 90 may proceed again to step 98, and steps 98 and 99 may repeat until the two values approximately match.
(48) Although
(49) Method 90 may be implemented using microcontroller core 18, components thereof or any other system such as those shown in
(50) Although the various systems and methods described herein contemplate reduction of audio artifacts in audio paths of personal audio devices, the systems and methods herein may also apply to any other audio systems, including, without limitation, home audio systems, theaters, automotive audio systems, live performances, etc.
(51) This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the exemplary 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 exemplary 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.
(52) All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the invention 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 inventions 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.