Abstract:
A controller may predict an estimated occurrence of a high-resistance state of a dimmer, wherein the high-resistance state occurs when the dimmer begins phase-cutting an alternating current voltage signal. The controller may also be configured to operate in a trailing-edge exposure mode for a period of time wherein the period of time includes a time of the estimated occurrence of the high-resistance state in order to allow the controller to detect the occurrence of the high-resistance state, wherein energy is transferred from an input to a dissipative element during the trailing-edge exposure mode. The controller may further be configured to minimize a time between a beginning of the period of time and the estimated occurrence of the high-resistance state by modifying the period of time based on an estimated charging time of a capacitor of the dimmer.

Description:
RELATED APPLICATIONS 
       [0001]    The present disclosure claims priority to U.S. Provisional Patent Application Ser. No. 61/980,954, filed Apr. 17, 2014, which is incorporated by reference herein in its entirety. 
     
    
     FIELD OF DISCLOSURE 
       [0002]    The present disclosure relates in general to the field of electronics, and more specifically to systems and methods for ensuring compatibility between one or more low-power lamps and the power infrastructure to which they are coupled. 
       BACKGROUND 
       [0003]    Many electronic systems include circuits, such as switching power converters or transformers that interface with a dimmer. The interfacing circuits deliver power to a load in accordance with the dimming level set by the dimmer. For example, in a lighting system, dimmers provide an input signal to a lighting system. The input signal represents a dimming level that causes the lighting system to adjust power delivered to a lamp, and, thus, depending on the dimming level, increase or decrease the brightness of the lamp. Many different types of dimmers exist. In general, dimmers generate an output signal in which a portion of an alternating current (“AC”) input signal is removed or zeroed out. For example, some analog-based dimmers utilize a triode for alternating current (“triac”) device to modulate a phase angle of each cycle of an alternating current supply voltage. This modulation of the phase angle of the supply voltage is also commonly referred to as “phase cutting” the supply voltage. Phase cutting the supply voltage reduces the average power supplied to a load, such as a lighting system, and thereby controls the energy provided to the load. A particular type of phase-cutting dimmer is known as a trailing-edge dimmer. A trailing-edge dimmer phase cuts from the end of an AC cycle, such that during the phase-cut angle, the dimmer is “off” and supplies no output voltage to its load, but is “on” before the phase-cut angle and in an ideal case passes a waveform proportional to its input voltage to its load. 
         [0004]      FIG. 1  depicts a lighting system  100  that includes a trailing-edge, phase-cut dimmer  102  and a lamp  142 .  FIG. 2  depicts example voltage and current graphs associated with lighting system  100 . Referring to  FIGS. 1 and 2 , lighting system  100  receives an AC supply voltage V SUPPLY  from voltage supply  104 . The supply voltage V SUPPLY , indicated by voltage waveform  200 , is, for example, a nominally 60 Hz/110 V line voltage in the United States of America or a nominally 50 Hz/220 V line voltage in Europe. Trailing edge dimmer  102  phase cuts trailing edges, such as trailing edges  202  and  204 , of each half cycle of supply voltage V SUPPLY . Since each half cycle of supply voltage V SUPPLY  is 180 degrees of the supply voltage V SUPPLY , the trailing edge dimmer  102  phase cuts the supply voltage V SUPPLY  at an angle greater than 0 degrees and less than 180 degrees. The phase cut, input voltage V Φ     —     DIM  to lamp  142  represents a dimming level that causes the lighting system  100  to adjust power delivered to lamp  142 , and, thus, depending on the dimming level, increase or decrease the brightness of lamp  142 . 
         [0005]    Dimmer  102  includes a timer controller  110  that generates dimmer control signal DCS to control a duty cycle of switch  112 . The duty cycle of switch  112  is a pulse width (e.g., times t 1 −t 0 ) divided by a period of the dimmer control signal (e.g., times t 3 −t 0 ) for each cycle of the dimmer control signal DCS. Timer controller  110  converts a desired dimming level into the duty cycle for switch  112 . The duty cycle of the dimmer control signal DCS is decreased for lower dimming levels (i.e., higher brightness for lamp  142 ) and increased for higher dimming levels. During a pulse (e.g., pulse  206  and pulse  208 ) of the dimmer control signal DCS, switch  112  conducts (i.e., is “on”), and dimmer  102  enters a low resistance state. In the low resistance state of dimmer  102 , the resistance of switch  112  is, for example, less than or equal to 10 ohms. During the low resistance state of switch  112 , the phase cut, input voltage V Φ     —     Dim  tracks the input supply voltage V SUPPLY  and dimmer  102  transfers a dimmer current i DIM  to lamp  142 . 
         [0006]    When timer controller  110  causes the pulse  206  of dimmer control signal DCS to end, dimmer control signal DCS turns switch  112  off, which causes dimmer  102  to enter a high resistance state (i.e., turns off). In the high resistance state of dimmer  102 , the resistance of switch  112  is, for example, greater than 1 megaohm. Dimmer  102  includes a capacitor  114 , which charges to the supply voltage V SUPPLY  during each pulse of the dimmer control signal DCS. In both the high and low resistance states of dimmer  102 , the capacitor  114  remains connected across switch  112 . When switch  112  is off and dimmer  102  enters the high resistance state, the voltage V C  across capacitor  114  increases (e.g., between times t 1  and t 2  and between times t 4  and t 5 ). The rate of increase is a function of the amount of capacitance C of capacitor  114  and the input impedance of lamp  142 . If effective input resistance of lamp  142  is low enough, it permits a high enough value of the dimmer current i DIM  to allow the phase cut, input voltage V Φ     —     DIM  to decay to a zero crossing (e.g., at times t 2  and t 5 ) before the next pulse of the dimmer control signal DCS. 
         [0007]    Dimming a light source with dimmers saves energy when operating a light source and also allows a user to adjust the intensity of the light source to a desired level. However, conventional dimmers, such as a trailing-edge dimmer, that are designed for use with resistive loads, such as incandescent light bulbs, often do not perform well when supplying a raw, phase modulated signal to a reactive load such as a power converter or transformer, as is discussed in greater detail below. 
         [0008]      FIG. 3  depicts a lighting system  100  that includes a lamp assembly  142  with controller  112  for providing compatibility between a low-power lamp comprising LEDs  132  and other elements of lighting system  100 , as is known in the art. As shown in  FIG. 3 , lighting system  100  may include a voltage supply  104 , a dimmer  102 , and a lamp assembly  142 . Voltage supply  104  may generate a supply voltage V SUPPLY  that is, for example, a nominally 60 Hz/110 V line voltage in the United States of America or a nominally 50 Hz/220 V line voltage in Europe. 
         [0009]    Dimmer  102  may comprise any system, device, or apparatus for generating a dimming signal to other elements of lighting system  100 , the dimming signal representing a dimming level that causes lighting system  100  to adjust power delivered to a lamp, and, thus, depending on the dimming level, increase or decrease the brightness of lamp assembly  142 . Thus, dimmer  102  may include a trailing-edge dimmer similar to that depicted in  FIG. 1 , or any other suitable dimmer. 
         [0010]    Lamp assembly  142  may comprise any system, device, or apparatus for converting electrical energy (e.g., delivered by dimmer  102 ) into photonic energy (e.g., at LEDs  132 ). For example, lamp assembly  142  may comprise a multifaceted reflector form factor (e.g., an MR16 form factor) with a lamp comprising LEDs  132 . As shown in  FIG. 3 , lamp assembly  142  may include a bridge rectifier  134 , a power converter  136 , a load capacitor  154 , a controller  112 , and a dissipative network comprising a resistor  122  and switch  124 . 
         [0011]    Bridge rectifier  134  may comprise any suitable electrical or electronic device as is known in the art for converting the whole of alternating current voltage signal V Φ     —     DIM  into a rectified voltage signal v REC  having only one polarity. 
         [0012]    Power converter  136  may comprise any system, device, or apparatus configured to convert an input voltage (e.g., v REC ) to a different output voltage (e.g., v OUT ) wherein the conversion is based on a control signal (e.g., a pulse-width modulated control signal communicated from controller  112 ). Accordingly, power converter  136  may comprise a boost converter, a buck converter, a boost-buck converter, or other suitable power converter. 
         [0013]    Output capacitor  154  may comprise any system, device, or apparatus to store energy in an electric field. Output capacitor  154  may be configured such that it stores energy generated by power converter  136  in the form of the voltage v OUT . 
         [0014]    LEDs  132  may comprise one or more light-emitting diodes configured to emit photonic energy in an amount based on the voltage v OUT  across the LEDs  132 . 
         [0015]    Controller  112  may comprise any system, device, or apparatus configured to determine one or more characteristics of voltage v REC  present at the input of power converter  136  and control an amount of current i REC  drawn by power converter  136  or dissipated through resistor  122  based on such one or more characteristics of voltage v REC . 
         [0016]    A typical trailing-edge dimmer often requires a low-impedance input path when its dimmer switch (e.g., switch  112 ) opens. This low impedance path allows it to charge an internal capacitor (e.g., capacitor  114 ) of the trailing-edge dimmer, and thus to also appear to an LED lamp as a trailing-edge dimmer. In addition, such low impedance path may “expose” the trailing edge of the dimmer of a controller (e.g., controller  112 ), such that the controller may detect occurrence of the trailing edge in order to operate lamp assembly  142  in a desired manner. Accordingly, in lighting system  100 , controller  112  may be configured to enable (e.g., activate, close, turn on, etc.) switch  124  via signal ENABLE to apply a low-impedance path comprising resistor  122  during a period of time proximate in time to the trailing edge in order to provide such required low impedance at the trailing edge. However, such low impedance cannot be applied all of the time, as it may result in high power dissipation in lamp assembly  142  compared to its wattage rating. 
         [0017]    Although not depicted in  FIG. 3 , in some embodiments, a lighting system  100  may include a transformer (e.g., an electronic transformer) coupled between dimmer  102  and lamp assembly  142 . 
         [0018]      FIGS. 4A and 4B  illustrate example voltage and current graphs associated with lighting system  100  shown in  FIG. 3 , and depicts traditional approaches to providing a low impedance to a trailing-edge dimmer at the trailing-edge of the dimmer. In such approaches, switch  124  may be enabled, as shown in waveform  402  for enable signal ENABLE, for a period of time ending at an estimated end of the conduction angle at time t end  of the trailing-edge dimmer and beginning at a fixed time offset t offset  from time t end . The time t end  may be estimated by determining when rectified voltage signal v REC  crosses below a predetermined threshold voltage V T . Accordingly, the low impedance of the dissipation network comprising resistor  122  and switch  124  is not turned on at all times. However, different trailing-edge dimmers may have different capacitances of their charging capacitors  114 . Thus, the fixed offset t offset  must typically be set for a dimmer with the largest charging capacitor capacitance supported by a lamp assembly, as a fall time of the trailing edge of rectified voltage signal v REC  is directly proportional to dimmer capacitance. Thus, while these existing approaches may minimize power dissipation in resistor  122  when a lamp assembly  142  is coupled to a dimmer  102  having a large charging capacitor capacitance, such existing approaches may lead to high power dissipation in resistor  122  when a lamp assembly  142  is coupled to a dimmer  102  having a smaller charging capacitor capacitance. For example, in lighting systems  100  having a dimmer  102  with a relatively small capacitance ( FIG. 4A ) the time period t overlap1  in which enable signal ENABLE may overlap with the conduction period of dimmer  102  (e.g., periods t cond ) may be larger than an analogous time period t overlap2  in lighting systems  100  having a dimmer  102  with a larger capacitance ( FIG. 4B ), potentially resulting in higher power dissipation in lamp assembly  142  when coupled to a dimmer  102  with smaller capacitance. 
       SUMMARY 
       [0019]    In accordance with the teachings of the present disclosure, certain disadvantages and problems associated with ensuring compatibility of a low-power lamp with a dimmer and a transformer may be reduced or eliminated. 
         [0020]    In accordance with embodiments of the present disclosure, a controller may provide compatibility between a load and a trailing-edge dimmer, and may be configured to predict based on an input signal received at an input coupled to the load an estimated occurrence of a high-resistance state of a trailing-edge dimmer coupled to load, wherein the high-resistance state occurs when the trailing-edge dimmer begins phase-cutting an alternating current voltage signal. The controller may also be configured to operate in a trailing-edge exposure mode for a period of time wherein the period of time includes a time of the estimated occurrence of the high-resistance state in order to allow the controller to detect the occurrence of the high-resistance state, wherein energy is transferred from the input to a dissipative element during the trailing-edge exposure mode. The controller may further be configured to minimize a time between a beginning of the period of time and the estimated occurrence of the high-resistance state by estimating a charging time of a capacitor of the trailing-edge dimmer and modifying the period of time based on the charging time. 
         [0021]    In accordance with these and other embodiments of the present disclosure, a method for providing compatibility between a load and a trailing-edge dimmer coupled to the load may include predicting based on an input signal received at an input coupled to the load an estimated occurrence of a high-resistance state of the trailing-edge, wherein the high-resistance state occurs when the trailing-edge dimmer begins phase-cutting an alternating current voltage signal. The method may also include operating in a trailing-edge exposure mode for a period of time wherein the period of time includes a time of the estimated occurrence of the high-resistance state in order to allow the controller to detect the occurrence of the high-resistance state, wherein energy is transferred from the input to a dissipative element during the trailing-edge exposure mode. The method may further include minimizing a time between a beginning of the period of time and the estimated occurrence of the high-resistance state by estimating a charging time of a capacitor of the trailing-edge dimmer and modifying the period of time based on the charging time. 
         [0022]    Technical advantages of the present disclosure may be readily apparent to one of ordinary skill in the art from the figures, description and claims included herein. The objects and advantages of the embodiments will be realized and achieved at least by the elements, features, and combinations particularly pointed out in the claims. 
         [0023]    It is to be understood that both the foregoing general description and the following detailed description are examples and explanatory and are not restrictive of the claims set forth in this disclosure. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]    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: 
           [0025]      FIG. 1  illustrates a lighting system that includes a phase-cut trailing-edge dimmer, as is known in the art; 
           [0026]      FIG. 2  illustrates example voltage and current graphs associated with the lighting system depicted in  FIG. 1 , as is known in the art; 
           [0027]      FIG. 3  illustrates a lighting system that includes a phase-cut trailing-edge dimmer, as is known in the art; 
           [0028]      FIGS. 4A and 4B  illustrate example voltage and current graphs associated with the lighting system depicted in  FIG. 3 , as is known in the art; 
           [0029]      FIG. 5  illustrates an example lighting system including a controller for providing compatibility between a low-power lamp and an electronic transformer driven by a trailing-edge dimmer, in accordance with embodiments of the present disclosure; 
           [0030]      FIG. 6  illustrates example voltage and current graphs associated with embodiments of the lighting system depicted in  FIG. 5 , in accordance with embodiments of the present disclosure; 
           [0031]      FIG. 7  illustrates selected components of a trailing-edge enable signal control circuit of a controller for the lighting system depicted in  FIG. 5 , in accordance with embodiments of the present disclosure; and 
           [0032]      FIG. 8  illustrates example voltage graphs associated with embodiments of the trailing-edge enable signal control circuit depicted in  FIG. 7 , in accordance with embodiments of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0033]      FIG. 5  illustrates an example lighting system  500  including a controller  512  for providing compatibility between a low-power lamp assembly  542  and other elements of a lighting system including a dimmer  502 , in accordance with embodiments of the present disclosure.  FIG. 6  depicts example voltage and current graphs associated with lighting system  500  depicted in  FIG. 5 , in accordance with embodiments of the present disclosure. As shown in  FIG. 5 , lighting system  500  may include a voltage supply  504 , a dimmer  502 , and a lamp assembly  542 . Voltage supply  504  may generate a supply voltage V SUPPLY  that is, for example, a nominally 60 Hz/110 V line voltage in the United States of America or a nominally 50 Hz/220 V line voltage in Europe. 
         [0034]    Dimmer  502  may comprise any system, device, or apparatus for generating a dimming signal to other elements of lighting system  500 , the dimming signal representing a dimming level that causes lighting system  500  to adjust power delivered to a lamp, and, thus, depending on the dimming level, increase or decrease the brightness of lamp assembly  542 . Thus, dimmer  502  may include a trailing-edge dimmer similar to that depicted in  FIGS. 1 and 3 , or any other suitable dimmer. 
         [0035]    Lamp assembly  542  may comprise any system, device, or apparatus for converting electrical energy (e.g., delivered by dimmer  502 ) into photonic energy (e.g., at LEDs  532 ). In some embodiments, lamp assembly  542  may comprise a multifaceted reflector form factor (e.g., an MR16 form factor). In these and other embodiments, lamp assembly  542  may comprise an LED lamp. As shown in  FIG. 5 , lamp assembly  542  may include a bridge rectifier  534 , a power converter  536 , a load capacitor  554 , a controller  512 , and a dissipative network comprising a resistor  522  and a switch  524 . 
         [0036]    Bridge rectifier  534  may comprise any suitable electrical or electronic device as is known in the art for converting the whole of alternating current voltage signal V Φ     —     DIM  into a rectified voltage signal v REC  having only one polarity. 
         [0037]    Power converter  536  may comprise any system, device, or apparatus configured to convert an input voltage (e.g., v REC ) to a different output voltage (e.g., v OUT ) wherein the conversion is based on a control signal (e.g., a pulse-width modulated control signal communicated from controller  512 ). Accordingly, power converter  536  may comprise a boost converter, a buck converter, a boost-buck converter, or other suitable power converter. 
         [0038]    Output capacitor  554  may comprise any system, device, or apparatus to store energy in an electric field. Output capacitor  554  may be configured such that it stores energy generated by power converter  536  in the form of the voltage v OUT . 
         [0039]    LEDs  532  may comprise one or more light-emitting diodes configured to emit photonic energy in an amount based on the voltage v OUT  across the LEDs  532 . 
         [0040]    Controller  512  may comprise any system, device, or apparatus configured to, as described in greater detail elsewhere in this disclosure, determine one or more characteristics of voltage v REC  present at the input of power converter  536  and control an amount of current i REC  drawn by power converter  536  based on such one or more characteristics of voltage v REC . Operation of controller  512  may be described by reference to  FIG. 6 . 
         [0041]    In operation, controller  512  may receive and analyze the rectified V REC  to determine one or more characteristics of the rectified voltage V REC . For example, controller  512  may be configured to detect an estimated occurrence of a beginning (occurring at time t A ) of the half line cycle of the supply voltage V SUPPLY  and dimmer voltage V Φ     —     DIM . For example, the estimated occurrence of the beginning of the half-line cycle of supply voltage V SUPPLY  of dimmer  502  may be predicted by determining when dimmer voltage V Φ     —     DIM  increases above some predetermined threshold voltage, and estimating the beginning of the half-line cycle based on such determination. As another example, controller  512  may be configured to detect an estimated occurrence of a negative edge of the V REC  waveform occurring at time t D  during each half-line cycle corresponding to the trailing edge of output signal V Φ     —     DIM  of dimmer  502  (e.g., the estimated occurrence of the high-resistance state of dimmer  502 ). The estimated occurrence of the trailing edge/high-resistance state of dimmer  502  may be predicted in any suitable manner, for example, using systems and methods disclosed in U.S. patent application Ser. No. 13/298,002 filed Nov. 16, 2011 and entitled “Trailing Edge Dimmer Compatibility with Dimmer High Resistance Prediction,” which is incorporated in its entirety herein for all purposes. Alternatively, the estimated occurrence of the trailing edge/high-resistance state of dimmer  502  may be predicted by determining when dimmer voltage V Φ     —     DIM  decreases below some predetermined threshold voltage, and estimating the trailing edge/high-resistance state of dimmer  502  based on such determination. 
         [0042]    From such determination of the estimated occurrences of the beginning of a half-line cycle, the negative edge, and/or other parameters of the signal present on the input of lamp assembly  542 , controller  512  may determine the estimated half-line cycle of supply voltage V SUPPLY  (e.g., based on the difference between successive estimated occurrences of the beginning of the half-line cycle, negative edge or other parameters), the estimated phase angle of dimmer  502  (e.g., based on the difference between an estimated occurrence of the beginning of the half-line cycle and an estimated occurrence of a subsequent negative edge), and/or other characteristics of the rectified voltage V REC . Thus, during each half-line cycle, controller  512  may use characteristics determined during the previous half-line cycle to control operation of lamp assembly  542 . 
         [0043]    Based on one or more of the characteristics of the rectified voltage V REC  described above, controller  512  may sequentially operate power converter  536  in a plurality of modes. For example, in some instances, controller  512  may operate sequentially in a high-current power mode (during the period labeled as “POWER” in  FIG. 6 ), a low-current idle mode (during the period labeled as “IDLE” in  FIG. 6 ), a low-impedance trailing-edge exposure mode (during the period labeled as “EXPOSE TE” in  FIG. 6 ), and a low-impedance glue mode (during the period labeled as “GLUE” in  FIG. 6 ), as described in greater detail below. 
         [0044]    For example, from approximately the estimated occurrence of the beginning of the half-line cycle at time t A  to a subsequent time t B , controller  512  may operate in a high-current power mode in which it enables power converter  536 , allowing power converter  536  to draw a substantially non-zero current I REC  such that energy is transferred from the input of lamp assembly  542  to LEDs  532 . A duration of the power mode (e.g., t B −t A ) may be based on the estimated phase angle of dimmer  502  determined by controller  512 . 
         [0045]    Following the power mode, controller  512  may enter a low-current idle mode from time t B  to time t C  in which it disables power converter  536  such that substantially no energy is delivered from the input of lamp assembly  542  to output capacitor  554 . 
         [0046]    Following the idle mode, controller  512  may enter a high-current trailing-edge exposure mode in which it enables switch  524  via enable signal ENABLE from time t C  to time t E  to allow controller  512  to detect the negative edge and allow lamp assembly  542  to provide a low input impedance to dimmer  502  via resistor  522 . The time t C  may occur at a period of time before a predicted occurrence of the negative edge (based on the determination of the estimated occurrence of the negative edge from the previous half-line cycle) and time t E  may occur at the detection of the estimated occurrence of the negative edge at time t D . In some embodiments, during the trailing-edge exposure mode, power converter  536  may draw a substantially non-zero current (in addition to or in lieu of dissipation of energy via resistor  522  and switch  524 ) such that energy is transferred from the input of lamp assembly  542  to output capacitor  554 , which may also allow controller  512  to detect the negative edge and allow lamp assembly  542  provide a low input impedance to dimmer  502 . In these and other embodiments, controller  512  may enable the dissipative network of resistor  522  and switch  524 , such that resistor  522  provides all or part of the low-impedance path during the trailing-edge exposure mode. In these and other embodiments, controller  512  may control the cumulative durations of the power mode and the trailing-edge exposure mode such that the power delivered from the input of lamp assembly  542  to LEDs  532  in each half-line cycle is commensurate with the control setting and phase-cut angle of dimmer  502 . 
         [0047]    Following the trailing-edge exposure mode, from time t E  to the beginning of the subsequent power mode at time t A  (e.g., at the estimated occurrence of the beginning of a subsequent half-line cycle), controller  512  may enter a low-impedance glue mode in which it continues to enable power converter  536 , but substantially zero current I REC  is delivered to power converter  536 , on account of the phase cut of dimmer  502  and a substantially zero voltage V REC . The glue mode may apply a low impedance to the input of lamp assembly  542 , thus allowing discharge of any residual energy stored in lighting system  500 . After glue mode, controller  512  may again enter the power mode. 
         [0048]      FIG. 7  illustrates selected components of a trailing-edge enable signal control circuit  700  of controller  512 , in accordance with embodiments of the present disclosure.  FIG. 8  illustrates example voltage graphs  800  associated with embodiments of trailing-edge enable signal control circuit  700  depicted in  FIG. 7 , in accordance with embodiments of the present disclosure. As shown in  FIG. 7 , control circuit  700  may comprise a dual comparator  701 , a state machine  702 , a timer  703 , a switch driver  704 , a multiplier calculator  705 , a multiplier  706 , and a summer  707 . Dual comparator  701  may comprise any system, device, or apparatus configured to determine whether rectified voltage signal v REC  is above or below a first predetermined threshold voltage V THRESH     —     HIGH  and determine whether rectified voltage signal v REC  is above or below a second predetermined threshold voltage V THRESH     —     LOW  which is lesser than first predetermined threshold voltage V THRESH     —     HIGH . Based on these determinations, state machine  702  may be configured to estimate a phase angle ANGLE of dimmer  502 , a partial fall time T FALL ′ of the rectified voltage signal v REC  during a trailing edge, and/or a time T LINE     —     HI  within each half-line cycle of rectified voltage signal v REC  in which the rectified voltage signal v REC  remains above first predetermined threshold voltage V THRESH     —     HIGH  (e.g., which may approximate a conduction period t cond  of dimmer  502 ). For example, the phase angle ANGLE may be determined by dividing time T LINE     —     HI  of a previous half-line cycle by a duration of time between the two most recent crossings of rectified voltage signal v REC  from below to above first predetermined threshold voltage V THRESH     —     HIGH . As another example, partial fall time t FALL ′ may be estimated as a period of time between a previous crossing of rectified voltage signal v REC  from above to below second predetermined threshold voltage V THRESH     —     LOW  and a previous crossing of rectified voltage signal v REC  from above to below first predetermined threshold voltage V THRESH     —     HIGH . Such partial fall time t FALL ′ may be a function of a capacitance of a charging capacitor present in dimmer  502 . 
         [0049]    It is noted that the value of partial fall time t FALL ′ will include only a portion of the actual fall time of rectified voltage signal v REC . The actual fall time is a multiplicative factor K multiplied by partial fall time t FALL ′, wherein multiplicative factor K is a function of the phase angle ANGLE. For example, for medium values of phase angle ANGLE (e.g., 50% conduction), multiplicative factor K may be higher than for lower or higher values of phase angle PHASE (e.g., 10% conduction, 90% conduction). Thus, based on a phase angle estimated by state machine  702 , multiplier calculator  705  may calculate multiplicative factor K. In some embodiments, multiplier calculator  705  may calculate multiplicative factor K with a polynomial function, for example, with an equation K(ANGLE)=A×ANGLE 2 +B×ANGLE+C, where coefficients A, B, and C may be programmable by a user or set based on characterization and testing of a lamp assembly  542 . 
         [0050]    Multiplier  706  may estimate a time offset t offset  equal to multiplicative factor K multiplied by partial fall time t FALL ′, such that time offset t offset  is approximately equal to an actual fall time of rectified voltage signal v REC  and thus serves as an estimate of the actual fall time. Such actual fall time may also approximate a charging time of a charging capacitor of dimmer  502 , such that time offset t offset  serves as an estimate of the actual fall time charging time of such charging capacitor of dimmer  502 . 
         [0051]    Summer  707  may subtract time offset t offset  from time T LINE     —     HI , with such resulting time duration being output to a timer  703 . Timer  703  may be configured to start/initialize upon rectified voltage signal v REC  rising from below to above first predetermined threshold voltage V THRESH     —     HIGH  and once started, times the duration T LINE     —     HI −t offset . Between expiration of timer  703  and its subsequent initialization, timer  703  may assert signal SWITCH_ON which in turn enables switch driver  704  to assert the enable control signal ENABLE, thus enabling switch  524 , providing a low impedance at the input of lamp assembly  542 , and thus carrying out the trailing-edge exposure mode. Between an initialization of timer  703  and its subsequent expiration, timer  703  may deassert signal SWITCH_ON which in turn enables switch driver  704  to deassert the enable control signal ENABLE, thus disabling switch  524 . 
         [0052]    Control circuit  700  may be implemented using controller  512  or any other system operable to control circuit  700 . In certain embodiments, control circuit  700  may be implemented partially or fully in software and/or firmware embodied in computer-readable media and executable on a processor (e.g., controller  512 ) of lamp assembly  542 . 
         [0053]    Accordingly, using the methods and systems described herein, the duration of a trailing-edge exposure mode of a lamp assembly may be minimized in accordance with a charging time of a trailing-edge dimmer (wherein such charging time may be a function of a capacitance of a charging capacitor of the dimmer), thus potentially reducing power consumed by a lamp assembly. In addition, as parameters (e.g., resistances, capacitances, inductances, etc.) of components of a lighting system vary with age, temperature, and/or other factors, the systems and methods described herein may dynamically control duration of the trailing-edge exposure mode to provide an adequate duration for the trailing-edge exposure mode while reducing power consumption. 
         [0054]    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 whether connected indirectly or directly, with or without intervening elements. 
         [0055]    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. 
         [0056]    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.