Abstract:
A voltage-boosting dc-to-dc converter that maintains a substantially constant output power into certain loads despite changes in input supply voltage, and whose output power is easily changed.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit of provisional patent application Ser. No. 60/429,871, filed 2002 Nov. 27 by the present inventor. 

   FEDERALLY SPONSORED RESEARCH 
   Not Applicable 
   SEQUENCE LISTING OR PROGRAM 
   Not Applicable 
   BACKGROUND—FIELD OF INVENTION 
   The present invention relates generally to battery-powered lights, and more particularly to d.c.-to-d.c. converters designed to supply power to light-emitting diode(s) (LED). 
   BACKGROUND—DESCRIPTION OF PRIOR ART 
   LEDs make robust, long-lasting, efficient light sources. Unlike ordinary incandescent bulbs, LEDs cannot be simply connected to a low-impedance battery, but need some form of driver circuit or current limiting. Additionally, the most common and economical single cells—1.5 v alkaline cells—do not produce adequate voltage to power, for example, a white GaN LED with a forward drop of 2.8 volts. Thus, the subject of making LED flashlights and the construction of dc-to-dc converters for this purpose has fascinated the public for some time. 
   D.C.-to-D.C. Converter Fundamentals 
   D.C.-to-D.C. converters are used to transform an available voltage source, such as a battery, to a desired voltage, such as the forward voltage Vf of a light emitting diode (LED). “Switching” converters commonly do this by storing energy into an inductor during an “on” time tON, and allowing that inductor to discharge—“flyback”—into the load during an “off” time tOFF. “OFF” and “ON” refer to the state of the power switching element, commonly a transistor, that applies the charging potential to the inductor. 
   Continuous and Discontinuous Modes 
   A continuous mode dc-to-dc converter is so-called if current flows at all times—i.e., continuously—in the inductor. This objective is achieved by terminating the flyback interval before the inductor has been fully discharged. When a converter&#39;s inductor is allowed to fully discharge during the off interval, this is known as discontinuous mode. In all cases, energy from the input supply is stored into the inductor during the “on” time, and removed (discharged into the load) during the flyback interval, or “off” time. 
   To illustrate the distinction,  FIG. 5  depicts a simplified boost converter. During each “on” time period tON switching transistor Q 500  is driven ON, grounding one side of inductor L 500 . The other side of inductor L 500  is connected to supply voltage Vcc. To a first approximation, the current iL flowing in inductor L 500  increases during time period tON according to
 
Δ iL=tON·Vcc/L.   (Eq. 1)
 
   When tON ends the inductor L 500  begins to discharge into the load, LED D 500 . At the end of time period tOFF the current iL in inductor L 500  will have decayed to:
 
 iL=iL   0   −tOFF·Vdischg/L   (Eq. 2),
 
   where Vdischg is the voltage across the inductor as it is discharged. In this case Vdischg is set by and is equal to the forward voltage of the load, LED D 500 . 
   If tOFF is long enough for the inductor L 500  to fully discharge (iL=0), then the converter is said to be operating in “discontinuous mode,” referring to the non-continuous current flowing in inductor L 500 .  FIG. 6   a  is an illustration of the current waveform in inductor L 500  when operating in discontinuous mode. 
   If tOFF ends (and tON commences) before inductor L 500  has fully discharged, then some current iL≠0 remains that will be added to during the next “on” cycle. As current is always flowing in inductor L 500 , the converter is termed a “continuous mode” converter.  FIG. 6   b  depicts the current waveform in inductor L 500  when operating in continuous mode. 
   Runaway and the Need for Limiting 
   Note that if more current is added to inductor L 500  with each “on” cycle tON than is discharged during tOFF, then inductor current iL will increase with each cycle until the limit of the switching transistor Q 500 , inductor L 500 , or some other circuit element is reached. This circumstance is ordinarily avoided in prior art circuits by use of feedback, inductor-current sensing schemes, or both, to regulate tON so as to maintain a desired range of currents in inductor L 500 . 
   DISCUSSION OF THE PRIOR ART 
   Horton 
   Horton[1] discloses how to make an LED flashlight from an existing flashlight. Horton&#39;s device comprises a constant voltage output boost/buck converter using a commercial integrated circuit, to be installed inside the flashlight. Current limiting to the LEDs is ensured by a 4.7 ohm resistor. 
   Stirling 
   Stirling[2–5] discloses construction of a prototype LED flashlight using a single AAA cell. An existing flashlight was retrofitted[2,3]: the bulb was replaced with an LED, and a voltage-boosting converter was installed inside the flashlight casing to power the LED. Stirling&#39;s boost converter used a two-transistor multivibrator to drive a third transistor, the third transistor being a switch used to drive an inductor.[4][5] 
   Dutcher 
   Dutcher[6] discloses a dc-coupled multivibrator whose off-time is equal to the discharge time of the inductor, and whose “on”-time is set by the point where the main power-switching transistor pops out of saturation. The Dutcher circuit&#39;s power supply voltage-compensation relies on a strategy of increasingly starving the switching transistor—causing it to pop out of saturation earlier than it otherwise would have, abbreviating the on-interval and reducing the converter&#39;s power output. Starved base drive, however, does not saturate the switching transistor optimally, resulting in a significant loss of power-conversion efficiency. The drive circuit disclosed also ensures that the switching transistor will still be fully on for the first portion of flyback, producing significant switching losses. 
   The Dutcher circuit&#39;s “on” timing is controlled by a current limit on the power-switching transistor&#39;s conduction current. Dutcher does not set on-time with timing components, nor stabilize the output power with a variable timing current into a capacitor. This “on”-time control strategy makes the circuit&#39;s output directly dependent on both the power-switching transistor Q2&#39;s [6] gain, and its saturation characteristics. These dependencies make the circuit difficult to manufacture in quantity while achieving the intended output power and stability. Transistor gains routinely vary over a 2:1 range from unit-to-unit, for example, directly affecting the circuit&#39;s on-time—and thus its power output—and the illumination level of the flashlight. The manufacturer&#39;s specification for the 2n3904 used in Dutcher&#39;s circuit, for example, states that its gain can range from 100-to-300 at 10 mA to less than ⅛th those values at 200 mA. Transistor gains also suffer from shifts with changes in temperature. These factors combine to make the ultimate power output of the Dutcher circuit difficult to predict. 
   Dutcher&#39;s circuit can also be designed such that the on-interval is terminated by allowing the inductor to saturate and pop the switching transistor out of saturation. Both this and the starved-transistor method result in high switching losses and high susceptibility to secondary characteristics of the components, e.g. inductor saturation current, V sat  and h fe  of the switching transistor, and change of same with temperature. 
   Wener 
   An astable multivibrator, such as in  FIG. 1   a , comprises two monostable pulse generators, each driving the other. The monostables&#39; timings are set by separate resistor-capacitor (R-C) time constants. If R 1 A&lt;&lt;R 2 A and R 4 A&lt;&lt;R 3 A then R 2 A*C 1 A controls the “off” time tOFF, and R 3 A*C 2 A controls the “on” time tON of output transistor Q 2 A.  FIG. 2   a  is a diagram showing the circuit&#39;s functional blocks. 
   With a minimum of change, an ordinary astable multivibrator ( FIG. 1   a ) can be pressed into service as a dc-to-dc converter. Wener et al.[7] disclose a single-cell LED flashlight employing an internal voltage boosting converter wherein one of the collector load resistors R 4 A of  FIG. 1   a  is replaced with inductor L 1 B to produce  FIG. 1   b , a boost-converter. As with  FIG. 1   a , R 2 B*C 2 B sets tOFF and R 3 B*C 2 B controls tON. The result is a boost converter comprising two R—C controlled monostable pulse generators, each triggering the other, where one of these also drives an inductor as a load. tON and tOFF are set by the RC networks, not the inductor.  FIG. 2   b  summarizes the circuit&#39;s function in block-diagram form. 
   The Wener converter is not regulated. Instead, the circuit shifts from discontinuous to continuous mode as supply voltage Vcc rises, adding current into inductor L 1 B with each cycle. The current in inductor L 1 B then quickly increases to high levels, the circuit becomes inefficient, and the final result is a power output that varies strongly with battery voltage. 
   These difficulties can be understood as follows: in  FIG. 1B  the timing currents controlling tON and tOFF flow into timing capacitors C 2 B and CIB, respectively, and are set by resistors R 3 B and R 2 B, respectively. As supply Vcc increases, both timing currents increase, decreasing both tON and tOFF. During tOFF, tON timing capacitor C 2 B is charged to the flyback voltage less Vbe(Q 1 B), typically 3.4 volts when DIB is a white LED. By contrast the tOFF timing capacitor CIB is charged only to Vcc−Vbe(Q 2 B), typically 1.3V−0.6V=0.7 volts with a moderately used single alkaline cell providing supply voltage Vcc. Because the off-timing resistor R 2 B has a much lower voltage across it than resistor R 3 B, small absolute changes in supply voltage Vcc produce greater percentage changes in the timing current resistor that R 2 B generates. tOFF thus decreases more rapidly than tON. Meanwhile, the time needed to fully discharge inductor L 1 B increases with supply voltage Vcc according to:
 
 tOFF=i ( L 1 B )· L 1 B/[Vf ( D 1 B )− Vcc].   (Eq. 2 a )
 
   tOFF, therefore, decreases as Vcc rises, the opposite of what&#39;s desired. The result is that, at some intermediate value of voltage Vcc, tOFF becomes too short to allow full discharge of inductor L 1 B. The converter enters continuous mode, whereafter inductor L 1 B current rises very rapidly with Vcc. The power delivered to the load increases even more rapidly, because additional energy is pumped into the boost inductor even as the need for that boost energy is decreasing. Since inductor L 1 B doesn&#39;t have time to fully discharge, its standing current rises with each successive switching cycle. The buildup of standing current in inductor L 1 B is such that, in a very short time, switching transistor Q 2 B can no longer switch the excessive current. Thereafter, tON is curtailed when transistor Q 2 B pops prematurely out of saturation. Inductor L 1 B then flies back while transistor Q 2 B is still fully conducting, producing excessive dissipation/waste in transistor Q 2 B. At high current and flyback voltage levels, such as when driving multiple LEDs, transistor Q 2 B may be destroyed. A further disadvantage is that the illumination level from the LED D 1 B falls off precipitously with falling supply voltage Vcc, before the battery has been fully utilized. 
   A third related problem stemming from this transition to continuous mode is sensitivity to component values: as the output power is highly dependent on the tON and tOFF selected, input voltage, and duty cycle, small changes in component characteristics will affect the point where the converter enters runaway/continuous mode, producing large unit-to-unit variations in said output power. 
     FIG. 4  plots actual measurements of the input-current vs: battery-voltage responses of Wener and the instant invention. Curve  401 . depicts the Wener circuit&#39;s ( FIG. 1B ) performance, showing the rapid increase in input current with increasing supply voltages, resulting in an output power that increases exponentially with battery voltage. From 0.75 v to 1.55 v the Wener circuit&#39;s input power varies over a ratio of 33:1. Additionally, at higher supply voltages Vcc the circuit is grossly inefficient. 
   Prior Art Output Stabilization 
   In prior art converters, inductor current and output power are usually controlled by the use of feedback circuitry to sense and control the switch current, output voltage or current, or a combination of these. The feedback system then adjusts the switch&#39;s duty cycle to maintain the desired output. 
   Prior art continuous mode circuits must have some sort of feedback to prevent the inductor&#39;s standing current from increasing each cycle until the inductor—or the switching transistor driving it—saturates out of control. One of several common feedback techniques is to sense the inductor&#39;s charging current on a cycle-by-cycle basis and terminate the “on”-time when this peak current reaches a certain target value. As the battery voltage changes, so must the duty factor of the boost circuit. Such circuits add to the cost and complexity of a converter.
     [1] Apr. 19, 1995 “Re: LED Flashlight”, Kevin Horton, sci.electronics*   [2] Mar. 17, 1997 “Re: Mini-Maglite Alternatives”, Ian Stirling, misc.survivalism*   [3] Mar. 21, 1997 “LED brightness”, Ian Stirling, sci.electronics.design*   [4] Mar. 22, 1997 “Re: Mini-Maglite Alternatives”, Ian Stirling, misc.survivalism*, message 199703220548.FAA20600.mauve.demon.uk   [5] Mar. 22, 1997 “Re: Mini-Maglite Alternatives”, Ian Stirling, misc.survivalism*, message 199703220551.FAA22127.mauve.demon.uk   [6] Jun. 18, 2001“Single-cell flashlight uses any type of LED”, Al Dutcher, Electronic Design, Jun. 18, 2001, p162–3   [7] U.S. Pat. No. 6,366,028 B1, Wener, et al. *Internet USENET discussion forum   

   
     BRIEF DESCRIPTION OF DRAWING FIGURES 
     In the drawings, closely related figures have the same number but different alphabetic suffixes. 
       FIG. 1   a . Multivibrator circuit diagram 
       FIG. 1   b . Prior art multivibrator boost-converter circuit diagram 
       FIG. 1   c . The invention—circuit diagram 
       FIG. 2   a . Multivibrator, block diagram 
       FIG. 2   b . Prior art converter, block diagram 
       FIG. 2   c . Block diagram of the instant invention 
       FIGS. 3   a–e  Examples of alternate timing current sources, circuit diagrams 
       FIG. 4 . Graph showing line regulation of Wener &amp; present invention 
       FIG. 5 . Simplified schematic diagram of a boost converter 
       FIGS. 6   a–c . Inductor current waveforms for a discontinuous-mode converter, a continuous mode converter, and the instant invention, respectively. 
   

   OBJECTS AND ADVANTAGES 
   The present invention achieves numerous objects and advantages, including:
         (a) to make an efficient converter capable of stepping up the output voltage of one or more cells so as to be able to power an LED having a forward voltage greater than said cells;   (b) to make a converter that transforms the voltage of one or more cells to drive an LED or LEDs with substantially constant power despite variations in the converter&#39;s input voltage supply;   (c) to make a converter that is capable of producing multiple selectable power outputs, thus permitting user selection between high-illumination and long battery life;   (d) to make a converter that is free from parts&#39; sensitivities, and whose output is predictably set by non-critical components;   (e) to make a converter whose output power versus input voltage characteristic is easily customized.       

   DESCRIPTION OF THE INVENTION 
   The invention, depicted in  FIG. 1   c ., consists of an astable multivibrator-style oscillator comprising two transistors, cross-coupled with capacitors, where the collector load of one transistor has been replaced with an inductor, and the traditional timing capacitor to the base of this same transistor has been replaced with a relatively large-valued d.c. blocking capacitor instead. 
   For economy and simplicity, the preferred version of the invention uses a resistor to provide a timing current that varies with supply Vcc, yielding an output power characteristic that increases approximately linearly with Vcc, however more complicated timing current networks such as a resistor in series with a diode, or current sources, may be used to further reduce the variation of output power over changes in Vcc (e.g.  FIGS. 3   a–e ). 
   Operation of the Invention 
   Start-up 
   Referring to  FIG. 1   c , during initial startup the time constants ensure that resistor-capacitor timing network R 3 C—C 2 C charges first, driving transistor Q 1 C into a linear region of operation. Q 2 C&#39;s base charges up to Vbe(Q 2 C) via R 2 C until Q 2 C conducts. At this point each transistor amplifies its own noise, producing an output. Said outputs are each coupled to the other transistor, amplified, then coupled back to the first transistor. The effect is regenerative and oscillation rapidly ensues. 
   D.c. blocking capacitor Cinf serves to allow startup with Vce(Q 1 C)&lt;Vbe(Q 2 C), a condition where startup could otherwise fail with Q 1 C “on” and Q 2 C “off”. If operation over a more limited supply voltage range is acceptable it is possible to eliminate R 2 C and Cinf by connecting the base of Q 2 C directly to the collector of Q 1 C. As a guideline, design calculations should be made to ensure that the timing current supplied by R 3 C (or other timing current generator) during startup is less than approximately [Vcc−Vbe(Q 2 C)]/[R 1 C*hfe(Q 1 C)]. 
   Normal Operation 
   Once oscillating, consider: when transistor Q 2 C switches off, L 1 C will flyback, driving transistor Q 1 C into saturation while the magnetic field stored in L 1 C decays. When its flyback current decreases to zero, the voltage across L 1 C decays rapidly. The C 2 C-L 1 C node voltage falls, and with it the voltage at transistor Q 1 C&#39;s base, biasing transistor Q 1 C into cutoff. Transistor Q 1 C&#39;s collector voltage rises, biasing switch transistor Q 2 C “on” via blocking capacitor Cinf. Transistor Q 2 C stays on either until the timing current from R 3 C charges C 2 C to Vbe(Q 1 C), or until Q 2 C&#39;s collector current through L 1 C exceeds the level supportable by transistor Q 2 C&#39;s base current. When one of these terminating conditions is reached, transistor Q 2 C&#39;s collector voltage abruptly rises, transistor Q 1 C is biased on, transistor Q 2 C is cut off, and the cycle repeats. 
   Optional rectifier DIC and filter capacitor C 3 C serve to filter the converter&#39;s output, providing direct-current drive for the LED D 2 C. If desired these can be omitted &amp; the LED allowed to run on pulsating current present at the collector of Q 2 C. 
   It can be seen that the present invention dispenses with the need for external feedback, setting a stabilized output power predictably by setting a single timing parameter—tON—with non-critical components. Specifically, replacing off-timing capacitor CiB of  FIG. 1B  with d.c.-blocking capacitor Cinf, transforms the astable multivibrator of  FIG. 1   b  into the flyback-controlled converter of  FIG. 1   c . The new circuit&#39;s “on” time tON is set by R 3 C*C 2 C. Adjusting this one time-constant now provides a simple, single-point means of setting this converter&#39;s output power. 
   Output Stabilization Action 
   The new circuit&#39;s “off” time is “flyback” controlled: controlled by the discharge/flyback time of inductor L 1 C. Inductor L 1 C&#39;s discharge time, in turn, is proportional to its initial current, and inversely proportional to the voltage across it, i.e.
 
 tOFF=iL·L 1 C/[Vf ( D 2 C )+ Vf ( D 1 C )− Vcc].   (Eq. 3)
 
   This happy fact serves to stabilize the converter&#39;s output: when the input voltage (Vcc) is high and the flyback voltage across the inductor is reduced, tOFF is extended. The longer off-time, in turn, reduces the overall duty cycle
 
duty cycle=( tON /( tON+tOFF ))  (Eq. 4),
 
reducing the converter&#39;s power output.
 
   As the input voltage is lowered, a larger flyback voltage appears across the inductor L 1 C during tOFF, discharging it more rapidly. Reducing tOFF serves to increase the overall duty cycle (Eq. 1), boosting power output, tending to offset the effect of the lower supply voltage (see  FIG. 4 ). 
   More particularly, tOFF is approximated by
 
 tON*Vcc /( Vout+Vf ( D 2 C )− Vcc )  (Eq. 5).
 
   Note that the numerator in this expression increases with Vcc, whereas the denominator term decreases. Both serve to increase tOFF with increasing Vcc, stabilizing the output power. 
   A second Vcc-related compensation is simultaneously present, operating as follows: as Vcc falls the voltage across tON timing resistor R 3 C is reduced, causing it to charge tON timing capacitor C 2 C more slowly. tON is extended, allowing inductor L 1 C to charge to higher currents, and the converter&#39;s output power increases, opposing the drop in its supply voltage.  FIG. 4 . graph  402  shows actual input-current vs. input-voltage performance of a prototype of the invention;  FIG. 6   c  illustrates the current waveform in inductor L 1 C. 
   It can be seen that replacing the off-timing capacitor C 1 B ( FIG. 1B ) with d.c.-blocking capacitor Cinf ( FIG. 1C ) creates a new, compensated topology whose output power increases approximately linearly with input voltage, in contrast with traditional circuits whose output powers increase exponentially or in uncontrolled fashion under the same conditions. 
   Further Compensation 
   If desired, a voltage divider network from Vcc to ground, with the divider tap connected to C 2 C, with or without non-linear elements such as diodes, may also be employed instead of a simple timing resistor R 3 C. Using a divider serves to decrease the effective voltage applied to the resulting effective timing resistor, extending on-time as Vcc decreases (because more time is needed to reach the voltage at which Q 1 &#39;s conduction terminates the on-cycle). 
   Replacing the on timing-resistor R 3 C with a more complex network, such as a resistive divider, current source, or resistor-diode networks ( FIGS. 3   a–e , respectively) are all effective ways to produce a power output characteristic that is substantially constant despite changes in Vcc. 
   A voltage divider network, with or without non-linear elements such as diodes, may also be employed instead of a simple timing resistor. 
   Buck-boost 
   In the case where Vcc is greater than the forward voltage of the LED D 2 C, the grounded terminals of C 3 C and D 2 C can be instead connected to Vcc. This allows the converter to be used in multi-cell and lithium-cell applications. 
   Alternate Timing Current Generators 
   It is possible to tailor the invention&#39;s output-power vs input-voltage response, which might be desired, for example, to give warning of a depleted battery, or to provide the most constant possible light intensity if that is desired.  FIGS. 3   a–e  depict alternative timing current networks to replace timing resistor R 3 C of  FIG. 1C . 
     FIG. 3   a . shows a diode in series with a resistor, with the combination shunted by a second resistor. The diode serves to provide a voltage below which the timing current is very small, and to increase the timing current more rapidly about this voltage than would be supplied by a simple resistor. The shunt resistor is optional, and provides a minimum current proportional to Vcc. It is thusly possible to create a timing current that reduces the converter&#39;s overall input current with increasing Vcc, resulting in constant (or even decreasing) power output, i.e., constant LED brightness. 
     FIG. 3   b . and  3   c . depict current sources: the constant current source of  3   b . produces constant tON and a power output that varies linearly with Vcc. The Vcc-dependent current source of  FIG. 3   c . produces a tON that varies inversely with Vcc, yielding constant power output. 
     FIG. 3   d . depicts two switchable timing resistors in series with a diode, which produces a converter with two switch-selectable output powers that are stabilized over variations in Vcc. 
     FIG. 3   e . depicts a variable resistor in series with a diode, providing a compensated, variable power source for dimmable lighting applications. 
   Obviously these are not the only possible timing current generators, but are merely examples intended to show the flexibility and ease of adjustment of the present invention. 
   Review 
   From the description above, a number of advantages of the invention become evident:
         (a) The present invention achieves output power control without added feedback circuitry or current-sensing schemes required in prior-art circuits. This is possible because the flyback-control mechanism of the instant invention provides inherent feedback. Further output stabilization is afforded by a simple timing current generator that abbreviates “on” time with increases in supply voltage.   (b) A further advantage is that the present invention&#39;s output power versus input voltage characteristic is easily compensated by employing alternate timing current generators, e.g.  FIGS. 3   a–e , to supply a customizable result.   (c) The present invention switches “on” at the zero-current point, improving efficiency.   (d) Flyback control of off-time guarantees that the invention will not enter a runaway continuous-mode region of operation, as is inherent with the prior art. The instant invention&#39;s topology ensures that off-time will increase with increasing supply voltages. By contrast, the prior-art multivibrator converter&#39;s off-times decrease with increasing supply voltage, permitting less of the inductor&#39;s energy to be discharged and increasing the possibility for runaway, undesirable saturation of the inductor, and/or overcurrent in the load or switching transistor.   (e) The output power of the present invention is substantially stable over variations in input voltage.  FIG. 4  curve  402 . shows the performance of the instant invention of  FIG. 1   c , whose input current is substantially stable, operation is highly efficient, and input power varies over a ratio of 2.6:1 over the input voltage range, a 13-fold improvement when compared to the prior art curve  401 .   (f) If desired, even greater output stability can be produced using alternate timing current generators ( FIGS. 3   a–e ) to produce the desired output power versus input voltage characteristics.   (g) A further advantage of the instant invention is that its output can be readily controlled by changing the timing current flowing into a single node (i.e.,  FIG. 1   c , junction of Q 1 C(base) and C 2 C). This makes the circuit suitable for applications where more than one power output level is needed, such as in a flashlight with multiple brightness levels. Ordinary multivibrator circuits have two independent time constants and so cannot be as easily adjusted.       

   CONCLUSIONS, RAMIFICATIONS, AND SCOPE OF INVENTION 
   In summary, changing the function of C 1 B ( FIG. 1B ), in a prior-art configuration, produces a new circuit and functionally different topology, with profoundly different and highly desirable characteristics. 
   The new topology employs a new mode of operation, and possesses a number of important advantages. Among these advantages are dramatically improved stability of output over variations in input voltage, insensitivity to component tolerances, freedom from runaway, and the ability to control the circuit&#39;s output power via a single-point adjustment. Although this invention has been set forth as an ideal driver for light-emitting diodes, the invention is useful as a general-purpose d.c.-to-d.c. converter with numerous diverse applications that will be apparent to those skilled in the art.