Abstract:
A method and apparatus for fast charging a battery with optimal charging. In an arrangement, a system includes a battery charger for applying a voltage to a rechargeable battery; and a controller coupled to the battery charger and monitoring at least one of a battery voltage, a battery temperature, and the current flowing into the battery; wherein the system is configured to apply a charging current from the battery charger by calculating an open cell anode voltage and an anode resistance of the battery, and determining the charging current. In additional arrangements, lithium ion plating is prevented by the charging current. Additional methods and arrangements are disclosed.

Description:
TECHNICAL FIELD 
       [0001]    The present application relates to generally to battery charging and in particular to rapid charging of rechargeable lithium batteries without battery degradation due to lithium plating. 
       BACKGROUND 
       [0002]    The recent development of light weight rechargeable lithium batteries, with the capability to store comparatively large amounts of energy in a relatively small package, has made lithium batteries the power source of choice for portable electronic devices. Once manufactured, the life span of a lithium battery is largely determined by the type of use and by the recharge approaches used. While the use of the lithium ion battery is determined primarily by the consumer, the type of recharging can be determined by the device manufacturer and/or by the charger manufacturer. Although the battery manufacturer can supply recharging guidelines, these guidelines typically prescribe fairly conservative charge rates in order to keep any detrimental battery charging effects at a minimum. This leads to battery recharge times in the 2 to 4 hour range or even greater times. Consumers naturally prefer to charge portable devices in much shorter times in many cases, such as in less than 1 hour. Thus there is a conflict between the conservative charging guidelines written to ensure a long battery life, and the actual practices and preferences in the use of the batteries in the field. Improper rapid charging of lithium battery packs can greatly shorten the battery life, and in worst case scenarios, can lead to battery pack swelling or rupture of a battery pack and under certain circumstances, rapid charging can also create a possible fire risk. 
         [0003]    A battery&#39;s capacity, described as the “C” rating, is defined as the sum of a constant current that a rated battery cell can deliver during a 20 hour discharge cycle and still remain within the rated voltage limits at room temperature. For example, an ideal battery that can produce 50 mA of current for 20 hours while staying within the prescribed voltage window would have a C rating of 50 mA×20 H=1000 mAh or 1 Ah. A “perfect” battery would be 100 % efficient during charge and discharge. If a perfect battery had a C rating of 1 Ah, then it could deliver the 1 A for 1 hour, or 0.5 A for 2 hours, or 100 mA for 10 hours, or 50 mA in 20 hours, and so on. In addition, a perfect battery with a C rating of 1 Ah could be recharged in 1 hour by charging at 1 A for 1 hour, or 0.5 A in 2 hours, or 100 mA in 10 hours. Other terms commonly used in the description of a battery&#39;s charge and battery capacity are the state-of-charge (SOC) and the depth-of-discharge (DOD). SOC and DOD both have units of % and are complimentary definitions. SOC indicates the relative amount of energy stored in a battery compared to its fully charged state. DOD indicates how much of the battery&#39;s energy has been used compared to its fully charged state. For example, for a perfect 1 Ah battery, when drained of 0.25 Ah the battery would have a SOC of 75 % and a DOD of 25 %, and if drained of 0.5 Ah the battery would have a SOC of 50 % and a DOD of 50 %. The voltage of a battery is often specified as the open-cell-voltage (OCV) where the cell voltage is measured without external load. And the full-charge-capacity (FCC) is the capacity of the cell with a full charge at any given point in its life. Using the example of the perfect battery described above when new, the FCC would be 1 Ah. As the battery ages, the FCC is reduced. 
         [0004]    While battery capacity can be arbitrarily increased or decreased with the addition/reduction of battery material, the voltage characteristic of a given battery chemistry remains independent of the battery capacity. For this reason, the discharge and recharge of a cell is commonly discussed in terms of the C rating. For example, if the perfect 1 Ah battery is discharged at a maximum rate of 1 C, then the maximum discharge rate would be 1 A. The same perfect battery, charged at a maximum rate of 2 C would see a maximum discharge current of 2 A. 
         [0005]    In a rechargeable lithium ion battery, energy is stored and retrieved in a chemical reaction via the migration of lithium ions between electrode pairs. The positive electrode (cathode) and the negative electrode (anode) are both able to bind lithium ions. During discharge, the lithium ions move from the anode to the cathode, releasing energy in the process. During a charge cycle, an electric field created between the cathode and anode forces the lithium ions back to the anode, absorbing energy in the process. Under some circumstances, including high C rate charging, a small portion of lithium ions form metallic lithium and are deposited on the anode during the recharge phase. This lithium material partially reacts with electrolyte and is then no longer available for charge storage and as a result the capacity of the battery is diminished. This phenomenon is referred to as “lithium plating.” The lithium plating reduces the capacity and the life of the battery. 
         [0006]    In conventional prior known approaches, a prior known approach to battery charging methodology has two phases, a constant current or “CC” phase, followed by a constant voltage or “CV” phase. During the CC phase, a current that is considered a safe current for the battery is applied until the cell voltage reaches a target voltage, for example, 4.2 Volts, and then the current is reduced while the voltage is maintained in the constant voltage phase, until the current falls to a minimum when charging stops. Known prior battery chargers also monitor conditions such as temperature and may prior known approaches may stop charging when temperature falls below a minimum such as 10 degrees C., or 0 degrees C. 
         [0007]      FIG. 1A  illustrates in a flow diagram a known prior approach dual stage constant current CC and constant voltage CV or “CC/CV” charge process; and  FIG. 1B  illustrates a graph of a typical battery charge cycle using the CC/CV process. 
         [0008]    The flow diagram illustrated in  FIG. 1A  shows the steps used in a controller for operating the CC/CV charge process. Step  110  begins the process. At step  111 , the charge process begins. The maximum current is applied to the battery at this step. At step  113 , the constant current phase begins. During this phase the charge process charges the battery at a predetermined maximum current. The current may be the maximum available from the charger, or, a maximum current considered safe according to manufacturer specifications, such as 1 C. The process continues at step  113  and tests to see if a maximum voltage “Max V” has been reached. Until the maximum voltage is reached, the constant current charging continues by remaining at step  113 . 
         [0009]    When the test at step  113  indicates that the maximum voltage Max V has been reached, the charging process transitions to a “constant voltage” mode of operation at step  115 . During the constant voltage charging process, the current into the battery is allowed to fall as the battery reaches full capacity. At step  117  the current flowing into the battery is tested to see if the cutoff limit has been reached (current into the battery is measured and found to be less than a minimum charging current) and when the cutoff is reached, the process transitions to step  119 , the “stop” state. 
         [0010]    In  FIG. 1B , the left vertical axis of charging graph  120  depicts the charge voltage which is represented by data line  124 . The right vertical axis depicts the charge current which is represented by data line  122 . The units of the right axis are labeled as C indicating the C rating of the battery. The bottom axis is the charge time in hours. The two distinct phases of a CC/CV charger are indicated near the top of the graph with the CC phase as  130  and the CV stage as  132  The maximum charge rate in this example is 1 C as indicated by the peak value of the charge current line  122  in the constant current or CC phase  130 . Following the current line  122  from the CC phase into the constant voltage of CV phase to the last current value in the CV phase  132 , the cutoff current is approximately 0.15 C. The maximum charge voltage is seen by the value of voltage line  124  in the CV stage  132  and is approximately 4.2V. In this example charging case, the total charge time is about 1 hours and 10 minutes as seen by the termination of the charge current line  122 . 
         [0011]    To achieve lower recharge times, the current in the CC phase can be increased to 2 C or higher. However, it is known that the life and capacity of the lithium battery is greatly diminished when repeatedly charging at these higher rates compared to charging at lower rates, such as 0.5 C. Obviously, a charging system that is able to charge a battery in the least amount of time, without accelerating battery degradation, is desired. 
         [0012]      FIG. 2  is a graph that illustrates cell capacity degradation with increasing C rate. The data depicted in graph  200  illustrates the detrimental effects that charging a battery at a higher C rate can have on the usable capacity of a battery cell as are described in an article titled “Factors that affect cycle-life and possible degradation mechanisms of a Li-ion cell based on LiCoO2 ”, Journal of Power Sources, Vol. 111, Issue 1, pp. 130 -136, by S. S. Choi et. al. (2002 ). Referring to the graph of  FIG. 2 , it can be seen that when using a CC/CV charger with a charging rate as little as 1.4 C, the capacity of the cell illustrated in the graph has dropped to about 27 % of its initial capacity in 500 charge cycles. The same chemistry cell, charged at a 1 C rate still retains about 800 mA after 500 cycles. As shown in the graph in  FIG. 2 , a higher constant current charging rate degrades a battery quickly and shortens battery life. 
         [0013]    The open cell voltage (OCV) of a battery cell can be calculated as shown in Equation 1: 
         [0000]        V   cell   =V   cathode   −V   anode    EQUATION 1
 
         [0014]    Direct measurement of the battery voltages Vcathode and Vanode is typically done by inserting a 3 rd  reference electrode in the electrolyte region of the battery. Because of the delicate nature of the procedure, it is typically only performed in a laboratory setting by the battery manufacturer. When successful, the cathode and anode potentials are extracted from a battery with very few cycles and usually at room temperature. However these voltages are not available for a battery in actual use because there is no 3 rd  reference electrode. 
         [0015]    Battery degradation is classified in two basic categories: active material loss and internal impedance increase. In the first category, active material loss, the loss of material reduces the available chemicals for the ionic processes needed to create current. Although battery manufacturers seal the batteries, there is still some electrolyte loss due to parasitic reactions inside the cell. A battery cell pack that is charged inappropriately can exhibit swelling due to the gas produced and the swelling can, in extreme cases, damage the device the battery pack is installed in. 
         [0016]    In the second category, impedance increase, the usable amount of energy available for external loads is reduced by increases in the internal resistance. Increasing impedance increase is the prevalent degradation a lithium battery cell experiences. Internal resistance increases with age of the battery and with the number of charge/discharge cycles. Further, at lower temperatures, the internal resistance increases. When the internal impedance increases, lithium plating is more likely during charging as the increased internal impedance negatively affects internal potentials. Because of the impedance increase at lower temperatures, some prior known approach chargers include a cut off temperature sensor and will not charge below certain temperatures, like 10 degrees C. or 0 degrees C. However impedance increases also occur at higher temperatures than these and charging that is acceptable at room temperature may cause lithium plating at lower temperatures, particularly as the battery cells age. 
         [0017]    Lithium plating causes both types of degradation, active material loss and internal impedance increase. When the lithium ions become lithium metal and react with the solvent, the number of lithium ions available to transport charge is reduced. In addition, as the lithium metal decomposition products accumulate at the anode, there are less locations for lithium ions to exchange their charge. Because of this dual degradation, it is desirable to avoid conditions that accelerate lithium plating. Lithium plating reduces capacity and life of the battery cells. 
         [0018]    It is known that during charging of lithium ion battery cells, lithium plating occurs when the voltage drop across anode material causes the graphite surface potential at the anode of the lithium cells to fall below the lithium potential.  FIG. 3  depicts in a graph  300  the limitations on charging presented by the lithium plating phenomenon. In graph  300 , the vertical axis is a plot of the anode potential compared to the lithium potential, in volts. The horizontal axis illustrates the state of charge (SOC) in percent, for a charging cycle. At the left side of the graph, the SOC is at 0 % and charging begins, the charging ends when the SOC is 100 % representing a full charge. Trace  305  illustrates the graphite anode open cell voltage for a lithium ion cell. The OCV for the anode is greater than zero for the entire charging cycle. However, the trace  307  depicts the anode potential v. the lithium potential, For low temperature, or rapid charging, or for an aged battery cell, the internal resistance can increase, resulting in an anode potential that falls to zero or becomes negative compared to the lithium potential. This is shown inside the area  309  in  FIG. 3 , in this area, lithium plating can occur. Thus the lithium plating phenomenon is a limit on the rate of charge that can be achieved without damaging the battery. It is also known that the impedance of the battery changes with temperature. Because battery impedance increases at lower temperatures, charging at lower temperatures, for example when charging outdoors or in vehicles, can cause lithium plating to occur even at charging current levels that would be appropriate at room temperatures. 
         [0019]    A charge methodology that avoids lithium plating and thus extends battery life while maintaining battery capacity is clearly desired. U.S. patent application Ser. No. 14/014,195, published Mar. 6, 2014, filed Aug. 29, 2013, titled “METHOD AND APPARATUS OF CHARGING THE BATTERY WITH GLOBALLY MINIMIZED INTEGRAL DEGRADATION POSSIBLE FOR PREDEFINED CHARGING DURATION,” naming Yevgen Barsukov et al. as inventors, which is co-owned with the present application, is hereby incorporated herein by reference in its entirety. In the above referenced patent application, improvements are made in reducing the recharge time of a lithium cell. In laboratory testing and modeling of specific battery chemistry, multiple charging profiles are developed to suit battery age, impedance, temperature and state of charge (SOC). With the lithium chemistry empirically characterized, a set of optimized constant current-constant voltage (CC/CV) charging profiles can be loaded into a battery charging apparatus. These charging profiles can then be used to reduce the overall charge time while avoiding charging conditions that degrade the battery, including degradation due to lithium plating at high charge rates. The approach described in the above referenced patent application is a step forward beyond previous known prior approaches towards the goal of fast battery recharge without additional cell degradation. This approach requires substantial computations offline in order to characterize each of the particular battery cells and to create the CC/CV charging profiles for each battery pack made, and if the material or battery cells are modified, these computations must be repeated and new profiles are required. However, further optimization of the charging methodology is desired to further reduce the charge time without incurring additional battery degradation. 
         [0020]    Improvements are thus needed in battery chargers and in methods for charging lithium ion batteries. The avoidance of battery degradation during charging would maintain battery cell capacity at higher levels over a larger number of cycles while extending battery life. Damage to the battery cells and to the equipment in which the battery cells are installed due to improper charging could be avoided. 
       SUMMARY 
       [0021]    In arrangements of the present application, recognition is made that in charging batteries, optimal charging current should charge the battery quickly while avoiding battery degradation due to lithium plating. Methods and systems for charging batteries are provided where a computation for an open cell anode voltage is used to compute the charging current in a manner that avoids lithium plating problems, and these arrangements can be used to charge batteries at an optimal current. 
         [0022]    In an example system arrangement, the system includes a battery charger for applying a current to a rechargeable battery; and a controller coupled to the battery charger and monitoring at least one of a battery voltage, a battery temperature, and current flowing into the battery; wherein the system is configured to apply a charging current from the battery charger to the battery during a battery charging cycle where the current is determined by calculating an open cell anode voltage and calculating an anode resistance of the battery, and determining the charging current from the calculated open cell anode voltage and the calculated anode resistance. 
         [0023]    In a further arrangement, the above described system further includes an application processor coupled to the controller and configured to control the battery charger. In still another arrangement, the above described system is configured to compute the anode resistance using stored parameters for the anode resistance. In still a further arrangement, in the above described system, the system further comprises a CPU and an instruction store in the controller, the instruction store containing instructions configured to cause the CPU to calculate the charging current proportional to a computed open cell anode voltage divided by an anode resistance. 
         [0024]    In additional arrangements, in the above described system, the system further includes a data store containing stored parameters for the battery including anode resistance parameters compensated for depth of discharge. In still another arrangement, in the above described system the controller further includes a data store containing stored parameters for the battery including resistance parameters compensated for battery temperature. In a further alternative arrangement, in the above described system the controller further includes inputs configured to receive a battery voltage, a temperature sensor for the battery, and to a current sensor for the battery. In still another arrangement, in the above described system, the controller is configured to control the battery charger to apply the charging current to the battery until a predetermined battery voltage is reached. In a further alternative arrangement, in the above described system, the controller is configured to control the battery charger to apply a constant voltage to the battery subsequent to the predetermined battery voltage being reached. In yet another arrangement, the above described system is provided wherein the system further includes a lithium ion battery coupled to the battery charger and the controller. In another alternative arrangement, in the above described arrangement, the system is configured to apply a charging current from the battery charger computed to avoid lithium plating within the lithium ion battery. 
         [0025]    In another arrangement of the present application, a method for charging a battery includes providing a controller coupled to a battery charger; determining a charging current in the controller by computing an open cell anode voltage for the battery and determining the charging current from the computed open cell anode voltage and an anode resistance of the battery; and applying the charging current from the battery charger to the battery. In a further alternative arrangement, the above described method further includes determining whether a predetermined battery voltage has been reached; if the predetermined battery voltage has not been reached, computing the charging current from another computed open cell anode voltage and an anode resistance of the battery; and dynamically adjusting the charging current and applying the adjusted charging current to the battery. 
         [0026]    In still additional alternative arrangements, the above described methods are performed, where if the predetermined battery voltage has been reached, the method includes computing a battery voltage from an open cell anode voltage computation, and applying the battery voltage from the battery charger. In a further alternative arrangement, in the above described methods, computing the charging current further comprises computing a maximum charging current that can be applied without causing lithium plating. In an additional arrangement, the above described methods further include wherein determining the charging current by computing an open cell anode voltage for the battery and determining the charging current from the computed open cell anode voltage further comprises: retrieving stored data corresponding to open cell anode voltage parameterized by temperature. In still another alternative arrangement, the above methods are performed and further include computing the open cell anode voltage by retrieving stored open cell anode voltages characterized by battery depth of discharge. In still another arrangement, in the above described methods, providing the controller further comprises providing a battery gauge integrated circuit device coupled to the battery charger. 
         [0027]    In still another arrangement, a system for charging a lithium ion battery includes a battery charger integrated circuit having a battery output for outputting a battery charging current and a battery charging voltage to the lithium ion battery; and a battery gauge integrated circuit coupled to the battery charger integrated circuit and having inputs coupled to sense the battery voltage, a temperature sensor coupled to the battery, and a current sensor coupled to the battery; wherein the battery gauge integrated circuit is further configured to determine a charging current for charging the battery by computing an open cell anode voltage and an anode resistance and to control the battery charger to output the charging current. In still another arrangement, in the above described system, the charging current is computed to be a maximum charging current that will result in an open cell anode voltage that avoids lithium plating. 
         [0028]    Use of the advantageous methods and apparatus of the arrangements that form aspects of the present application enable rapid charging of a rechargeable battery or a battery pack using a charging current that is optimized for recharge speed while avoiding lithium plating. The methods dynamically adjust the charging current during the charge cycle to avoid a lithium plating situation that would otherwise occur, thereby extending battery life and maintaining battery capacity over many cycles, in sharp contrast to the charging approaches of the prior art. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0029]    For a more complete understanding of the illustrative examples of aspects of the present application that are described herein and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which: 
           [0030]      FIG. 1A  illustrates a flow diagram for a CC/CV process of a known prior approach, and  FIG. 1B  illustrates a graph of the battery charging process of  FIG. 1A ; 
           [0031]      FIG. 2  is a graph that illustrates battery cell capacity for 500 cycles using different charging rates; 
           [0032]      FIG. 3  illustrates in a graph the anode potential for a charging cycle of a battery; 
           [0033]      FIG. 4  illustrates in a circuit diagram a battery coupled to a battery charging apparatus for use with the arrangements; 
           [0034]      FIG. 5  illustrates in another circuit diagram a battery coupled to battery charging apparatus for use with the arrangements; 
           [0035]      FIG. 6A  illustrates in a flow diagram an arrangement for optimal charging of a battery and  FIG. 6B  illustrates in a graph a battery charging cycle using the process of  FIG. 6A , and  FIG. 6C  illustrates in a comparison graph the charge time for a charging cycle using the arrangements of the present application and a prior known approach; 
           [0036]      FIG. 7  is a simplified block diagram of a battery gauge circuit for use with the arrangements ; and 
           [0037]      FIG. 8  is a graph comparing the battery degradation rate measured for a conventional CC/CV battery charging process to an optimized charging process incorporating the arrangements of the present application. 
       
    
    
       [0038]    Corresponding numerals and symbols in the different figures generally refer to corresponding parts unless otherwise indicated. The figures are drawn to clearly illustrate the relevant aspects of the illustrative example arrangements and are not necessarily drawn to scale. 
       DETAILED DESCRIPTION 
       [0039]    The making and using of various examples of illustrative arrangements that incorporate aspects of the present application are discussed in detail below. It should be appreciated, however, that the illustrative examples disclosed provide many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific examples and arrangements discussed are merely illustrative of specific ways to make and use the various arrangements, and the examples described do not limit the scope of the specification, nor do they limit the scope of the appended claims. 
         [0040]    For example, when the term “coupled” is used herein to describe the relationships between elements, the term as used in the specification and the appended claims is to be interpreted broadly, and while the term “coupled” includes “connected”, the term “coupled” is not to be limited to “connected” or “directly connected” but instead the term “coupled” may include connections made with intervening elements, and additional elements and various connections may be used between any elements that are described as “coupled.” 
         [0041]    The arrangements disclosed herein can be implemented in a variety of ways. The methods can be implemented and performed by programmable devices executing instructions, for example. The methods can be implemented in software or in firmware or machine language instructions. Alternatively, programmable logic can be used to form dedicated hardware solutions. Devices that can be configured to perform the methods, including field programmable gate arrays (FPGAs), complex logic programmable devices (CPLDs) and application specific integrated circuits (ASICs) can be used to implement the arrangements. A processor such as a CPU, microcontroller unit (MCU), mixed signal processor (MSP) or a digital signal processor (DSP) and memory including RAM, ROM, Flash, volatile and non-volatile types, EEPROM and the like can be used. The arrangements can be implemented using several commercially available integrated circuits on a circuit board or on a module to form a complete solution. 
         [0042]    Aspects of the present application include a maximum life battery charger and methodology. In this arrangement, a charging apparatus is specifically configured to charge a lithium battery using a novel charging algorithm in which the charging current is optimized to a maximum current level that can be used without decreasing the anode electrode potential below lithium metal potential and therefore without causing lithium plating. The methods include a constant anode potential (CAP) phase and a subsequent constant voltage (CV) phase. These arrangements allow a lithium battery cell to be charged in the least possible time with an optimal charging current without accelerating battery degradation due to lithium plating. In sharp contrast to the prior approaches, the charging current is dynamically adjusted to provide an optimized maximum charging current on an ongoing basis during a first portion of the charging cycle, the CAP phase, that roughly corresponds to the prior “constant current” phase. The charging current is adjusted to prevent lithium plating and the battery degradation that results from overcharging. The method arrangements include information about the age, depth of discharge, and temperature of the battery and avoids overcharging by modeling the conditions within the battery at a given time and by performing calculations on an on-going basis and dynamically adjusting the charging current to reflect those conditions. The model includes information about the anode potential, thus avoiding lithium plating that can occur using the prior known solutions. 
         [0043]      FIG. 4  illustrates a typical schematic for a battery charging and monitoring apparatus that can be used with the arrangements of the present application. In circuit  400 , application processor  410  is coupled to the battery cell gauge  422 . Battery cell gauge  422  can be, for example, a stand-alone integrated circuit. The battery cell gauge  422  can also be implemented as a circuity board or system, or, in an alternative arrangement, as firmware that includes instructions for a programmable microprocessor. The battery cell gauge  422  is coupled to the lithium battery cell  430  and the charger  420 . Again, charger  420  can be, in a typical example, a stand-alone integrated circuit. Alternatively charger  420  can be a circuit board or system. The charger  420  is coupled to the gauge  422  and the battery cell  430 . In this example arrangement, the battery cell gauge  422  monitors the battery voltage and the input labeled “VOLTAGE SENSE”, battery temperature at the inputs labeled “TEMP SENSE,” and battery current at the inputs labeled “CURRENT SENSE.” During operation in this arrangement, the battery cell gauge  422 , which can be implemented for example as an integrated circuit or circuit board, operates the charger  420  during charge cycles using the interface labeled I2 C. When the system is operating under battery power, the battery charger  420  provides the power to the system load from the battery  430 , while the battery gauge  422  can provide information on the state of the battery such as remaining operating time to the system. When power is applied to the VBUS input of the charger  420 , then the system load is powered by a DC supply that is provided, and, the charger  420  is used to charge the battery  430 . 
         [0044]      FIG. 5  illustrates another arrangement for a battery charging and monitoring apparatus that can be used with the arrangements of the present application. In arrangement  500 , the application processor  510  is coupled to the charger  520  and coupled to the gauge  522 . The gauge is coupled to the processor  510  and the lithium ion battery pack  530 . The charger  520  is coupled to the application processor  510  and the lithium ion battery pack  530 . The gauge  522  monitors the battery voltage, battery current and battery temperature. In the arrangement of  FIG. 5 , the application processor  510  controls the charger  520  using an I2 C interface bus using information provided by the battery gauge device  522 . A family of products that implement fuel gauges and battery chargers to form battery management solutions is commercially available from Texas Instruments Incorporated. An example commercially available battery gauge device is the BQ27530 Battery Management Unit Impedance Track Fuel Gauge; an example battery charger device is the BQ24161. Additional battery gauge and battery charger ICs are also available from Texas Instruments, Incorporated. 
         [0045]    In both arrangements  400  and  500 , many battery parameters, such as the number of charge and discharge cycles, the full charge capacity, impedance, voltage, temperature, SOC and calendar age, are captured and stored in memory within the gauge  422  or processor  510  so that the battery pack  430  or  530  can be charged in an efficient and safe manner. Further during battery powered operations the battery gauge and/or application processor can provide an estimate of remaining operating time to the system for display to a user, for example, using the battery parameters the gauge  422  or  522  can sense, e.g. temperature, current and voltage. 
         [0046]    Aspects of the present application describe the configuration of a system including a charge apparatus to continuously supply charge current at an optimal level based on calculating the maximum charge current (I CH   _   MAX ) as shown in Equation 2: 
         [0000]        I   CH   _   MAX =OCV AN (DOD,  T )/ R   AN (DOD, T )   EQUATION 2
 
         [0047]    Where
       I CH   _   MAX  is the maximum charge current to be delivered to the cell,   OCV AN  is the estimated open cell voltage of the anode electrode at the current temperature and discharge level,   R AN  is the resistance of the anode,   DOD is the depth of discharge,   T is the temperature in degrees C.,       
 
         [0000]      OCV AN =OCV AN 25(DOD)+OCV B (DOD)*( T− 25 )   EQUATION 2 A
 
         [0053]    Where
       OCV AN  is the estimated open cell voltage of the anode electrode in Equation. 2,   OCV AN  25 is the OCV AN  at 25° C.,   OCV B  is temperature compensation coefficient for the open cell voltage at a given temperature,       
 
         [0000]        R   AN (DOD,  T )=( R   A (DOD,  T )− R   TRACE )* F   ANODE    EQUATION 2 B
 
         [0057]    Where
       R AN  is the resistance of the anode electrode from EQ. 2, compensated for Depth of Discharge (DOD) and temperature (T),   R A  the resistance of the Anode compensated for DOD and T,   R TRACE  is the sum of all parasitic resistances present in the measurement of the cell impedance.,   F ANODE  is the anode factor, the ratio between total cell resistance and anode resistance.       
 
         [0000]    
       
         
           
             
               
                 
                   
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                             ( 
                             
                               
                                 ( 
                                 
                                   
                                     R 
                                     
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                                
                               
                                 
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         [0062]    Where
       F ANODE  is the anode factor from EQ. 2 B,   AN SHARE  is the contribution of the anode to the total cell impedance,   R PRESENT  is the last recorded cell impedance value,   R NEW  is the cell impedance value when the cell was new,   R TRACE  is the impedance value of the entire anode trace,   F ANODE0  is the initial value of F ANODE .   The values of F ANODE0  and AN SHARE  are provided to the charger using data collected by off line cell characterization.       
 
         [0070]    Equations 2, 2 A, 2 B and 2 C have been discovered to provide a capability for dynamically adjusting the charging current applied to a battery on an on-going basis to ensure the open cell voltage at the anode (OCVan) is maintained at a positive voltage, that is a constant anode potential (CAP) is used. In the arrangements of the present application, methods incorporating these calculations are performed, charging batteries at an optimal charging current while avoiding lithium plating and thereby avoiding premature battery degradation. Charging can be performed as rapidly as possible while maintaining a healthy battery pack, and the lifetime of the battery pack can therefore be extended to a “maximum lifetime” that is many cycles longer than the battery life obtained using prior known approaches. 
         [0071]    To use the equations, certain parametric information is needed. In one example approach that forms an arrangement that is an aspect of the present application, the open cell anode voltage, a depth of discharge, and a temperature dependency are obtained by performing a direct measurement with a three electrode battery that includes a reference electrode, a cathode electrode and an anode electrode. 
         [0072]    In another alternative arrangement, an anode factor is obtained by performing direct measurement of the full cell impedance and a direct measurement of anode impedance using a three electrode battery that includes a reference electrode, a cathode electrode and an anode electrode. 
         [0073]    In another further alternative arrangement, the open cell voltage anode, a depth of discharge, and a temperature dependency parameters are obtained by performing a decomposition of a full cell open cell voltage profile for the depth of discharge (DOD) into known anode and cathode open cell voltage profiles, the decomposition being accomplished through optimization of an anode state of charge, the cathode state of charge and the anode to cathode material ratios of a battery to achieve a closest match of the open cell voltage profiles for a depth of discharge OCV(DOD) to the relationship: the open cell voltage cathode for the depth of discharge (OCVcathode(DOD)) minus the open cell voltage anode for the depth of discharge (OCVanode(DOD)). 
         [0074]    In a further arrangement, the resistance factor is found by fitting cycling data obtained at nominal and elevated charge rates for a battery to a battery degradation model that includes lithium plating degradation effects dependent on the resistance factor. 
         [0075]    In another arrangement, the resistance factor is found by performing a pulse scan test on a battery, where a combination of charge pulse, relaxation, discharge pulse and relaxation is applied to the battery at different rates until a rate is determined where the effective impedance derived from a response to a charge pulse differs from the impedance derived from the discharge pulse; subsequently, after finding a limiting charge rate, the resistance factor is found by using known total cell impedance and the open cell voltage anode for the depth of discharge and the battery temperature of the test. 
         [0076]      FIG. 6A  illustrates in a flow diagram an example method arrangement  600  for charging of a battery, and a corresponding graph that depicts the charge voltage and current. The method uses a CAP/CV two phase approach. The method  600  has a start block  610  coupled to the following blocks in succession:  618 ,  620 ,  622 ,  630 ,  632 ,  636 , and  640  as shown. Block  612  is coupled to  618  and  632 , block  614  and block  616  are coupled to block  620 . Block  616  is also coupled to block  632 . Block  634  is coupled to decision block  636 . The first portion of the flow chart, from start block  610  thru block  622 , performs the constant anode potential optimized charging (CAP) of the charge operation indicated by bracket  646  in the graph  602  of  FIG. 6B . The second portion of the flow chart, performed in block  630  thru the stop at block  640 , performs a constant voltage (CV) stage of the charge operation in graph  602  indicated by bracket  648 . 
         [0077]    Graph  602  in  FIG. 6B  depicts the CAP/CV charging of  FIG. 6A . The charging current is shown in curve  638  and the charge voltage is shown in curve  634 . The left vertical or Y axis indicates the cell voltage, the right side Y axis indicates the charge current in units of battery capacity (C) or “C” rating. The horizontal or X axis illustrates the charge time in hours (hr). The portion  646  of the graph  602  illustrates the constant anode potential charge (CAP) stage and the traditional CV stage is illustrated in portion  648 . The time brackets  646  and  648  in  FIG. 6B  correspond to the brackets on flow chart  600  in  FIG. 6A  with the same numerals. 
         [0078]    Prior to beginning the charging process, the maximum charging current capability of the charge circuit is made available to the process as represented by block  614 , (Apparatus Max Amp). Although in the example arrangement shown here, the maximum current obtained from Equation 2 that can be applied during the optimum current charging process is calculated dynamically and continuously in the novel charging approach of the present application, that calculated current may exceed the amount of current a particular charger can actually provide in some portions of the process, in which case the current is simply limited to the Apparatus Max Amp value at that time. Similarly, the maximum cell voltage for the lithium battery chemistry is made available to the process as represented by block  616  (Battery Max Volts). An initial FCC (Full Charge Capacity) is made available in block  634 , Full Charge Capacity, and that value is updated and maintained over the life of the lithium battery cell by the battery charging and monitoring apparatus by storing data in a read/write memory. Battery data from cell characterization at the factory, and additional “real time” data such as temperature, cathode voltage and current, is made available in block  612 , (Battery Data). 
         [0079]    Various storage methodologies for retrieval of stored data, and for storing updated data, are provided with the battery charging apparatus. For example, the battery data from the manufacturer or factory can be provided as a look up table (LUT) in a ROM, EPROM or FLASH memory that retains data when no power is available. The data needed to calculate the maximum current is provided either by a battery gauge circuit as shown in  FIGS. 4, and 5  for example, or from values stored in a memory that can be used by the battery charging apparatus to make the calculations in Equations 2, 2 A, and 2 B. For example the anode factor Fanode is stored from measurements made by the battery manufacturer or by the charger manufacturer and can be stored as a look up table, for example. 
         [0080]    In the flow diagram in  FIG. 6A , the charging process starts in step  610  and proceeds to the calculation of the open cell anode voltage (OCV AN ) at block  618 . The calculations are performed using equations 2 A and 2 B. The equations take into account the information at Battery Data  612  which includes the cell impedance, battery age, DOD and cell temperature as recorded by the charging apparatus for this specific lithium battery cell. In block  620  of the flow diagram, Equation 2 is performed using the open cell anode voltage OCVan to determine the maximum charge current that can be applied (I CH   _   MAX ) while charging in a manner to prevent lithium plating. The charge current for the charging process is limited by I CH   _   MAX . In an example where the charger can only supply a lower current (Apparatus Max. Amp) based on the maximum current capability  614  of the charger, then that lower current will be the maximum charge current used for that time period. Block  620  also comprehends the maximum charge voltage and will limit the charge current to ensure the maximum battery voltage  616  is not exceeded. Following the setting of the charge current  620  a test and decision is formed in block  622 . The test performed in block  622  determines if the cell voltage is now equal to or has exceeded the maximum cell voltage. If false, then the continuous evaluation of the charge current continues back at block  618 . Otherwise, if the maximum voltage has been reached, the charge process exits the CAP stage and proceeds to block  630  where the constant voltage or CV stage begins. During the CAP process steps  618  through  622 , the charging apparatus, such as  400  in  FIG. 4 or 500  in  FIG. 5  for example, continues to update various battery data  612  including DOD, battery age, battery voltage and temperature which allows fresh anode voltage and anode resistance calculations to be made to keep the constant anode potential (CAP) (since the OCVanode cannot be measured and so, must be calculated as shown in Equation 2 ). 
         [0081]    In the CV charging stage, beginning with step  630  in  FIG. 6A , in an example the open cell anode voltage (OCV AN ) is calculated using equation 2 A and also utilizing equation 2 B. These equations take into account battery data  612  which includes the cell impedance, battery age, and DOD and cell temperature as recorded by the charging apparatus for this specific lithium battery cell. With the OCV AN  determined along with the max battery voltage  616  and battery data  612 , the charge voltage is set in block  632  as the lower of the voltages. As indicated in the current data  638  shown in graph  602  in the CV stage  648 , in order to meet the lower of the charge voltages, the charge current  638  typically drops. A test of the charge current is performed in block  636 . The final charge current I CUTOFF  may be determined to be a portion, typically 5 % to 10 %, of the full charge capacity  634 . When the charge current is less than the pre-determined I CUTOFF , charging is terminated in block  640 . Otherwise the flow loops back to block  630  where OCV AN  is again computed. 
         [0082]    Graph  602  in  FIG. 6B  depicts the operation the CAP/CV charger described in the present application by showing sample charge voltage and charge current data for the CAP/CV charger. In graph  602 , the CAP phase is indicated by time frame  646 , the CV phase is indicated by time frame  648  and these two time frames are aligned with the data lines in graph  602 . The dashed line indicate the charge voltage of the CAP/CV charger, with the CAP/CV charge current as curve  638  and the CAP/CV charge voltage as curve  634 . In this non-limiting, illustrative example, the maximum charge current capability of the charger is 1.35 C and the maximum battery charge voltage is 4.20V. 
         [0083]    Utilizing aspects of the current application, the CAP charge current  632  begins at the charger maximum current of 1.35 C in graph  602 . The current is limited by the maximum capability of the charging apparatus. Following the charge current data line  632  right to near the 0.5 hour position, the current level drops below the maximum current of 1.35 A thereby protecting the battery from lithium plating that could otherwise occur. The charge current is reduced below the 1 C charge level close to 0.9 C and then gradually rises back to near 1.0 C at the end of the CAP stage  646 . For the last portion of the charging, the CV stage  648 , the maximum battery voltage has been reached so the charge current is continually reduced until it falls below the cutoff current. At that time the charging is terminated. 
         [0084]    The CAP/CV charge profiles depicted in this example are dependent on the battery age, SOC, temperature and charger capacity and therefore are not the only charge profile that the arrangement can produce. In addition, it is advisable that a guard band, such as 10 % to 20 %, be incorporated within the calculation of EQUATION 2 to ensure that no lithium plating will occur due to a measurement tolerance or calculation rounding error. 
         [0085]      FIG. 6C  compares the results obtained using an example CAP/CV charging arrangement of the present application to a constant current/constant voltage (CC/CV) charging cycle of a prior known approach. Graph  650  is a plot of the charging current (Current) depicted on the vertical axis in terms the C rate, v. the charging time on the horizontal axis, in hours. The line  653  depicts the charging current and charge time for the CAP/CV approach of the present application, while the line  655  depicts the results obtained for a traditional CC/CV charging approach. The total time required for the CAP/CV approach in this non-limiting, illustrative example, was just over 1 hour. The total time required for the CC/CV cycle of the known prior approaches was about 1.75 hours. The CAP/CV approach begins charging at a relatively high current level at time 0 hours, and this current is initially increased to above 2 C rate. However, as the dynamically adjusted current is determined, the charging current is reduced (to avoid the possibility of lithium plating) and after the maximum voltage is reached, the current continues to reduce to the end of the charging time (the last phase is a constant voltage phase). In contrast, the prior known approach begins with a constant current that is reduced to less than 1 C, and maintained for a long time, over 1 hour in the graph  650 , and then once the maximum voltage is reached, the current falls until the end of the charging cycle. 
         [0086]    As can be seen in the graph  650  in  FIG. 6C , use of the CAP/CV approaches with the optimized charging current of the present application thus results in a substantially shorter charging time, while lithium plating is avoided, increasing battery life and maintaining charge capacity over the battery life (since increases in internal resistance are also avoided). 
         [0087]      FIG. 7  depicts in a simplified circuit diagram for an apparatus such as a battery gauge for implementing the method arrangements of  FIG. 6 . In  FIG. 7 , a circuit  700  which can be implemented as a stand-alone integrated circuit, as part of a larger integrated circuit, or as a circuit board or module, is shown in a simplified circuit diagram. Inputs for the battery voltage (BAT), the temperature sensor (Temp) and the state of charge (SOC) are input to a multiplexer  701 . The output of the multiplexer  701  is fed into at least one analog to digital converter (ADC)  703 . The analog to digital converter outputs digital data for use by the CPU  705 . CPU  705  is further coupled to a memory for storing instructions labeled Instruction Store  709 ; these instructions can include program code for configuring the CPU  705  to perform the CAP/CV method of  FIG. 6A , for example. In addition the CPU  705  is coupled to a data buss DATA which is coupled to static RAM  711  and a non-volatile storage Data Store  713  for storing battery parameters such as the anode factor Fanode, Ranode, and the age of the battery, the number of cycles, temperature compensation factors for the calculation of the potential OCVanode, Ranode, and the other parameters of the equations shown above. Data store  713  can include data stored as a look up table (LUT), for example. The battery gauge circuit  700  can be coupled to the battery charger and/or the application processor as shown in  FIGS. 4 and 5  above, for example, using I2 C interfaces I2 CA  717  and I2 CB  719 . 
         [0088]      FIG. 8  depicts in a graph a comparison of battery degradation as a percentage rate/second plotted on the vertical axis and time on the horizontal axis. An optimized charging profile, such as can be accomplished using the method of  FIG. 6A , for example, is compared to prior known constant current/constant voltage or CC/CV approach. The degradation for the prior known approach has a peak value between about 0.4 and 0.6 hours. This peak degradation of the battery indicates that for that portion of the charging cycle, lithium plating is occurring. For the optimized charging profile such as one achieved using the example arrangements of the present application described herein, for example, the battery degradation curve is fairly constant and does not indicate the lithium plating problem. This occurs because the novel charging profiles used are arranged to avoid the conditions that cause lithium plating. The arrangements of the present application use a continuous dynamic adjustment to the charging current in the first portion (CAP) of the charging profile, a constant anode potential is maintained. This phase of the novel arrangements roughly corresponds to the “constant current” portion of the prior known approach, however in the arrangements provided in the present application the charging is performed in a manner determined to avoid the lithium plating phenomenon of the prior approaches. 
         [0089]    As described above, in some arrangements a battery gauge can control a battery charger, in other arrangements, the battery gauge can provide sensed and stored data parameters to the application processor which can then control the battery charger. In another arrangement, the battery charger and battery gauge circuits can be implemented as a single integrated circuit, for example. 
         [0090]    Various modifications can also be made in the order of steps and in the number of steps to form additional novel arrangements that incorporate aspects of the present application, and these modifications will form additional alternative arrangements that are contemplated by the inventors as part of the present application and which fall within the scope of the appended claims. 
         [0091]    Although the example illustrative arrangements have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the present application as defined by the appended claims. 
         [0092]    Moreover, the scope of the present application is not intended to be limited to the particular illustrative example arrangement of the process, machine, manufacture, and composition of matter means, methods and steps described in this specification. As one of ordinary skill in the art will readily appreciate from the disclosure, processes, machines, manufacture, compositions of matter, means, methods or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding example arrangements described herein may be utilized according to the illustrative arrangements presented and alternative arrangements described, suggested or disclosed. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.