504PET23.pdf

Power Electronics Technology April 2005 www.powerelectronics.com40

Charging Li-ion Batteriesfor Maximum Run Times

An understanding of battery-charging fundamen-tals and system requirements enable designers tochoose a suitable linear or switch-mode chargingtopology and optimize battery performance in theapplication.

By Scott Dearborn, Principal Applications Engineer,Microchip Technology, Chandler, Ariz.

Far too often, the battery-charging sys-tem is given low priority, especially incost-sensitive applications. However,the quality of the charging system playsa key role in the life and reliability of

the battery. To develop an optimized charging systemfor lithium-ion (Li-ion) batteries, designers must befamiliar with the fundamental requirements for charg-ing these batteries. Designers also should be aware ofthe tradeoffs of linear versus switch-mode chargingsolutions.

The rate of charge or discharge often is expressedin relation to the capacity of the battery. This rate isknown as the C-rate and equates to a charge or dis-charge current and is defined as:

I=M Cn⋅where I is the charge or discharge current, expressed

in amperes (A); M is a multiple or fraction of C; C is anumerical value of rated capacity expressed in ampere-hour(Ah); and n is the time in hours at which C is declared.

A battery discharging at a C-rate of 1 will deliver itsnominal-rated capacity in 1 hr. For example, if the ratedcapacity is 1000 mAh, a discharge rate of 1 C correspondsto a discharge current of 1000 mA. A rate of C/10 corre-sponds to a discharge current of 100 mA.

Typically, manufacturers specify the capacity of a bat-tery at a 5-hr rate, where n = 5. For example, the batterymentioned previously would provide 5 hr of operating timewhen discharged at a constant current of 200 mA. In theory,the battery would provide 1 hr of operating time whendischarged at a constant current of 1000 mA. In practice,however, the operating time will be less than 1 hr becauseof inefficiencies in the discharge cycle.

The preferred charge algorithm for Li-ion battery chem-istries is a constant current-constant voltage (CC-CV)algorithm. The charge cycle can be broken up into fourstages: trickle charge, constant current charge, constant volt-age charge and charge termination (Fig. 1).

In stage one, a trickle charge is employed to restorecharge to deeply depleted cells. These are cells in which thecell voltage is below approximately 3 V. During this stage,the cell is charged with a constant current of 0.1 C maxi-mum. After the cell voltage has risen above the tricklecharge threshold, the charge current is raised to performconstant current charging (stage two). The constant cur-rent charge should be in the 0.2 C to 1 C range. The con-stant current does not need to be precise and semi-con-stant current is allowed. Often, in linear chargers, the cur-rent is ramped up as the cell voltage rises in order to mini-mize heat dissipation in the pass transistor.

Charging at constant current rates above 1 C does notreduce the overall charge cycle time and should be avoided.When charging at higher currents, the cell voltage rises

Fig. 1. The charge profile for a Li-ion battery consists of four stages:trickle charging of deeply depleted cells, constant-current charging,constant-voltage charging and charge termination.

Cell Voltage

Capacity

Charge Current

www.powerelectronics.com Power Electronics Technology April 200541

LI-ION BATTERIES

more rapidly due to overvoltage in the electrode reactionsand the increased voltage across the internal resistance ofthe cell. The constant-current stage becomes shorter, butthe overall charge cycle time is not reduced because thepercentage of time in the constant voltage stage increasesproportionately.

The constant-current charge ends when the cell voltagereaches 4.2 V. At that point, the third stage of charging—the constant voltage stage—begins. To maximize perfor-mance, the voltage regulation tolerance on the voltage ap-plied to the cell should be better than ±1%.

In the fourth and final stage, the constant voltage charg-ing is terminated. Unlike nickel-based batteries, it is notrecommended to continue to trickle charge Li-ion batter-ies, which can cause plating of metallic lithium, a condi-tion that makes the battery unstable. The result can be sud-den, automatic and rapid disassembly.

Charging is typically terminated by one of two meth-ods—a minimum charge current or a timer. However, acombination of the two techniques also may be applied.The minimum current approach monitors the charge cur-rent during the constant-voltage stage and terminates thecharge when the charge current diminishes in the range of0.02 C to 0.07 C.

The second method determines when the constant-volt-age stage is invoked. Charging continues for an additional2 hr, and then the charge is terminated. Charging in thismanner replenishes a deeply depleted battery in roughly2.5 hr to 3 hr.

Advanced chargers employ additional safety features.For example, the charge is suspended if the cell tempera-ture is outside a specified window, typically 0°C (32°F) to45°C (113°F). That safe charging window is specified bythe cell manufacturer.

An understanding of battery-charging fundamentalsand system requirements enable designers to choose a suit-able linear or switch-mode charging topology and opti-mize battery performance in the application.

System ConsiderationsA high-performance charging system is required to re-

charge any battery quickly and reliably. To ensure a reli-able, cost-effective solution, designers must consider sev-eral system parameters, including input source, constant-current charge rate and accuracy, output voltage regula-tion accuracy, charge termination method, cell tempera-ture monitoring, and battery discharge current or reverseleakage current.

Many applications use inexpensive wall cubes for theinput supply. The wall cube is simply a linear transformer-based supply with a bridge-rectified output, but no volt-age regulation. The output voltage of the supply is highlydependent on the ac input voltage and the load currentbeing drawn from the wall cube.

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In this equation, a is the turns ration (nP/n

S). R

EQ is the

resistance of the transformer’s secondary winding plus thereflected resistance of the primary winding (R

P/ a2). R

PTC is

the resistance of the PTC fuse, and VFD

is the forward dropof the bridge rectifiers. In addition, transformer core losswill reduce the output voltage slightly.

Applications that charge from a car adapter can experi-ence a similar problem with supply voltage variations. Theoutput voltage of a car adapter will have a typical range of9 V to 18 V.

The choice of topology for a given application may bedetermined by the desired constant current. Many highconstant-current or multiple-cell applications rely on aswitch-mode charging solution for improved efficiency andless heat generation.

Linear solutions are desirable in low to moderate fastcharge-current applications because of their superior sizeand cost considerations. However, a linear solution pur-posely dissipates excess power in the form of heat.

The tolerance on the constant-current charge becomesextremely important in a linear system. If the regulationtolerance is loose, pass transistors and other componentswill need to be oversized, adding size and cost. In addition,if the constant-current charge is low, the complete chargecycle will be extended.

Another system parameter, output-voltage regulationaccuracy, is critical to maximizing battery-capacity usage.A small decrease in output-voltage accuracy results in alarge decrease in battery capacity. However, the output volt-age cannot be set arbitrarily high because of safety and re-liability concerns. Fig. 2 depicts the importance of output-voltage regulation accuracy.

Overcharging is the Achilles’ heal of Li-ion cells. Accu-rate charge termination methods are essential for a safe,reliable charging system.

Cell temperature also impacts the reliability of the charg-ing system. The temperature range over which a Li-ionbattery should be charged is 0°C to 45°C, typically. Charg-ing the battery at temperatures outside this range mightcause the battery to become hot. During a charge cycle, thepressure inside the battery increases, causing the batteryto swell. Temperature and pressure are directly related. Asthe temperature rises, the pressure can become excessive.This can lead to a mechanical breakdown inside the bat-tery or venting. Charging the battery outside this tempera-ture range may also harm the performance of the batteryor reduce the battery’s life expectancy.

Generally, thermistors are included in Li-ion batterypacks to measure the battery temperature accurately. Thecharger measures the resistance value of the thermistor be-tween the thermistor terminal and the negative terminal.Charging is inhibited when the resistance and, therefore,the temperature is outside the specified operating range.

In many applications, the charging system remains con-nected to the battery in the absence of input power. Thecharging system should minimize the current drain from

ing a nominal input voltage of 120 VRMS

, the tolerance is+10%, -25%. The charger must provide proper regulationto the battery independent of its input voltage. The inputvoltage to the charger will scale according to the ac mainsvoltage and the charge current. The input to the charger orthe output voltage of wall cube can be expressed as:

Fig. 2. A loose tolerance on the charging voltage during the constant-voltage stage results in undercharging of Li-ion battery and reducesthe effective battery capacity.

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mize space while maintaining the desired performance. Inthis design example, fast charge rates of 1 C and 0.5 C havebeen compared. For a charge rate of 0.5 C, one of the par-alleled resistors was removed.

External pass transistor.The external P-channel MOSFETis determined by the gate-to-source threshold voltage, in-put voltage, output voltage and fast charge current. Theselected P-channel MOSFET must satisfy the thermal andelectrical design requirements. The worst-case power dis-sipation in the external pass transistor occurs when theinput voltage is at the maximum and the device hastransitioned from the preconditioning phase to the con-stant-current phase. In this case, the power dissipation is:

where VDDMAX

is the maximum input voltage, IREGMAX

isthe maximum fast charge current and V

PTHMIN is the mini-

mum transition threshold voltage. Maximum power dissi-pation in this design example occurs when charging at the1 C rate.

Utilizing a Fairchild NDS8434 or an International Recti-fier IRF7404 mounted on a 1-inch2 pad of 2-oz copper, thejunction temperature rise is 99°C (210°F), approximately.This would allow for a maximum operating ambienttemperature of 51°C (124°F). By increasing the size of thecopper pad, a higher ambient temperature can be realizedor a lower-value sense resistor could be utilized.

Alternatively, different package options can be used formore or less power dissipation. Again, design tradeoffsshould be considered to minimize size while maintainingthe desired performance.

The gate-to-source threshold voltage and RDSON

of theexternal P-channel MOSFET must also be considered inthe design phase. The worst-case V

GS provided by the con-

troller occurs when the input voltage is at the minimumand the fast charge current regulation threshold is at themaximum. The worst-case V

GS is:

where VDRVMAX

is the maximum sink voltage at the VDRV

output; VDDMIN

is the minimum input voltage source; andV

FCSMAX is the maximum fast charge current regulation

threshold. Worst-case VGS

:

At this worst-case VGS

, the RDSON

of the MOSFET mustbe low enough as to not impede the performance of thecharging system. The maximum allowable R

DSON at the

worst-case VGS

is:

the battery when input power is not present. The maxi-mum current drain should be below a few microamperesand, typically, should be below one microampere.

Linear ChargersTaking the previously mentioned system considerations

into account, an appropriate charge management systemcan be developed using either linear or switch-mode charg-ing solutions. Linear charging solutions are generally em-ployed when a well-regulated input source is available. Inthese applications, linear solutions offer advantages suchas ease of use, size and cost. Due to the low efficiency of alinear charger, the most important factor is the thermaldesign. The thermal design is a direct function of the in-put voltage, charge current and thermal impedance be-tween the pass transistor and the ambient cooling air.

The worst-case situation for a linear charger is whenthe device transitions from the trickle-charge stage to theconstant-current stage. In this situation, the pass transis-tor has to dissipate the maximum power. A tradeoff mustbe made between the charge current, size, cost and ther-mal requirements of the charging system.

For example, take an application required to charge a1000-mAh, single Li-ion cell from a 5-V ±5% input at aconstant-current charge rate of 0.5 C or 1 C. Fig. 3 depictsMicrochip’s MCP73843 in a low-cost, standalone chargerdesign that uses few external components. The MCP73843combines high-accuracy constant-current, constant-volt-age regulation with automatic charge termination. In thisdesign, selection of the external components is crucial tothe integrity and reliability of the charging system, as re-flected in the following guide to component selection.

Sense resistor. The preferred fast charge current forLi-ion cells is at the 1 C rate with an absolute maximumcurrent at the 2 C rate. For this design example, the 1000-mAh battery pack has a preferred fast charge current of1000 mA. Charging at this rate provides the shortest chargecycle times without degradation to the battery-pack per-formance or life. The current-sense resistor is calculated by:

R=V

IFCS

REG

where IREG

is the desired fast charge current and VFCS

equals 110 mV, typically. A standard value 110-m�, 1% re-sistor provides a typical fast charge current of 1000 mAand a maximum fast charge current of 1091 mA. Worst-case power dissipation (PD) in the sense resistor is:

Two Panasonic ERJ-3RQFR22V 220-m�, 1%, 1/8-W re-sistors in parallel are more than sufficient for this applica-tion. A larger value sense resistor will decrease the fastcharge current and power dissipation in both the senseresistor and external pass transistor, but will increase chargecycle times. Design tradeoffs must be considered to mini-


LI-ION BATTERIES

Fig. 3. A typical linear charger solution offers simplicity, small size and low cost.

MA2Q7052 x 220 at 1C1 x 220 at 0.5C NDS8434

5 V

1 8

2

3

4

7

6

5

SingleLi-ionCell

+

-

MCP73843

SENSE

VDD

STAT 1

EN

DRV

VBAT

VSS

TIMER

The Fairchild NDS8434 and International RectifierIRF7404 both satisfy these requirements.

External capacitors. The MCP73843 isstable with or without a battery load. Inorder to maintain good ac stability in theconstant-voltage mode, a minimum ca-pacitance of 4.7 µF is recommended to by-pass the V

BAT pin to V

SS. This capacitance

provides compensation when there is nobattery load. In addition, the battery andinterconnections appear inductive at highfrequencies. These elements are in thecontrol feedback loop during constant-voltage mode. Therefore, the bypasscapacitance may be necessary to compen-sate for the inductive nature of the bat-tery pack.

Virtually any good-quality output fil-ter capacitor can be used, independent ofthe capacitor’s minimum effective seriesresistance (ESR) value. The actual valueof the capacitor and its associated ESRdepends on the forward transcon-ductance, g

m, and capacitance of the ex-

ternal pass transistor. A 4.7-µF ceramic,tantalum or aluminum electrolytic capaci-tor at the output is usually sufficient toensure stability for up to 1 A of outputcurrent.

Reverse-blocking protection. The op-tional reverse blocking protection diodedepicted in Fig. 3 provides protectionfrom a faulted or shorted input or from a

reversed-polarity input source. Withoutthe protection diode, a faulted or shortedinput would discharge the battery packthrough the body diode of the externalpass transistor.

If a reverse-protection diode is incor-porated in the design, it should be cho-sen to handle the fast charge currentcontinuously at the maximum ambienttemperature. In addition, the reverse-leakage current of the diode should bekept as small as possible. A PanasonicMA2YD100L, 1.5-A, 15-V, Schottky di-ode has been chosen. The forward volt-age drop is 350 mV at 1 A, which is im-portant when determining the maxi-mum allowable R

DSON of the pass tran-

sistor. With a reverse voltage of 4 V, theleakage is less than 1 �A.

Enable and charge status interfaces. In the standaloneconfiguration, the enable pin is generally tied to the inputvoltage. The MCP73843 automatically enters a low-powermode when voltage on the V

DD input falls below the

undervoltage lockout voltage, VSTOP

, typically reducing thebattery drain current to 0.23 µA. Meanwhile, a status out-put provides information on the state of charge. The cur-

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rent limited, open-drain output can be used to illuminatean external LED.

Safety timer. The TIMER input programs the period ofthe safety timers by placing a timing capacitor, C

TIMER, be-

tween the TIMER input pin and VSS

. Three safety timersare programmed via the timing capacitor.

The preconditioning safety timer period is:

The fast charge safety timer period is:

And the elapsed time termination period is:

The preconditioning timer starts after qualification andresets when the charge cycle transitions to the constant-current, fast charge phase. The fast charge timer and the

elapsed timer start after the MCP73843transitions from preconditioning. Thefast charge timer resets when the chargecycle transitions to the constant-voltagephase. The elapsed timer will expire andterminate the charge if the sensed cur-rent does not diminish below the ter-mination threshold. The design examplespecifies a charge termination time of6 hr. A standard value 0.22-�F ceramiccapacitor has been chosen.

Fully Integrated LinearChargers

In an effort to further reduce the size,cost and complexity of linear solutions,many of the external components can

be integrated into the charge management controller. Ad-vanced packaging and reduced flexibility come along withhigher integration. These packages require advanced equip-ment for manufacturing and, in many instances, precluderework.

Typically, integration encompasses charge-current sens-ing, the pass transistor and reverse-discharge protection.In addition, these charge management controllers typicallyemploy some type of thermal regulation. Thermal regula-tion optimizes the charge cycle time while maintaining de-vice reliability by limiting the charge current based on thedevice’s die temperature. Thermal regulation greatly re-duces the thermal design effort.

Fig. 4 depicts a fully integrated, linear solution usingMicrochip’s MCP73861. The MCP73861 incorporates allthe features of the MCP73843 along with charge-currentsensing, the pass transistor, reverse-discharge protectionand cell temperature monitoring.

In this case, external component selection consists ofdetermining the value of the charge-current programmingresistor and the components required for monitoring thetemperature of the Li-ion cell. Current sensing is performedinside the MCP73861; therefore, a low ohmic-value senseresistor is not required. The fast charge current is set plac-ing a programming resistor (R

PROG) between the PROG pin

and VSS

. The following formula calculates the value forR

PROG:

R =13.2-11 I

12 I -1.2PROGREG

REG

⋅⋅

⎛⎝⎜

⎞⎠⎟

where IREG is the desired fast charge current in am-peres and R

PROG is in kilo-ohms.

The MCP73861 continuously monitors temperature bycomparing the voltage between the THERM input and V

SS

with the upper and lower comparator thresholds. A nega-tive or positive temperature coefficient (NTC; PTC) ther-mistor and an external voltage divider typically developthis voltage. The temperature-sensing circuit has its own

LI-ION BATTERIES

Fig. 5. Charge cycle waveforms for the MCP73843 are shown withconstant-current charge rates of 1 C and 0.5 C.

Fig. 4. In a fully integrated linear charger solution, functions such as charge current sensing, thepass transistor, reverse-discharge protection and cell temperature monitoring can be broughton chip.

��

�

�


reference to which it performs a ratio metric comparison;therefore, it is immune to fluctuations in the supply input,V

DD. The temperature-sensing circuit is removed from the

system when VDD

is not applied, eliminating additional dis-charge of the battery pack.

Fig. 5 depicts complete charge cycles using theMCP73843 with constant-current charge rates of 1 C and0.5 C. Charging at a rate of 0.5 C instead of 1 C, it takesabout 1 hr longer for the end of charge to be reached. TheMCP73843 scales the charge termination current propor-tionately with the fast charge current. The result is an in-crease of 36% in charge time with thebenefit of a 2% gain in capacity andreduced power dissipation. Thechange in termination current from0.07 C to 0.035 C results in an increasein final capacity from ~98% to ~100%.The system designer has to make atradeoff between charge time, powerdissipation and available capacity.

Switch-mode ChargersSwitch-mode charging solutions

are generally employed in applicationsthat have a wide-ranging input or ahigh input-to-output voltage differen-tial. In these applications, switch-modesolutions have the advantage of im-proved efficiency. The disadvantage issystem complexity, size and cost.

For example, take an applicationrequired to charge a 2200-mAh, singleLi-ion cell from a car adapter at a con-stant-current charge rate of 0.5 C or1 C. It would be extremely difficult toutilize a linear solution in this appli-cation due to the thermal issues in-volved. A linear solution employingthermal regulation could be used, butthe charge cycle times at the reducedcharge currents might be prohibitive.

The first step in designing a suc-cessful switch-mode charging solu-tion is to choose a topology: buck,boost, buck-boost, flyback, single-ended primary inductive converter(SEPIC) or other. Knowing the inputand output requirements and experi-ence quickly narrows the choicesdown to two for this application: buckor SEPIC. A buck converter has theadvantage of requiring a single induc-tor. Disadvantages of this topologyinclude an additional diode requiredfor reverse-discharge protection,high-side gate drive and current sense,

and pulsed input current (an EMI concern).The SEPIC topology has advantages that include low-

side gate drive and current sense, continuous input cur-rent, and dc isolation from input to output. The main dis-advantage of the SEPIC topology is the use of two induc-tors and an energy transfer capacitor.

Fig. 6 depicts a schematic for a switch-mode charger.Microchip’s high-speed pulse-width modulator, theMCP1630, has been utilized in a pseudo smart-batterycharger application. The MCP1630 is a high-speed,microcontroller adaptable, pulse-width modulator. When

LI-ION BATTERIES



used in conjunction with a microcontroller, the MCP1630will control the power system duty cycle to provide outputvoltage or current regulation.

The PIC16F684 microcontroller can be used to regu-late output voltage or current, switching frequency, andmaximum duty cycle. The MCP1630 generates duty cycleand provides fast overcurrent protection based on variousexternal inputs. External signals include the input oscilla-tor, the reference voltage, the feedback voltage and the cur-rent sense. The output signal is a square-wave pulse. Thepower train used for the charger is SEPIC.

The microcontroller provides a great amount of designflexibility. In addition, the microcontroller can communi-cate with a battery monitor, such as Microchip’s PS700, in-side the battery pack to reduce charge-cycle times. Fig. 7depicts complete charge cycles utilizing the switch-modecharging solution. The battery monitor eliminates sensingthe voltage produced across the packs protection circuitryand contact resistance by the charging current.

The proposed switch-mode architecture charges Li-ionbatteries with the preferred charge algorithm by regulat-ing or controlling the current supplied to the battery. APWM signal is generated by the microcontroller (ISET1),scaled and filtered to create a dc reference voltage. This

reference voltage establishes a charge-current command.The RMS current flowing in L2 is equal to the output orcharge current. This current establishes a voltage acrosssense resistor R26. U3A scales and inverts this voltage andfeeds it back to the MCP1630. The MCP1630 regulates thecharge current to the commanded current by varying theduty cycle of the switch, Q1.

The voltage change on the battery occurs at a slow rate,so the voltage loop is closed in the PIC16F684. Based onthe measured battery voltage, the current command isscaled accordingly. In addition, the PIC16F684 has an in-ternal comparator used to quickly shut down the converterin the event of an overvoltage on the output. Because thisarchitecture acts as a controlled current source, an over-voltage condition will result if the battery is removed dur-ing a charge cycle.

A complete design analysis of the SEPIC converter isbeyond the scope of this article. However, key features ofthe design will be addressed here. These include the re-quirements for the bias supply, inductors, energy transfercapacitor, MOSFET switch and catch diode.

Bias supply. A bias supply is necessary to provide powerto the microcontroller and the high-speed pulse-widthmodulator (MCP1630). The bias supply must be able to

LI-ION BATTERIES

Fig. 6. A pulse-width modulator in combination with a PIC microcontroller implements a switch-mode SEPIC charger in which parameters such asoutput voltage and charge current are programmable.

R26

Q1


LI-ION BATTERIES

interface directly with the input supply. In the proposeddesign, voltage regulation is performed in the digital do-main by measuring the output voltage with an analog-to-digital converter (ADC). The ADC reference voltage comesdirectly from the bias supply. The absolute tolerance onthe reference is not critical. Offsets created by the supplycan easily be calibrated out of the overall measurementtolerance. However, line regulation and the temperaturecoefficient of the bias supply are critical. These effects aremuch more difficult to factor out.

Inductors. In a SEPIC convertor, two inductors are re-quired. The voltages across the inductors are equal and inphase; as a result, both inductors may be integrated into asingle magnetic structure referred to as a coupled induc-tor. There are five main criteria used in selecting the in-ductor—inductance value, RMS and peak currents, physi-cal size, power losses and cost.

The actual inductance value affects the available outputpower, transient response of the system and peak currents.The inductor must be able to handle both RMS and peakcurrents. Peak currents are limited by core saturation; RMScurrents are limited by heating effects in the winding. Physi-cal size is another consideration, because the size of the in-ductor can be restricted by the application to fit the chargerwithin the desired form factor. In addition, power losses needto be considered to meet the desired performance of the con-verter. The last factor, inductor cost, is dependent on the con-struction and core materials, which affect overall size, effi-ciency, EMI and form factor. Size and cost become particu-larly complicated at higher frequencies.

As a starting point, choose an inductor value produc-ing a peak-to-peak ripple current equal to 10% of the maxi-mum load current. This will limit the RMS current in theoutput filter capacitor and, as a second-order effect, keepthe core losses in the inductor reasonable. The maximumpeak-to-peak ripple current will occur when the inputsource voltage is at its maximum potential and the batteryvoltage is at its lowest potential. Charging from a caradapter, the maximum steady state voltage—excludingtransient conditions—is 16 V. The required inductance is:

the load current is at its maximum. Here, the minimumsteady state voltage is 9 V, leading to this RMS current:

I =IV

VC17 RMS OUT MAX

BAT MAX

IN MIN( ) ( )

( )

( )

⋅⎛

⎝⎜

⎞

⎠⎟

I =2 A4.2 V

9 V=1.37 AC17 RMS( ) ⋅ ⎛

⎝⎜⎞⎠⎟

The voltage across the energy transfer capacitor is equalto the input voltage (V

IN(MAX) = 16 V). Therefore, a 1-�F,

25-V ceramic capacitor was chosen.MOSFET switch and catch diode. The switch (Q1) and

catch diode (D4) were chosen based on voltage and cur-rent rating. The switch, an N-channel MOSFET, and catchdiode both have a worst-case voltage stress of the maxi-mum input voltage plus the maximum output voltage. Theworst-case average current seen by the switch occurs whenthe input source voltage is at its minimum potential, thebattery is at its maximum potential and the load current isat its maximum. The average current through the catchdiode is equal to the output current:

I =IV

VQ1 AVG OUT MAX

BAT MAX

IN MIN( ) ( )

( )

( )

⋅⎛

⎝⎜

⎞

⎠⎟

I =2 A4.2 V

9 V=0.93 AQ1 AVG( ) ⋅ ⎛⎝⎜

⎞⎠⎟

I =I =2 AD4 AVG OUT MAX( ) ( )

The linear and switch-mode charging solutions pre-sented here are specific to Li-ion batteries. However, thesame guidelines and considerations apply when develop-ing any battery-charging system. PETech

Fig. 7. Switch-mode charge cycles for a 2200-mAh Li-ion cell areshown here with and without the PS700 battery monitor installed.

An inductance value of 15 �H was chosen.Energy transfer capacitor. The energy transfer capacitor,

C17, is chosen to handle the RMS current and voltage. Themaximum RMS current of the energy transfer capacitorwill occur when the input source voltage is at its minimumpotential, the battery voltage is at its highest potential, and

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