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  IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011 131 An Area and Power-Efficient AnalogLi-Ion Battery Charger Circuit Bruno Do Valle  , Student Member, IEEE  , Christian T. Wentz  , Member, IEEE  , andRahul Sarpeshkar  , Senior Member, IEEE   Abstract— The demand for greater battery life in low-powerconsumer electronics and implantable medical devices presentsa need for improved energy efficiency in the management of small rechargeable cells. This paper describes an ultra-compactanalog lithium-ion (Li-ion) battery charger with high energyefficiency. The charger presented here utilizes the tanh basisfunction of a subthreshold operational transconductance am-plifier to smoothly transition between constant-current andconstant-voltage charging regimes without the need for additionalarea- and power-consuming control circuitry. Current-domaincircuitry for end-of-charge detection negates the need for preci-sion-sense resistors in either the charging path or control loop.We show theoretically and experimentally that the low-frequencypole-zero nature of most battery impedances leads to inherentstability of the analog control loop. The circuit was fabricatedin an AMI 0.5- m complementary metal–oxide semiconductorprocess, and achieves 89.7% average power efficiency and an endvoltage accuracy of 99.9% relative to the desired target 4.2 V,while consuming 0.16 mm    of chip area. To date and to the bestof our knowledge, this design represents the most area-efficientand most energy-efficient battery charger circuit reported in theliterature.  Index Terms— Battery charger, constant-current (CC) charger,constant-voltage (CV) charger, lithium-ion (Li-ion) battery, wire-less power transfer. I. I NTRODUCTION T HIS PAPER presents a novel, ultra-compact, and highlyefficient lithium-ion (Li-ion) battery charging circuitthat addresses the unique challenges of battery managementfor small rechargeable cells (5–100 mAh). The entire circuitoperates in the analog domain and is particularly well suitedfor operation in implantable medical devices or portable con-sumer electronics applications, where energy and space are at apremium.Ultra-low power-electronic systems utilizing small recharge-able cells present a unique challenge for digitally controlled Manuscript receivedOctober 14, 2010; revised December 16, 2010; acceptedDecember 29, 2010. Date of publication February 17, 2011; date of current ver-sion May 18, 2011. This work was supported in part by the National Instituteof Health under Grant NS- 056140 and in part by the Office of Naval Researchunder Grant N00014-09-1-1015. This paper was recommended by AssociateEditor A. Bermak.B. Do Valle and R. Sarpeshkar are with the Department of Electrical Engi-neering and Computer Science, Massachusetts Institute of Technology, Cam-bridge, MA 02139 USA (e-mail:;, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139USA. He is now an Independent Consultant (e-mail: versions of one or more of the figures in this paper are available onlineat Object Identifier 10.1109/TBCAS.2011.2106125 charger circuitry. In these circuit architectures, the energyoverhead consumed by controller logic is fixed, while chargingcurrent varies with battery capacity. Thus, at low chargingcurrents, a significant fraction of total power may be con-sumed by the control circuitry. These designs may utilizelarge-area analog-to-digital converters (ADCs) or costly pre-cision-trimmed sense resistors in the voltage comparator foraccurate end-of-charge detection [1], [2].The circuit presented here addresses both of these issues. Asan alternative to digital control logic, we utilize the tanh basisfunction of an operational transconductance amplifier (OTA)operating in the subthreshold region to output a current pro-file that smoothly and automatically transitions between con-stant-current (CC) and constant-voltage (CV) charging regions.Asaresult,thiscircuitisanorderofmagnitudesmallerthanpre-vious designs, while achieving higher average power efficiency,at 89.7% efficiency over the entire charging period, from 3.0 Vto 4.2 V.In addition, this design entirely eliminates the need for pre-cision end-of-charge sense resistors to detect the small-signalchanges in battery voltage near the end of the charging profile.Instead, sense circuitry operates in the current domain, com-paring large-scale changes in charge current to a current refer-ence to determine the end of charge.The circuit utilizes an on-chip bandgap reference in a stan-dard complementary metal–oxide semiconductor (CMOS)process, thus enabling relatively temperature-invariant opera-tion over a wide range of temperatures.Overall, this design represents a simple analog power- andarea-efficient alternative to existing more complicated andpower-hungry designs. A previous version of this paper hadbeen presented at a conference [3]. In this invited journal paper,we presented improvements to the battery charger, includingan on-chip bandgap reference circuit in a standard CMOSprocess. We also presented stability analysis, confirmed by anexperiment that revealed the circuit’s intrinsic stability whendriving battery impedance. These impedances create a domi-nant low-frequency pole-zero pair in the loop transmission thatstabilizes the operation of the feedback loop.II. B ACKGROUND Li-ion batteries are a popular choice for long-life, space-con-strained systems, such as portable consumer electronics andimplantable medical devices, due to their ability to providehigh energy density and competitive power density (e.g., 158Wh/kg and 1300 W/kg, respectively [4]), while being immuneto memory effects.Despite these advantages over other battery chemistries, bat-tery longevity and capacity in Li-ion cells is highly sensitive to 1932-4545/$26.00 © 2011 IEEE  132 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011 Fig. 1. Theoretical Li-ion charging profile. final charging voltage accuracy. Thus, care must be taken to en-surethatthecircuitadherestoclosevoltagetolerances.Previousreports indicate that undercharging a Li-ion battery by 1.2% of the 4.2-V target value results in a 9% reduction in capacity [5].If the Li-ion battery is overcharged,dangerous thermal runawaycan occur. During discharge, deeply discharging the Li-ion bat-tery below 3 V can permanently reduce the cell’s capacity [6].These issues are of critical concern in implanted medical de-vices. These applications may additionally require reliable op-eration of the charger under varying supply voltages, as in thecase of a wirelessly charged system.The charging profile of a Li-ion battery can be divided intofour distinct regions as illustrated by Fig. 1: 1) trickle charge,2) constant current, 3) constant voltage, and 4) end of charge.Trickle charging is required only if the battery is deeply dis-charged (voltage is less than 3 V). During trickle charge, thebattery is charged with a small amount of current, typically nomore than 0.1 times the rated capacity of the battery, or (0.1 C)[5]. C represents the battery capacity expressed in terms of am-pere-hours (Ah). Charging currents greater than 0.1 C may behazardous since the battery has a high internal impedance attheselowvoltagesandissusceptibletothermalrunaway.Above3.0 V, the battery may be charged at higher currents, typicallylessthan1C;thisregimerepresentstheconstant-currentregion.As the battery voltage approaches 4.2 V, the charging profileenters the constant-voltage region. In this region, the chargingcurrent should be progressively decreased as the battery voltageapproaches 4.2 V. Charging current should be decreased until acertainthresholdismet—typicallyabout2%oftheratedbatterycapacity [5]. Once this charging current is reached, the chargerenters the end-of-charge region.III. C IRCUIT  D ESCRIPTION The simplified block diagram of our circuit topology isillustrated in Fig. 2. The circuit consists of four major blocks:1) a subthreshold operational transconductance amplifier(OTA), 2) a 4.2-V reference, 3) a current-gain stage, and 4) anend-of-charge detector. Fig. 2. Simplified battery charger block diagram.  A. OTA The OTA shown in Fig. 2 generates a tanh output current pro-file as a function of the instantaneous battery voltage relative tothe 4.2-V bandgap reference. By operating the OTA in the sub-threshold regime, where the linear range of the tanh is close to100 mV, we were able to automatically transition from CC toCV operationwithout any digitaloversight,thuseliminating theneed for charger-controller logic.The OTA was designed to operate in subthreshold to savepower and to reduce its linear range. The linear range is givenby the following equation [7]:(1)where is the thermal voltage and is the transistor’s sub-threshold exponential-slope parameter. According to (1), thelinear range is set by the technology being used, since it onlydepends on process parameter and the thermal voltage. Forour 0.5- m technology, we obtained a linear range of approxi-mately 100 mV. This linear range implies that for battery volt-ages less than approximately 4.1 V, the OTA output is saturated,and the output current is at its maximum value. For battery volt-ages equal to or more than 4.1 V, the difference in the OTA’sinput terminal voltages in Fig. 2 drives it into its linear regionof operation so that its output current begins to decrease. Equa-tion (2) relates the output current of the OTA to its input voltagedifference [7]. is the OTA bias current(2)In order to facilitate trickle charging, the OTA topology wasslightly modified: Fig. 3 shows the schematic of the OTA withtheadditionoftransistorsM1andM2toallowfortrickle-chargeoperation. If the battery voltage is less than 3 V, the  TrickleCharge Flag  is low, enabling M1. In this case, transistor M2conducts some current, which reduces the OTA’s output currentdue to shunting of its bias current. The reduction in chargingcurrent during trickle charge is proportional to the ratio of theW/L of M2 to the W/L of M6 or M8. Once the battery voltagecrosses the 3-V threshold, the  Trickle Charge Flag  goes high,disabling the current path through M1 and M2. As a result, thebiascurrentoftheOTAisincreasedtoitsmaximumvalue .  B. 4.2-V Reference As mentioned in Section II, optimizing charger design forbattery longevity places tight design tolerances on the end-of-  DO VALLE  et al. : AN AREA AND POWER-EFFICIENT ANALOG LI-ION BATTERY CHARGER CIRCUIT 133 Fig. 3. OTA and trickle-charge circuit schematic.Fig. 4. Bandgap schematic. charge detection circuit, over a range of operating temperaturesand supply voltages. To ensure proper circuit operation underthese conditions, we employ an on-chip bandgap reference cir-cuit shown in Fig. 4, followed by a noninverting op-amp circuitto generate an accurate 4.2-V reference.In the instance of wirelessly rechargeable devices, supplyvoltage variation is a significant concern. An example of an ex-perimental wireless power link and its analysis can be foundin [8]. The rectified voltage from this wireless power link hasa ripple of approximately 5 mV. In the context of an Li-ionbattery, we require an error tolerances of less than 0.25% inthe output voltage ripple of the bandgap reference. The power-supply rejection ratio (PSRR) is mainly determined by the am-plifier in Fig. 4. At the intentionally low-power levels that weran this operational amplifier at, it demonstrates approximately21 dB of the power-supply rejection ratio (PSRR) at 6.75 MHz,a typical operating frequency for many inductive power links.If we assume that the ripple voltage from such a wireless link is5 mV [8], our PSRR implies a ripple output voltage of approxi-mately 500 V, or a 0.012% error. Thus, the expected error dueto the ripple in the power supply is well below the acceptableerror tolerance of 0.25% in our design.A properly designed voltage reference maintains extremelysmall output voltage variation over a wide temperature rangeby utilizing the ratio of two resistors in the feedback path of an amplifier, rather than their absolute values. As the gain of a noninverting op-amp is itself only dependent on this resistorratio, the circuit output is also tolerant to resistor fabrica-tion error when fabricated using standard very-large-scaleintegrated (VLSI) layout techniques. To allow fabrication of this circuit in a standard CMOS process, we utilized parasiticbipolar diodes. To provide additional immunity to processvariation, we included 7 b of trimming in the gain of thenoninverting amplifier so that the voltage reference can bechanged by 15% in increments of 0.25%. Trimming consistsof changing the value of one of the resistors that sets the gainin the noninverting amplifier. Utilizing these techniques, weobtained a final charging voltage of 4.202 V, corresponding toan error of less than 0.1%. C. Current Gain The current-gain stage, shown in Fig. 5, is composed of stan-dard current mirrors to increase the current output of the OTAfrom a few hundred nanoamps to the appropriate charging cur-rent for the battery. In our application, we were constrained toabout 10 mW of power consumption, so the charging currentwas limited to approximately 2.5 mA. By increasing the gain inthecurrentmirrorstageinFig.5,thebatterychargercanbemod-ified to increase its charging current from a few milliamperes toseveral amps for other high-power applications.  D. End-of-Charge Detector  The end-of-charge detector shown in Fig. 6 compares theend-of-charge Input, shown in Fig. 3, to a reference current.In order to minimize error, the reference current utilized in theend-of-charge detector is proportional to the reference currentused to bias the OTA. Fig. 6 shows the schematic of the currentcomparator that we employed in the end-of-charge circuit [9].The end-of-charge output signal is normally at ground when theend-of-chargeinputishigherthan ,andtransitionstoV  134 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011 Fig. 5. Current-gain stage with the disable option.Fig. 6. End-of-charge detector. when this condition is no longer true. The transition to in-activates M3 in Fig. 5, thus reducing the battery charge currentto zero.In order to determine when the battery reaches the 3-Vthreshold for the trickle-charge region of operation, we de-signed a simple low-power detector circuit, shown in Fig. 7.As the battery voltage decreases, the voltage at the nodebetween transistors M2 and M3 decreases. The relationshipbetween the voltage at this node and the battery is linear, sothe current flowing through transistor M5 reduces quadraticallywhen M2 and M3 are in saturation, and exponentially whenthey enter subthreshold. When the battery voltage is less than3 V, the current output of M5 is smaller than the referencecurrent , so the trickle charge flag is low. Transistors M1through M5 were designed with large widths and lengths inorder to minimize process variation. This strategy also mini-mizes power consumption so that the threshold detector mayrun off the battery voltage directly. The designed thresholddetector consumes only 3 W, when the battery voltage isapproximately equal to 3.7 V, and very little layout area sincethe design does not require any resistors. Fig. 7. Trickle-charge threshold detector.Fig. 8. Simplified feedback block diagram. IV. S TABILITY The battery charger contains a negative-feedback loop com-prising the OTA, current-gain stage, and the battery itself. Sinceanyfeedback loopcan become unstablein certainsituations,weanalyzed the stability of our circuit. The circuit block diagramshown in Fig. 2 can be redrawn into a simplified feedback block diagram shown in Fig. 8 where is the transconductance of the OTA and is the current gain from the output of the OTAto the battery.The OTA in our circuit is biased with 125 nA and themaximum charging current during constant current is almost2.8 mA. This implies that the current gain has a maximumvalue of 22400. The transconductance of the OTA is given by(3) [7], where and are the OTA bias current and linearrange, respectively(3)According to (3), the for this circuit is equal to ap-proximately S. We modeled the battery as asimple resistor in series with a capacitor, assuming that as inmost electrode-electrolyte situations, the spreading resistanceand double-layer capacitance are dominant [7]. The battery’simpedance is then givenby (4), where and are the battery’sresistance and capacitance, respectively(4)The battery resistance is approximately 1 while the capac-itorofan8-mAhbatteryisapproximatelly26Farads[10].Thus,
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