Download An Area and Power-Efficient Analog Li-Ion Battery Charger Circuit

IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011
131
An Area and Power-Efficient Analog
Li-Ion Battery Charger Circuit
Bruno Do Valle, Student Member, IEEE, Christian T. Wentz, Member, IEEE, and
Rahul Sarpeshkar, Senior Member, IEEE
Abstract—The demand for greater battery life in low-power
consumer electronics and implantable medical devices presents
a need for improved energy efficiency in the management of
small rechargeable cells. This paper describes an ultra-compact
analog lithium-ion (Li-ion) battery charger with high energy
efficiency. The charger presented here utilizes the tanh basis
function of a subthreshold operational transconductance amplifier to smoothly transition between constant-current and
constant-voltage charging regimes without the need for additional
area- and power-consuming control circuitry. Current-domain
circuitry for end-of-charge detection negates the need for precision-sense resistors in either the charging path or control loop.
We show theoretically and experimentally that the low-frequency
pole-zero nature of most battery impedances leads to inherent
stability of the analog control loop. The circuit was fabricated
in an AMI 0.5- m complementary metal–oxide semiconductor
process, and achieves 89.7% average power efficiency and an end
voltage accuracy of 99.9% relative to the desired target 4.2 V,
while consuming 0.16 mm2 of chip area. To date and to the best
of our knowledge, this design represents the most area-efficient
and most energy-efficient battery charger circuit reported in the
literature.
Index Terms—Battery charger, constant-current (CC) charger,
constant-voltage (CV) charger, lithium-ion (Li-ion) battery, wireless power transfer.
I. INTRODUCTION
HIS PAPER presents a novel, ultra-compact, and highly
efficient lithium-ion (Li-ion) battery charging circuit
that addresses the unique challenges of battery management
for small rechargeable cells (5–100 mAh). The entire circuit
operates in the analog domain and is particularly well suited
for operation in implantable medical devices or portable consumer electronics applications, where energy and space are at a
premium.
Ultra-low power-electronic systems utilizing small rechargeable cells present a unique challenge for digitally controlled
T
Manuscript received October 14, 2010; revised December 16, 2010; accepted
December 29, 2010. Date of publication February 17, 2011; date of current version May 18, 2011. This work was supported in part by the National Institute
of Health under Grant NS- 056140 and in part by the Office of Naval Research
under Grant N00014-09-1-1015. This paper was recommended by Associate
Editor A. Bermak.
B. Do Valle and R. Sarpeshkar are with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]; [email protected]).
C. T. Wentz was with the Department of Electrical Engineering and Computer
Science, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139
USA. He is now an Independent Consultant (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TBCAS.2011.2106125
charger circuitry. In these circuit architectures, the energy
overhead consumed by controller logic is fixed, while charging
current varies with battery capacity. Thus, at low charging
currents, a significant fraction of total power may be consumed by the control circuitry. These designs may utilize
large-area analog-to-digital converters (ADCs) or costly precision-trimmed sense resistors in the voltage comparator for
accurate end-of-charge detection [1], [2].
The circuit presented here addresses both of these issues. As
an alternative to digital control logic, we utilize the tanh basis
function of an operational transconductance amplifier (OTA)
operating in the subthreshold region to output a current profile that smoothly and automatically transitions between constant-current (CC) and constant-voltage (CV) charging regions.
As a result, this circuit is an order of magnitude smaller than previous designs, while achieving higher average power efficiency,
at 89.7% efficiency over the entire charging period, from 3.0 V
to 4.2 V.
In addition, this design entirely eliminates the need for precision end-of-charge sense resistors to detect the small-signal
changes in battery voltage near the end of the charging profile.
Instead, sense circuitry operates in the current domain, comparing large-scale changes in charge current to a current reference to determine the end of charge.
The circuit utilizes an on-chip bandgap reference in a standard complementary metal–oxide semiconductor (CMOS)
process, thus enabling relatively temperature-invariant operation over a wide range of temperatures.
Overall, this design represents a simple analog power- and
area-efficient alternative to existing more complicated and
power-hungry designs. A previous version of this paper had
been presented at a conference [3]. In this invited journal paper,
we presented improvements to the battery charger, including
an on-chip bandgap reference circuit in a standard CMOS
process. We also presented stability analysis, confirmed by an
experiment that revealed the circuit’s intrinsic stability when
driving battery impedance. These impedances create a dominant low-frequency pole-zero pair in the loop transmission that
stabilizes the operation of the feedback loop.
II. BACKGROUND
Li-ion batteries are a popular choice for long-life, space-constrained systems, such as portable consumer electronics and
implantable medical devices, due to their ability to provide
high energy density and competitive power density (e.g., 158
Wh/kg and 1300 W/kg, respectively [4]), while being immune
to memory effects.
Despite these advantages over other battery chemistries, battery longevity and capacity in Li-ion cells is highly sensitive to
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IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011
Fig. 2. Simplified battery charger block diagram.
A. OTA
Fig. 1. Theoretical Li-ion charging profile.
final charging voltage accuracy. Thus, care must be taken to ensure that the circuit adheres to close voltage tolerances. Previous
reports 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 runaway
can occur. During discharge, deeply discharging the Li-ion battery below 3 V can permanently reduce the cell’s capacity [6].
These issues are of critical concern in implanted medical devices. These applications may additionally require reliable operation of the charger under varying supply voltages, as in the
case of a wirelessly charged system.
The charging profile of a Li-ion battery can be divided into
four 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 discharged (voltage is less than 3 V). During trickle charge, the
battery is charged with a small amount of current, typically no
more than 0.1 times the rated capacity of the battery, or (0.1 C)
[5]. C represents the battery capacity expressed in terms of ampere-hours (Ah). Charging currents greater than 0.1 C may be
hazardous since the battery has a high internal impedance at
these low voltages and is susceptible to thermal runaway. Above
3.0 V, the battery may be charged at higher currents, typically
less than 1 C; this regime represents the constant-current region.
As the battery voltage approaches 4.2 V, the charging profile
enters the constant-voltage region. In this region, the charging
current should be progressively decreased as the battery voltage
approaches 4.2 V. Charging current should be decreased until a
certain threshold is met—typically about 2% of the rated battery
capacity [5]. Once this charging current is reached, the charger
enters the end-of-charge region.
III. CIRCUIT DESCRIPTION
The simplified block diagram of our circuit topology is
illustrated 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) an
end-of-charge detector.
The OTA shown in Fig. 2 generates a tanh output current profile as a function of the instantaneous battery voltage relative to
the 4.2-V bandgap reference. By operating the OTA in the subthreshold regime, where the linear range of the tanh is close to
100 mV, we were able to automatically transition from CC to
CV operation without any digital oversight, thus eliminating the
need for charger-controller logic.
The OTA was designed to operate in subthreshold to save
power and to reduce its linear range. The linear range is given
by the following equation [7]:
(1)
is the thermal voltage and
is the transistor’s subwhere
threshold exponential-slope parameter. According to (1), the
linear range is set by the technology being used, since it only
and the thermal voltage. For
depends on process parameter
our 0.5- m technology, we obtained a linear range of approximately 100 mV. This linear range implies that for battery voltages less than approximately 4.1 V, the OTA output is saturated,
and the output current is at its maximum value. For battery voltages equal to or more than 4.1 V, the difference in the OTA’s
input terminal voltages in Fig. 2 drives it into its linear region
of operation so that its output current begins to decrease. Equation (2) relates the output current of the OTA to its input voltage
is the OTA bias current
difference [7].
(2)
In order to facilitate trickle charging, the OTA topology was
slightly modified: Fig. 3 shows the schematic of the OTA with
the addition of transistors M1 and M2 to allow for trickle-charge
operation. If the battery voltage is less than 3 V, the Trickle
Charge Flag is low, enabling M1. In this case, transistor M2
conducts some current, which reduces the OTA’s output current
due to shunting of its bias current. The reduction in charging
current during trickle charge is proportional to the ratio of the
W/L of M2 to the W/L of M6 or M8. Once the battery voltage
crosses the 3-V threshold, the Trickle Charge Flag goes high,
disabling the current path through M1 and M2. As a result, the
.
bias current of the OTA is increased to its maximum value
B. 4.2-V Reference
As mentioned in Section II, optimizing charger design for
battery 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 temperatures
and supply voltages. To ensure proper circuit operation under
these conditions, we employ an on-chip bandgap reference circuit shown in Fig. 4, followed by a noninverting op-amp circuit
to generate an accurate 4.2-V reference.
In the instance of wirelessly rechargeable devices, supply
voltage variation is a significant concern. An example of an experimental wireless power link and its analysis can be found
in [8]. The rectified voltage from this wireless power link has
a ripple of approximately 5 mV. In the context of an Li-ion
battery, we require an error tolerances of less than 0.25% in
the output voltage ripple of the bandgap reference. The powersupply rejection ratio (PSRR) is mainly determined by the amplifier in Fig. 4. At the intentionally low-power levels that we
ran this operational amplifier at, it demonstrates approximately
21 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 is
5 mV [8], our PSRR implies a ripple output voltage of approximately 500 V, or a 0.012% error. Thus, the expected error due
to the ripple in the power supply is well below the acceptable
error tolerance of 0.25% in our design.
A properly designed voltage reference maintains extremely
small output voltage variation over a wide temperature range
by 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 resistor
ratio, the circuit output is also tolerant to resistor fabrication error when fabricated using standard very-large-scale
integrated (VLSI) layout techniques. To allow fabrication of
this circuit in a standard CMOS process, we utilized parasitic
bipolar diodes. To provide additional immunity to process
variation, we included 7 b of trimming in the gain of the
noninverting amplifier so that the voltage reference can be
changed by 15% in increments of 0.25%. Trimming consists
of changing the value of one of the resistors that sets the gain
in the noninverting amplifier. Utilizing these techniques, we
obtained a final charging voltage of 4.202 V, corresponding to
an error of less than 0.1%.
C. Current Gain
The current-gain stage, shown in Fig. 5, is composed of standard current mirrors to increase the current output of the OTA
from a few hundred nanoamps to the appropriate charging current for the battery. In our application, we were constrained to
about 10 mW of power consumption, so the charging current
was limited to approximately 2.5 mA. By increasing the gain in
the current mirror stage in Fig. 5, the battery charger can be modified to increase its charging current from a few milliamperes to
several amps for other high-power applications.
D. End-of-Charge Detector
The end-of-charge detector shown in Fig. 6 compares the
end-of-charge Input, shown in Fig. 3, to a reference current.
In order to minimize error, the reference current utilized in the
end-of-charge detector is proportional to the reference current
used to bias the OTA. Fig. 6 shows the schematic of the current
comparator that we employed in the end-of-charge circuit [9].
The end-of-charge output signal is normally at ground when the
end-of-charge input is higher than
, and transitions to V
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IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS, VOL. 5, NO. 2, APRIL 2011
Fig. 7. Trickle-charge threshold detector.
Fig. 5. Current-gain stage with the disable option.
Fig. 8. Simplified feedback block diagram.
IV. STABILITY
Fig. 6. End-of-charge detector.
when this condition is no longer true. The transition to
inactivates M3 in Fig. 5, thus reducing the battery charge current
to zero.
In order to determine when the battery reaches the 3-V
threshold for the trickle-charge region of operation, we designed a simple low-power detector circuit, shown in Fig. 7.
As the battery voltage decreases, the voltage at the node
between transistors M2 and M3 decreases. The relationship
between the voltage at this node and the battery is linear, so
the current flowing through transistor M5 reduces quadratically
when M2 and M3 are in saturation, and exponentially when
they enter subthreshold. When the battery voltage is less than
3 V, the current output of M5 is smaller than the reference
, so the trickle charge flag is low. Transistors M1
current
through M5 were designed with large widths and lengths in
order to minimize process variation. This strategy also minimizes power consumption so that the threshold detector may
run off the battery voltage directly. The designed threshold
detector consumes only 3 W, when the battery voltage is
approximately equal to 3.7 V, and very little layout area since
the design does not require any resistors.
The battery charger contains a negative-feedback loop comprising the OTA, current-gain stage, and the battery itself. Since
any feedback loop can become unstable in certain situations, we
analyzed the stability of our circuit. The circuit block diagram
shown in Fig. 2 can be redrawn into a simplified feedback block
is the transconductance of
diagram shown in Fig. 8 where
the OTA and is the current gain from the output of the OTA
to the battery.
The OTA in our circuit is biased with 125 nA and the
maximum charging current during constant current is almost
2.8 mA. This implies that the current gain has a maximum
value of 22 400. The transconductance of the OTA is given by
and
are the OTA bias current and linear
(3) [7], where
range, respectively
(3)
for this circuit is equal to apAccording to (3), the
S. We modeled the battery as a
proximately
simple resistor in series with a capacitor, assuming that as in
most electrode-electrolyte situations, the spreading resistance
and double-layer capacitance are dominant [7]. The battery’s
impedance is then given by (4), where and are the battery’s
resistance and capacitance, respectively
(4)
The battery resistance is approximately 1 while the capacitor of an 8-mAh battery is approximatelly 26 Farads [10]. Thus,
DO VALLE et al.: AN AREA AND POWER-EFFICIENT ANALOG LI-ION BATTERY CHARGER CIRCUIT
135
Fig. 10. Die micrograph of the battery charger circuit.
Fig. 9. Bode plot of the loop transmission.
we obtain the following expression for the loop transmission of
our circuit:
(5)
Since the capacitance of the battery is 26 Farads, and the
resistance is 1
[10], the loop crossover frequency is near
1.1 mrads
while the loop-transmission zero is nearly 6.1
MHz. The next poles in our charger are caused by the last stage
of the current mirror and other dynamics within the transconductance amplifier and are estimated to be near 10 kHz, which
is well past the crossover frequency. Thus, the feedback loop
is quite stable for our settings. As long as the gain setting of
the feedback loop is not too high so that the fixed zero due to
the battery occurs well past the crossover frequency, the effect
of the high-frequency dynamics in the transconductor do not
matter, and the feedback loop is stable and exhibits nearly 90
of phase margin. For our settings, we found this situation to
be true for virtually any battery with a capacity greater than a
few milliampere-hours. The Bode plot of the loop transmission
described by (5), along with a couple of parasitic poles located
at approximately 10 kHz, is shown in Fig. 9.
V. RESULTS
The battery-management chip was fabricated in an AMI
0.5 m CMOS process, consuming 0.16 mm of chip area.
Fig. 10 shows the die micrograph of the test chip.
Fig. 11(a) shows the measured results of the battery-management integrated circuit (IC) charging an 8-mAh battery from
trickle charge to the beginning of the constant current region.
The battery was charged with 0.9 mA and 2.8 mA during the
trickle-charge and in the constant-current regime, respectively.
The supply voltage was set to 4.3 V. Fig. 11(b) shows the remaining regions of the charging profile: constant current, constant voltage, and end of charge, respectively. The constant-
voltage region begins when the battery reaches approximately
4.1 V and the OTA starts to enter its linear range. The transition
between constant-current operation and constant-voltage operation is continuous since the control loop is based on a simple
tanh function. According to Fig. 11(b), the charging current decreases as the battery voltage goes from 4.1 V to 4.2 V, reaching
the end of charge when the current is approximately 0.10 mA.
At the end of charge, the battery voltage is 4.202 V, providing
an accuracy higher than 99.9%.
While this chip is limited to about 2.8 mA of maximum
charging current, the design presented can accommodate currents of at least 100 mA by simply increasing the ratio of
current gain in Fig. 5 or by increasing the OTA bias current in
Fig. 3. Beyond 100 mA, stability degrades due to excessive gain
in the current mirror. If the desired charging current exceeds
100 mA, the system can be stabilized by adding a pole to the
feedback loop that forces the crossover frequency to occur well
below the high-frequency dynamics of the transconductor. This
pole can be added by including an off-chip capacitor between
the gate of M5 and ground in Fig. 5. The addition of this pole
does not affect the charging efficiency or the layout area since
the only required component is an off-chip capacitor.
The 4.2-V reference was measured over a temperature range
from 25 C to 50 C to demonstrate that it is relatively insensitive to temperature variation. The plot of the voltage reference
versus temperature is shown in Fig. 12. This battery charger was
designed to be part of an implantable medical device; therefore, the measured temperature range is well beyond the typical temperature variation within a human body. According to
Fig. 12, the reference error is always less than 0.3% and, therefore, negligible.
The power-supply rejection ratio (PSRR) of the 4.2-V reference was measured from 1 kHz to 10 MHz since the supply
voltage, which is generated from an inductive power link, might
have some noise with an amplitude close to 5 mV. The plot of
the 4.2-V PSRR is shown in Fig. 13. It demonstrates that the
PSRR around 6.785 MHz is approximately 21 dB, which causes
less than a 0.5% error at the output of the voltage reference.
Thus, the error due to power-supply noise is negligible.
Table I compares this design with previous Li-ion charger
circuits found in the literature. We only found one paper
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Fig. 11. Measured battery current and voltage when charging an 8-mAh battery with (a) showing the trickle-charge region and (b) showing the constant-current,
constant-voltage, and end-of-charge region.
TABLE I
LI-ION BATTERY CHARGER DESIGNS COMPARISON
Fig. 12. Voltage reference versus temperature.
Fig. 13. Voltage reference PSRR.
with comparable current in the literature that listed the layout
area and power efficiency. So we compared our design to
high-charging current designs as well. Overall, we obtain an
average power efficiency of approximately 89.7% during the
entire battery charging period, from 3.0 V to 4.2 V, for a supply
voltage of 4.3 V. We note that several alternative designs
presented in the literature only report the maximal charging
efficiency, rather than an average efficiency over the range of
battery voltage so that an exact comparison is difficult. We
propose the average charging power efficiency over the entire
battery range as a metric for future comparison. Even with our
more conservative average power-efficiency metric, our design
achieves higher power efficiency while consuming less area
than any other design found in the literature to date.
In order to have a fair comparison between layout area, the
charging current of this work must be increased from 3 mA
to about 700 mA, which is a factor of 230. One can easily increase the charging current by a factor of 20 by increasing the
bias current of the OTA in Fig. 3. The bias current is only 125
nA so that it can easily be increased to approximately 2.5 A
without requiring large widths in the input pair of the OTA to
guarantee that it operates in the subthreshold regime. The remaining factor of 11.5 can be obtained by increasing the current
gain in the last stage of the current mirror shown in Fig. 5. The
extra area required for the higher gain current mirror is approximately 0.4 mm . Therefore, if the current design is modified for
700-mA charging, the estimated layout area will be increased to
DO VALLE et al.: AN AREA AND POWER-EFFICIENT ANALOG LI-ION BATTERY CHARGER CIRCUIT
TABLE II
FINAL CHARGING VOLTAGE FOR DIFFERENT ICS
0.56 mm , which is still smaller than that of previously reported
designs.
Table II shows the final charging voltage when using different
ICs to charge an 8-mAh battery. As Table II illustrates, the final
charging voltage is always within 0.2% of the desired 4.2 V
because we can programmably trim it on our chip.
VI. CONCLUSION
We have presented and experimentally verified a novel design
for an Li-ion battery charger based on the tanh output current
profile of a subthreshold OTA. This design utilizes the OTA in
an analog feedback loop to control charging current, completely
eliminating the need for energy- and space-consumptive control
logic. Further, our design operates in the current domain, eliminating the need for precision-trimmed sense resistors to determine the end-of-charge point, reducing layout area, manufacturing complexity, and potential charging error due to resistor
mismatch. The layout area required for this chip is more than
an order of magnitude smaller than previous designs, as Table I
illustrates. The design achieved an average power efficiency of
89.7% over the 3.0-V to 4.2-V range of battery voltage. To our
best knowledge, this circuit represents the highest power efficiency and smallest layout area of any design presented in the
literature to date.
ACKNOWLEDGMENT
The authors would like to thank S. Arfin for his help during
the design process and for sharing some of his expertise in
Li-ion batteries.
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Bruno Do Valle (S’03) received the B.S. (Hons.) and
M.S. degrees in electrical engineering from Boston
University, Boston, MA, in 2006 and 2008, respectively, and is currently pursuing the Ph.D. degree at
the Analog VLSI and Biological Systems Group, the
Massachusetts Institute of Technology Research Laboratory of Electronics, Cambridge.
His research interests include low-power analog
and mixed-signal very-large-scale integrated circuits
for biomedical applications, and power electronics
for low-power applications.
Christian T. Wentz (M’10) received the M.Eng.
degree in electrical engineering and computer
science and the B.S. degree in electrical science
and engineering from the Massachusetts Institute of
Technology (MIT), Cambridge.
While at MIT, his research with the Synthetic
Neurobiology Group focused on the application of
low-power electronics to large-scale biopotential
recording and the development of hybrid biologics/implantable device therapies for neurological
disorders. He has published works on a variety of
topics from basic neuroscience to very-large-scale integrated circuits and
systems.
Rahul Sarpeshkar (SM’07) received the B.S.
degrees in electrical engineering and physics from
the Massachusetts Institute of Technology (MIT),
Cambridge, and the Ph.D. degree in electrical engineering from the California Institute of Technology,
Pasadena.
He then joined Bell Labs as a member of the
technical staff in the Department of Biological
Computation within its physics division. Since
1999, he has been on the faculty of MIT’s Electrical
Engineering and Computer Science Department
where he heads a research group on analog very-large-scale and biological
systems. He holds more than 25 patents and has authored many publications,
including one featured on the cover of Nature. He has authored Ultra Low
Power Bioelectronics: Fundamentals, Biomedical Applications and Bio-inspired Systems, which provides a broad and deep treatment of the fields of
low-power electronics and bioelectronics. He is an Associate Editor of the
IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS .
Dr. Sarpeshkar has received several awards, including the National Science
Foundation Career Award, the Office of Naval Research Young Investigator
Award, the Packard Fellows Award, and the Indus Technovator Award for his
interdisciplinary bioengineering research. He serves on the program committees
of several technical conferences