LTC3350
25
3350fc
For more information
www.linear.com/LTC3350
applicaTions inForMaTion
Note the minimum V
CAP
voltage can also be limited by the
peak inductor current limit (180% of maximum charge cur-
rent) and the maximum duty cycle in step-up mode (~90%).
Optimizing Supercapacitor Energy Storage Capacity
In most systems the supercapacitors will provide backup
power to one or more DC/DC converters. A DC/DC converter
presents a constant power load to the supercapacitor. When
the supercapacitors are near their maximum voltage, the
loads will draw little current. As the capacitors discharge,
the current drawn from supercapacitors will increase to
maintain constant power to the load. The amount of energy
required in back up mode is the product of this constant
backup power, P
BACKUP
, and the backup time, t
BACKUP
.
The energy stored in a stack of n supercapacitors available
for backup is:
1
2
nC
SC
CELL(MAX)
2
V
–
CELL(MIN)
2
V
(
)
where C
SC
, V
CELL(MAX)
and V
CELL(MIN)
are the capacitance,
maximum voltage and minimum voltage of a single ca-
pacitor in the stack, respectively. The maximum voltage
on the stack is V
CAP(MAX)
= n
•
V
CELL(MAX)
. The minimum
voltage on the stack is V
CAP(MIN)
= n
•
V
CELL(MIN)
.
Some of this energy will be dissipated as conduction loss
in the ESR of the supercapacitor stack. A higher backup
power requirement leads to a higher conduction loss for
a given stack ESR.
The amount of capacitance needed can be found by solving
the following equation for C
SC
:
P
BACKUP
•
t
BACKUP
=
1
4
nC
SC
γ
MAX
•
CELL(MAX)
2
V
–
γ
MIN
•
CELL(MIN)
2
V
–
4R
SC
•
P
BACKUP
n
ln
γ
MAX
•
V
CELL(MAX)
γ
MIN
•
V
CELL(MIN)
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
where:
γ
MAX
=
1
+
1–
4R
SC
•
P
BACKUP
n
CELL(MAX)
2
V
and,
γ
Min
=
1
+
1–
4R
SC
•
P
BACKUP
n
CELL(MIN)
2
V
R
SC
is the equivalent series resistance (ESR) of a single
supercapacitor in the stack. Note that the maximum power
transfer rule limits the minimum cell voltage to:
V
CELL(MIN)
=
V
CAP(MIN)
n
≥
4R
SC
•
P
BACKUP
n
To minimize the size of the capacitance for a given amount
of backup energy, the maximum voltage on the stack,
V
CELL(MAX)
, can be increased. However, the voltage is
limited to a maximum of 2.7V and this may lead to an
unacceptably low capacitor lifetime.
An alternative option would be to keep V
CELL(MAX)
at a
voltage that leads to reasonably long lifetime and increase
the capacitor utilization ratio of the supercapacitor stack.
The capacitor utilization ratio,
α
B
, can be defined as:
α
B
=
CELL(MAX)
2
V
–
CELL(MIN)
2
V
CELL(MAX)
2
V
If the synchronous controller in step-up mode is used then
the supercapacitors can be run down to a voltage set by the
