LTC3350
26
3350fc
For more information
www.linear.com/LTC3350
applicaTions inForMaTion
maximum power transfer rule to maximize the utilization
ratio. The minimum voltage in this case is:
V
CELL(MIN)
=
4R
SC
•
P
BACKUP
n
η
where
η
is the efficiency of the boost converter
(~90% to 96%). For the backup equation,
γ
MAX
and
γ
MIN
,
substitute P
BACKUP
/
η
for
P
BACKUP
.
In this case the energy
needed for backup is governed by the following equation:
P
BACKUP
η
t
BACKUP
≤
1
2
nC
SC
•
CELL(MAX)
2
V
•
α
B
+ α
B
2
–
1–
α
B
2
ln
1
+ α
B
1–
α
B
⎛
⎝
⎜
⎞
⎠
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
Once a capacitance is found using the above equation the
maximum ESR allowed needs to be checked:
R
SC
≤
η
1–
α
B
(
)
n
CELL(MAX)
2
V
4P
BACKUP
Capacitor Selection Procedure
1. Determine backup requirements P
BACKUP
and t
BACKUP
.
2. Determine maximum cell voltage that provides accept-
able capacitor lifetime.
3. Choose number of capacitors in the stack.
4. Choose a desired utilization ratio,
α
B
, for the superca-
pacitor (e.g., 80%).
5. Solve for capacitance, C
SC
:
C
SC
≥
2P
BACKUP
•
t
BACKUP
n
η
CELL(MAX)
2
V
•
α
B
+ α
B
2
–
1–
α
B
2
ln
1
+ α
B
(
)
1–
α
B
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
⎡
⎣
⎢
⎢
⎤
⎦
⎥
⎥
–1
6. Find supercapacitor with sufficient capacitance C
SC
and
minimum R
SC
:
R
SC
≤
η
1–
α
B
(
)
n
CELL(MAX)
2
V
4P
BACKUP
7. If a suitable capacitor is not available, iterate by choosing
more capacitance, a higher cell voltage, more capacitors
in the stack and/or a lower utilization ratio.
8. Make sure to take into account the lifetime degrada-
tion of ESR and capacitance, as well as the maximum
discharge current rating of the supercapacitor. A list of
supercapacitor suppliers is provided in Table 2.
Table 2. Supercapacitor Suppliers
AVX
www.avx.com
Bussman
www.cooperbussman.com
CAP-XX
www.cap-xx.com
Illinois Capacitor
www.illcap.com
Maxwell
www.maxwell.com
Murata
www.murata.com
NESS CAP
www.nesscap.com
Tecate Group
www.tecategroup.com
Inductor Selection
The switching frequency and inductor selection are inter-
related. Higher switching frequencies allow the use of
smaller inductor and capacitor values, but generally results
in lower efficiency due to MOSFET switching and gate charge
losses. In addition, the effect of inductor value on ripple
current must also be considered. The inductor ripple cur-
rent decreases with higher inductance or higher frequency
and increases with higher V
IN
. Accepting larger values of
ripple current allows the use of low inductances but results
in higher output voltage ripple and greater core losses.
For the LTC3350, the best overall performance will be
attained if the inductor is chosen to be:
L
=
V
IN(MAX)
I
CHG(MAX)
•
f
SW
for V
IN(MAX)
≤ 2V
CAP
and:
L
=
1–
V
CAP
V
IN(MAX)
⎛
⎝
⎜
⎞
⎠
⎟
V
CAP
0.25
•
I
CHG(MAX)
•
f
SW
for V
IN(MAX)
≥ 2V
CAP
, where V
CAP
is the final supercapaci-
tor stack voltage, V
IN(MAX)
is the maximum input voltage,
I
CHG(MAX)
is the maximum regulated charge current, and
f
SW
is the switching frequency. Using these equations, the
inductor ripple will be at most 25% of I
CHG(MAX)
.
