# Lithium Ion Battery : Cell Array Configuration (V.batt when converting to ≤ 4[V] )

## Question

I am seeking to array 6x 21700 lithium ion battery cells, leaving the option for:

• 1S • 6P (@ V.batt.nom = 03.7 [V], range: 02.7—04.2 [V])
• 2S • 3P (@ V.batt.nom = 07.4 [V], range: 05.4—08.4 [V])
• 3S • 2P (@ V.batt.nom = 11.1 [V], range: 07.8—12.6 [V])

Which is best?

## Background

My intent is to:

• Source power via USB-C PD @ 20 [V] 3—5 [A].
• Charge the battery with TI BQ25730.
• Convert V.usb or V.batt to: 2.9, 3.5, and 3.7 [V]

## (Dis)Charge Efficiencies:

• n.1S (@ V.batt.max = 04.2 [V], I.batt+I.sys = 12.50 [A]) = N/A (89% extrapolated)
• n.2S (@ V.batt.max = 08.4 [V], I.batt+I.sys = 06.25 [A]) = 96%
• n.3S (@ V.batt.max = 12.6 [V], I.batt+I.sys = 04.16 [A]) = 97%

• n.1S (@ V.batt.min = 02.7 [V], I.batt.worst = 6 [A]) = 93%
• n.2S (@ V.batt.min = 05.4 [V], I.batt.worst = 3 [A]) = 96%
• n.3S (@ V.batt.min = 07.8 [V], I.batt.worst = 2 [A]) = 97%

1S extends beyond the graph, which is undesirable. 2S, 3S are more efficient but require a balancing circuit.

## Consideration 1:

Are than any obvious undesirable configurations?

• Is it preferable to work with +8 [V] or +8 [A]?

• Lower current = less copper loss (produce less heat)
• Higher voltage = more clearance (need more space)
• Higher voltage isn't high enough to alter IPC-2221 spacing in the layout.
• Higher voltage could affect capacitors via higher V.dcBias.
• Larger packages needed, resonant frequency reduced
• Only until input of next DC-DC buck converter
• So higher voltage is preferable?
• Is 1S best avoided, as its state would be beyond the system efficiency graph limits?

• Are 2S and 3S best avoided simply to avoid the use of a battery balancing circuit?

• Or is battery balancing not all that bad?

## Consideration 2:

The range of V.1S (2.7—4.2 [V]) extends above and below the downstream V.bus values (2.9, 3.5, 3.7 [V]) and thus requires a 4-switch buck-boost converter.

V.min for 2S (5.4 [V]) and above is always above all V.bus values; thus a buck converter may be used.

In concept for a buck converter:

• Would higher V.batt -yield-> lower V.out/V.in = lower duty cycle D --> lower efficiency n?
• G.worst = V.bus.min / V.batt.max
• G.2S.worst = 2.9 / 08.4 = 0.35
• G.3S.worst = 2.9 / 12.6 = 0.23

Based on the below figure (Fundamentals of Power Electronics, Third Edition, Robert W. Erickson), is buck converter efficiency generally lower with lower duty cycle:

Although contemporary buck converters tend to operate much more efficiently than this:

• Would the potential difference in gain be a clear distinguisher in selection of 2S and 3S, due to the conceptual losses in a buck converter?
• n(@G.2S.worst) = 70%
• n(@G.3S.worst) = 45%

Of the solutions you listed, the best is 6P.

That's because the BMS is much easier (cheaper) without a string of cells in series:

• Charge protection is as simple as using a CCCV charger set for 4.2 V (as long as charging is always above freezing)
• Discharge protection is as simple as a 3.0 V low-voltage cut-off on the load and overcurrent detection/cutoff.
• There is no cell-balancing issue.

All your other considerations, though valid, pale in comparison to the advantage of BMS simplicity.

Having said that, the truly best solution is to buy a ready-made battery bank instead of designing your own. So many things can go wrong with a home-made battery and the risks are great. A battery bank is cheaper, safer, guaranteed to work, housed in a nice enclosure, can be shipped (meets the regulatory agency requirements). A homemade battery is none of these.

• Also, it's a portable, handheld electronic — does the 12 [A] set off any alarms regarding the thermals? I've had my eye on the 30+ degC/W temp rise .. I don't know what to do about that XD Commented Aug 29, 2023 at 17:39
• The heat generated by the cells is the same regardless of cell arrangement. Commented Aug 29, 2023 at 17:41
• Oh, I mean the thermals in the battery charger converter - not the cells. There's some savings with improved efficiency based on operating state but still it seems like the device is only intended for 1W, not the 100W I'm aspiring for.. Commented Aug 29, 2023 at 20:24
• I haven't found high-capacity 21700 battery packs on the mainstream market is all. Unprotected 21700 cells can be purchased at \$3.80, leaving it up to me to find means to protect them. Commented Sep 19, 2023 at 21:14