Li-ion / LiPo charge calculator

A lithium cell is charged at constant current until it reaches its full-charge voltage, then at that voltage until the current falls to a tenth of the rate, and the numbers are all multiples of the capacity: TI's SLAA287 charges a 500 mAh cell at 1C, 500 mA, precharges at 0.1C below 2.5 V, holds 4.2 V within ±50 mV, and stops at 0.1C. Enter the capacity, the rates and the chemistry to get the three currents, the voltage window, an estimate of the constant-current and constant-voltage times, how much of the capacity is in when the taper starts, and the heat a linear charger makes from a given input.

Fig 1 — The charge current: 50.0 mA of precharge if the cell is below the threshold, 500 mA of constant current for about 50 min, then a taper at constant voltage for about 25 min until the current falls to 50.0 mA and the charger stops. The times are an estimate from SSZTA38's 67/33 split with an exponential taper; a real cell's taper depends on its internal resistance and temperature.

Chemistry

Capacity (mAh)

Fast-charge rate (C)

Precharge rate (C)

Termination rate (C)

Cell voltage at start of CC (V)

Charger input (0 = not linear) (V)

Regulation accuracy (mV)

Currents: fast charge 1C · precharge 0.1C · termination 0.1C: 500 mA · 50.0 mA · 50.0 mA
Voltages: regulate to · window ±50 mV · precharge below: 4.20 V · 4.15–4.25 V · 2.5 V
Time estimate: constant current · constant voltage · total: 0 h 50 min · 0 h 25 min · 1 h 15 min
Charge delivered by the end of CC: 84 % of capacity
Linear charger from 5.00 V: dissipation at the start of CC · in precharge: 1.00 W · 125 mW
Charge temperature window (SLUAAR1): 0 °C to 45 °C

The 1 h 15 min is a model: SSZTA38's "CC is used roughly for the first 67 % of charging", an exponential taper in CV down to the 50.0 mA stop, and a total charge equal to the capacity. A cell with more internal resistance reaches 4.20 V sooner and tapers longer; 84 % in by the end of CC is the model's split, not a measurement.

1.00 W at the start of the fast charge is what a linear charger's pass element burns with the cell at 3 V — SLAA287's charger used a buck converter instead. A charger IC in a small package will fold back its current with die temperature before it delivers 500 mA into a cold cell; the LDO thermal calculator does the package sum.

SLAA287's three ways to decide the cell is full: the current "drops to 0.1C during the constant voltage charging stage", a temperature limit ("if the battery temperature exceeds 40 °C, the charging process is stopped"), and a safety timer. Overcharge is the failure: "it is critical that the final voltage be controlled to within ±50 mV".

How this is calculated

Standard: TI SLAA287; TI SSZTA38; TI SLUAAR1

$I_{fast} = C \cdot r, \qquad I_{pre} = C \cdot r_{pre}, \qquad I_{term} = C \cdot r_{term}$: SLAA287: currents in C-rate — 1C of a 500 mAh cell is 500 mA, 0.1C is 50 mA.
$t_{cv} = t_{cc}\,\frac{0.33}{0.67}, \qquad \tau = \frac{t_{cv}}{\ln(I_{fast}/I_{term})}$: SSZTA38's split of the charging time, and an exponential taper from the fast-charge to the termination current.
$C = I_{fast}\,t_{cc} + I_{fast}\,\tau\left(1 - \frac{I_{term}}{I_{fast}}\right)$: The charge delivered in both phases equals the capacity; solved for t_cc. A model, stated as one.
$P_{linear} = (V_{in} - V_{cell})\,I$: What a linear charger's pass element dissipates; worst at the start of the fast charge.

Assumptions

The CC/CV time split is SSZTA38's "roughly" 67/33 and the CV current decays exponentially; real cells differ with internal resistance and temperature.
The rated capacity is delivered in full by the end of the taper.
The precharge stage is not timed; SLAA287 notes it is rarely used.
The regulation window is symmetric about the chemistry's voltage.
No temperature derating of the current; the 0–45 °C window is reported, not enforced.

What sets a lithium-ion charge

A Li-ion or LiPo charger is a current source that turns into a voltage source. SLAA287 lays the process out in three stages, all in C-rate — "for a 500 mA-h battery, the current corresponding to 1C is 500 mA and the current corresponding to 0.1C is 50 mA". Precharge: "a constant low charge current of 0.1C if the battery voltage is below 2.5 V", a stage that "is rarely used during the charging process of a Li-ion battery" because the cell is seldom that empty. Constant current: "the battery is first charged with a constant current of 1C until the battery voltage reaches 4.1 V or 4.2 V." Constant voltage: the charger holds that voltage, "the charging current starts to fall due to internal cell resistance", and "when the charging current falls below 0.1C, the charging process must stop."

The voltage is the chemistry's and the accuracy is not negotiable: "Li-ion batteries are extremely sensitive to overcharging, and it is critical that the final voltage be controlled to within ±50 mV of 4.1 V or 4.2 V." SLUAAR1's table gives 3.9–4.2 V for Li-ion and 3.5–3.65 V for LiFePO₄, both to be charged between 0 °C and 45 °C. The time is a model. SSZTA38 says "CC is used roughly for the first 67 % of charging … CV kicks in during the last 33 % of the remaining charging time"; the calculator takes that split, lets the CV current fall exponentially from the fast-charge current to the termination current, and sets the total charge equal to the capacity — which gives the constant-current time, the taper time, and the share of the capacity that is in by the end of CC. A linear charger's dissipation is the input minus the cell voltage times the current, worst at the start of the fast charge.

Worked example: SLAA287's 500 mAh cell at 1C

The defaults are the note's: 500 mAh, 1C fast charge, 0.1C precharge below 2.5 V, 0.1C termination, 4.2 V ± 50 mV, the fast charge starting with the cell at 3 V, and a 5 V input.

currents        1C = 500 mA  ·  0.1C = 50 mA precharge and termination
window          4.15 – 4.25 V
CC time         C / (I × (1 + τ/t_cc × 0.9)), τ/t_cc = 0.49/ln 10   → 50 min, 84 % of the capacity in
CV time         0.49 × 50 min                                        → 25 min, tapering 500 → 50 mA
total           about 1 h 15 min at 1C; 2 h 30 min at 0.5C
linear charger  (5 − 3.0) V × 500 mA = 1.0 W at the start of CC; (5 − 2.5) V × 50 mA = 125 mW in precharge

Two things the numbers say. A 1C charger is not a one-hour charger: the last sixth of the capacity goes in slowly, at constant voltage, and a charger that stops at a higher termination current is faster because it leaves that part out. And a linear charger on USB is a heater during the fast charge — a watt into a SOT-23 or a small QFN is the reason single-chip chargers thermally regulate their current, and why SLAA287 used a buck converter whose output only had to sit at "4.2 + 500 mA × 0.75 = 4.575 V".

Where the charge model stops being valid

The time split is a rule of thumb. SSZTA38's 67/33 is "roughly", and for a 4.2 V cell; a cell with high internal resistance, a cold cell, or a fast-charge rate near its limit reaches the regulation voltage earlier and spends longer in CV.
The taper is assumed exponential. Real tapers are close to it but not identical; the model's purpose is the order of the time and the split, not minutes.
Capacity is the rated figure at the rated rate. A cell charged at 1C and stopped at 0.1C holds a little less than one charged at 0.5C and stopped at 0.05C; the difference is the termination, and cell datasheets specify both.
Temperature is a limit, not a variable. The window is 0–45 °C; below 0 °C the cell plates lithium, and SLAA287's firmware stops at 40 °C. Nothing here derates the current with temperature, as a charger IC does.
Protection is separate. The charger's limits protect against the charger; the pack's protection circuit protects against everything else. SLUAAR1: Li-ion "requires protection circuit for safe operation".

Common charging mistakes

Charging at the discharge rating. The "25C" on a LiPo pack is discharge; the charge rate is on the cell datasheet and is usually 1C or less.
A voltage that is right on average. A divider of 1 % resistors is "about 1.4 % total error" (SNVA557) — 60 mV on 4.2 V, outside the ±50 mV — before the reference's own tolerance.
No termination. Holding 4.2 V indefinitely is the overcharge SLAA287 warns of; the current must be watched and the charger must stop.
Floating a lithium cell like a lead-acid one. Stop, let it sag, then recharge; a "trickle" during CV is a cell-life trade, not a default.
A LiFePO₄ cell on a Li-ion charger. 4.2 V is half a volt over its 3.65 V; the chemistry selector is the difference.