Battery charger

1. A battery charger comprising:

a memory storing battery parameters, including a battery time constant and a present state of charge; and

a charger controller coupled to the memory, and configured to:

determine a transitional state of charge based on a difference between the predetermined current and a taper current, the full charge capacity, the battery time constant, and the present state of charge;

determine a total charge time based on the battery time constant, the present state of charge, and the transitional state of charge;

determine a charging start time based on the total charge time;

maintain the battery at the present state of charge below a full charge capacity of the battery before the charging start time;

supply a predetermined current to charge the battery after the charging start time and before the battery reaches the transitional state of charge; and

supply a predetermined voltage to charge the battery after the battery reaches the transitional state of charge.

2. The battery charger of claim 1 , wherein the present state of charge is received from a gauge coupled to the battery, and the present state of charge is below the full charge capacity when received.

3. The battery charger of claim 1 , wherein the charger controller is configured to maintain the battery at the present state of charge by providing a charging signal to increase the present state of charge by 2% or less, and terminating the charging signal until the battery returns to the present state of charge.

4. The battery charger of claim 1 , wherein the battery comprises a lithium ion battery.

5. The battery charger of claim 1 , wherein the charger controller is configured to determine the battery time constant based on the full charge capacity and the predetermined current.

6. The battery charger of claim 1 , wherein the battery time constant characterizes the product of a resistance and a capacitance of an equivalent circuit for the battery.

7. The battery charger of claim 1 , wherein the charger controller is configured to update the battery time constant at a charge termination time according to:

τ

=

FCC

⁡

(

1

-

SOC

st

)

-

I

st

*

t

last

I

st

-

I

tap

+

I

st

*

ln

⁡

(

I

tap

I

st

)

in which:

τ is the battery time constant for the battery;

I st is a constant current provided to the battery during a charging of battery;

I tap is the taper current provided after termination of a charging of the battery;

FCC is the full charge capacity of the battery; and

t last is a measured charging time for charging the battery from a starting SOC (SOC st ) to an SOC of about 100%.

8. The battery charger of claim 1 , wherein the charger controller is configured to determine the total charge time according to:

t

tot

⁡

(

SOC

p

,

τ

)

=

{

τ

⁡

(

ln

⁡

(

FCC

-

FCC

*

SOC

p

+

I

tap

*

τ

I

st

*

τ

)

-

ln

⁡

(

1

I

st

*

I

tap

)

)

,

SOC

p

≥

SOC

-

CV

FCC

⁡

(

1

-

SOC

p

)

-

τ

⁡

(

I

st

-

I

tap

)

I

st

-

τ

*

ln

⁡

(

I

tap

I

st

)

,

SOC

p

<

SOC

-

CV

in which:

t tot is the total charge time of the battery;

τ is the battery time constant for the battery;

I st is a constant current provided to the battery during a charging of the battery;

I tap is the taper current provided after termination of a charging of the battery;

FCC is the full charge capacity of the battery;

SOC p is the present state of charge of the battery; and

SOC CV is the transitional state of charge of the battery.

9. A non-transitory machine readable medium having instructions, which upon being implemented by a processor, cause the processor to:

determine a transitional state of charge of a battery based on a difference between the predetermined current and a taper current, the full charge capacity, the battery time constant, and the present state of charge;

determine a total charge time based on the battery time constant, the present state of charge, and the transitional state of charge;

determine a charging start time based on the total charge time;

maintain the battery at the present state of charge below a full charge capacity of the battery before the charging start time;

supply a constant current to charge the battery after the charging start time and before the battery reaches the transitional state of charge; and

supply a constant voltage to charge the battery after the battery reaches the transitional state of charge.

10. The non-transitory machine readable medium of claim 9 , wherein the instructions, which upon being implemented by the processor, cause the processor to maintain the battery at the present state of charge by providing a charging signal to increase the present state of charge by 2% or less, and terminating the charging signal until the battery returns to the present state of charge.

11. The non-transitory machine readable medium of claim 9 , wherein the instructions, which upon being implemented by the processor, cause the processor to determine the battery time constant based on the full charge capacity and the predetermined current.

12. The non-transitory machine readable medium of claim 9 , wherein the instructions, which upon being implemented by the processor, cause the processor to update the battery time constant at a charge termination time according to:

τ

=

FCC

⁡

(

1

-

SOC

st

)

-

I

st

*

t

last

I

st

-

I

tap

+

I

st

*

ln

⁡

(

I

tap

I

st

)

in which:

τ is the battery time constant for the battery;

I st is a constant current provided to the battery during a charging of battery;

I tap is the taper current provided after termination of a charging of the battery;

FCC is the full charge capacity of the battery; and

t last is a measured charging time for charging the battery from a starting SOC (SOC st ) to an SOC of about 100%.

13. A battery charging system comprising:

a battery pack including a battery;

a battery gauge configured to determine a present state of charge of the battery; and

a battery charger configured to provide a charging signal to the battery pack, the battery charger comprising a charger controller configured to:

determine a transitional state of charge based on a difference between the predetermined current and a taper current, the full charge capacity, the battery time constant, and the present state of charge;

determine a total charge time based on the battery time constant, the present state of charge, and the transitional state of charge;

determine a charging start time based on the total charge time;

maintain the battery at the present state of charge below a full charge capacity of the battery before the charging start time;

supply a constant current to charge the battery after the charging start time and before the battery reaches the transitional state of charge; and

supply a constant voltage to charge the battery after the battery reaches the transitional state of charge.

14. The battery charging system of claim 13 , wherein the battery charger is configured to maintain the battery at the present state of charge by providing a charging signal to increase the present state of charge by 2% or less, and terminating the charging signal until the battery returns to the present state of charge.

15. The battery charger of claim 13 , wherein the charger controller is configured to determine the battery time constant based on the full charge capacity and the predetermined current.