Batteries Specifications
Estimating when they will be fully
discharged
Batteries
• Batteries are electrochemical cells.
– A chemical reaction inside the battery produces a
voltage between two terminals.
– Connecting the terminals (or electrodes) of a
battery to a circuit allows the charge that is built
up around the terminals to flow.
• This causes the electrochemical reaction to continue
until either the terminals are disconnected from the
circuit or there are no longer enough chemicals
available inside the battery to react and produce a
voltage.
Battery Voltage
• The voltage generated by a battery depends
on the chemistry of the electrochemical cell
and how many cells are stacked in series.
– A lead acid cell produces ~2 V. Six cells are placed
in series to produce 12 V, the nominally voltage
produced by a car battery.
Battery Current
• The current produced by the battery depends
on the number of charges freed during the
electrochemical reaction.
– This is a function of the chemistry and the surface
area of the electrodes.
Pb(s) + PbO2(s) + 2HSO4-(aq) + 2H+(aq) ----> 2PbSO4 (s) + 2H2O
mA-hours
• Since a battery has a finite amount of charge
that it can supply current before it is fully
discharged, we can calculate the amount of
time that the battery can supply a particular
current if we know the mA-hours of the
battery.
– Since A is C/s, then a mA-hour is equal to 3.6 C.
– The mA-hour specification is available in the
battery datasheet.
Peukert's law
• Cp is the mA-hours of the battery.
• I is the current that will flow to the external circuit in
mA.
• k is Peukert’s constant, which is equal to 1.1-1.6,
depending on the chemistry and age of the battery.
• t is the time that the current can be supplied by the
battery in hours.
Cp
t k
I
Battery Condition
• State of Charge (SOC) – An expression of the present battery capacity as a
percentage of maximum capacity. SOC is generally calculated using current
integration to determine the change in battery capacity over time.
• Depth of Discharge (DOD) – The percentage of battery capacity that has
been discharged expressed as a percentage of maximum capacity. A
discharge to at least 80 % DOD is referred to as a deep discharge.
• Terminal Voltage – The voltage between the battery terminals with load
applied. Terminal voltage varies with SOC and discharge/charge current.
• Open-circuit voltage – The voltage between the battery terminals with no
load applied. The open-circuit voltage depends on the battery state of
charge, increasing with state of charge.
• Internal Resistance – The resistance within the battery, generally different
for charging and discharging, also dependent on the battery state of
charge. As internal resistance increases, the battery efficiency decreases
and thermal stability is reduced as more of the charging energy is
converted into heat.
http://web.mit.edu/evt/summary_battery_specifications.pdf
Duracell AA Battery
From the graph on the left, you should be able to determine Cp. If we assume that
k = 1, how long can this battery supply 15 mA of current?
What is the Thévenin equivalent resistance of the battery when only 30% of the
charge remains? Draw the circuit when the battery is connected to a 10W resistor,
assuming that the discharge rate is low. How much power is lost as heat when 15
mA is flowing out of the battery?
http://ww2.duracell.com/media/en-US/pdf/gtcl/Product_Data_Sheet/NA_DATASHEETS/MV1500_US_UL.pdf
Summary
• The voltage generated by the battery depends on the chemistry of
the battery and the number of electrochemical cells in series.
• Information in a datasheet for battery can be used to determine
whether the battery can supply sufficient current for the length of
time that a portable embedded system must run.
– The maximum current that can be supplied by the battery is
determined by the electrochemical reaction and the surface area of
the battery electrodes.
• A battery is more accurately drawn as an ideal dc voltage source in
series with resistor, where the value of the ideal voltage depends
on the DOD as well as temperature and the amount of current
drawn by the external circuit.
• The internal resistance of the battery can be used to determine the
amount of power lost as heat as the battery is operated.
