1. Batteries Specifications Estimating when they will be fully discharged

2. 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.

3. 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.

4. 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) + PbO 2 (s) + 2HSO 4 - (aq) + 2H + (aq) ----> 2PbSO 4 (s) + 2H 2 O

5. 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.

6. 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.

7. 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

8. Duracell AA Battery http://ww2.duracell.com/media/en-US/pdf/gtcl/Product_Data_Sheet/NA_DATASHEETS/MV1500_US_UL.pdf 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 10  resistor, assuming that the discharge rate is low. How much power is lost as heat when 15 mA is flowing out of the battery?

9. 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.