handbook of modern sensors

5.10 Batteries for Low Power Sensors 223
Often, batteries are characterized by energy per unit weight, however, for miniature
sensor applications energy per unit volume often becomes more critical.
Table A.20 (Appendix) shows typical characteristics of the carbon–zinc and alkaline
cells (power density in watt·hour per liter and per kilogram.)
In general, the energy delivered by a battery depends on the rate at which power
is withdrawn. Typically, as the current is increased, the amount of energy delivered
is decreased. Battery energy and power are also affected by the construction of the
battery, the size, and the duty cycle of current delivery. The manufacturers usually
specify batteries as ampere-hours or watt-hours when discharged at a specific rate to
a specific voltage cutoff. For instance, if the battery capacitance is C (in mA·h) and
the average current drain is I (mA), the time of a battery discharge (lifetime for a
primary cell) is defined as
t = C In , (5.86)
where n is the duty cycle. For instance, if the battery is rated as having capacity of 50
mA h, the circuit operating current consumption is about 5 mA, and the circuit works
only 5 min every hour (duty cycle is 5/60), the battery will last for
t = C In = (50)(60)
(5)(5)
= 120 h
Yet, the manufacturer’s specification must be used with a grain of salt and only as
a guideline, for the specified discharge rate rarely coincides with the actual power
consumption. It is highly recommended to determine the battery life experimentally,
rather than rely on the calculation. When designing the electronic circuit, its power
consumption shall be determined during various operating modes and over the operating
temperature range. Then, these values of power consumption must be used in the
simulation of the battery load to determine the useful life with a circuit-specific cutoff
voltage in mind. Sometimes, a circuit draws high currents during short times (pulse
mode) and the battery’s ability to deliver such a pulse current should be evaluated. If
a battery cannot deliver a high pulse current, a parallel electrolytic capacitor serving
as a storage tank may be considered.
It should be noted that the accelerated life tests of a battery must be used with
caution, because as it was noted earlier, the useful capacity of a battery greatly depends
on the load, operational current profile, and duty cycle.
5.10.1 Primary Cells
The construction of a battery cell determines its performance and cost. Most primary
cells employ single, thick electrodes arranged in a parallel or concentric configuration
and aqueous electrolytes. Most small secondary cells are designed differently; they
use a “wound” or “jelly roll” construction, in which long, thin electrodes are wound
into a cylinder and placed into a metal container. This results in a higher power
density, but decreased energy density and higher cost. Due to the low conductivity of
electrolytes, many lithium primary cells also use the “wound” construction [18].