**Care must be exercised when you try to “quickly” charge
a nickel-cadmium (NiCd) cell or battery pack at a current
density that approaches or exceeds one-third of its
capacity (C/3)**. As the battery becomes fully charged, the high
charging current raises both the internal cell pressure and temperature,
which can quickly degrade the battery or destroy it.

One way to avoid damage is to monitor the differential temperature
(T_{DIFF}) between the battery’s surface temperature
(T_{B}) and the ambient (T_{A}) and to proportionally reduce the
charging current (I_{CH}) as the differential temperature increases.
Of course, you must make sure that the sensor monitoring
the ambient environment is attached to a structure that
approximates the thermal mass of the battery pack. Otherwise,
the resulting difference in thermal delays will adversely
affect results.

Consider an example design that must convert a differential temperature ranging from 0°C to 10°C into a charging current that decreases proportionally from C/3 to 0 A. If C equals 750 mA, C/3 equals 250 mA and the equation to describe this linear system is:

*Figure 1 *represents this design equation (*Fig. 1a*), including
graphical and mathematical descriptions of the main circuit
elements: temperature sensor circuitry (*Fig. 1b*), a differentialvoltage-
to-voltage converter (*Fig. 1c*), and a voltage-to-highcurrent
converter (*Fig. 1d*). The circuit measures the two relevant
temperatures, T_{B} and T_{A}, individually using two matched
low-cost silicon-diode temperature sensors.

The sensor outputs, V_{B} and V_{A}, are applied to the inputs of
a differential amplifier that subtracts, scales, and offsets these
voltages, producing a single-ended control voltage (V_{SET})
that’s inversely proportional to TDIFF. Finally, a voltage-tohigh-
current converter delivers the needed charging current
(ICH), which is directly proportional to VSET.

Figure 1 shows that at a T_{DIFF} of 0°C
(V_{DIFF} = 0 V), VSET is chosen to be 2.5 V
and will set the maximum charging current
of 250 mA. When the T_{DIFF} rises to 10°C
(V_{DIFF} = -20 mV), V_{SET} will have linearly
dropped to 0 V, causing I_{CH} to drop to 0
and charging to cease.

The design begins by writing three linear
equations that describe each of the circuit
elements depicted graphically. The two
temperature-derived diode voltages (*Fig.
2*) are applied to the inputs of a standard
difference amplifier (IC_{1}), which subtracts
sensor voltage V_{A} = (-2 mV/°C)T_{A} + 670
mV from V_{B} = (-2 mV/°C)T_{B} + 670 mV to
produce a differential voltage (V_{DIFF}):

In addition to performing the subtraction
described by Equation 2, IC_{1} amplifies
V_{DIFF} by a differential gain (A_{DIFF}), determined
to be 125, and adds an offset voltage
of +2.5 V to the output. The differential
amplifier’s performance equation is:

The components are selected by simply comparing gain and offset terms to design the needed signal-conditioning circuit described by:

Notice that comparing terms also shows
how to correctly wire the inputs—i.e., V_{B} must be wired to the V_{(+)} input and V_{A}
must be wired to the V_{(–)} input. IC_{1}’s differential
gain is:

V_{REF} is set by IC_{2}, a low-output-impedance
reference chip (a REF-03) that creates
precisely 2.50 V.

The design of the voltage-to-highcurrent
converter starts by noting that ICH
is directly proportional to the temperaturedependent
voltage, V_{SET}, and circuit performance
is:

Finally, note that negative feedback
around IC_{3} forces V_{SET} to be applied
directly across the current-setting resistor,
R_{SET}, making: