**This article is part of the Ideas for Design**** Series: ****Vol. 3, No. 1**

Batteries based on the nickel-metal-hydride (NiMH) and lithium-ion (Li-ion) chemistries have largely replaced the older nickel-cadmium (NiCd) battery in many of today’s applications. Still, NiCds are the preferred choice when high discharge currents and a rapid recharge cycle (between one and two hours) are principal concerns.

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Precautions must be taken, however, when you try to recharge a standard NiCd cell “fast” at current levels that approach or exceed the rated capacity of the battery (called its C-rating). As the battery becomes fully charged, these high-current levels (at 1C or higher) cause a rapid increase in electrochemical reaction (oxidation/reduction) within the cell, with a corresponding rapid increase in both internal cell pressure and temperature.

Therefore, as the cell approaches or exceeds 100% capacity, the high charging current must be reduced or the cell’s overcharge safety vent may open, causing gasses to escape with a possible loss of electrolyte. Additionally, repeated overcharging could degrade the cell’s life—the useful number of charge/discharge cycles—or even render it permanently useless.

One way to avert the potential damage that can result from repeated cell overcharging at high currents is to monitor the differential temperature T_{DIFF} = T_{B} – T_{A} between the battery’s surface temperature (T_{B}) and ambient temperature (T_{A}) and proportionally reduce or “taper” the charging current I_{CH} as the differential temperature increases.

Consider a design that must convert a differential temperature rise (battery surface temperature above ambient) that ranges from 0°C to 5°C into a charging current that decreases proportionally from a maximum current level of 1C to 0 A. If the rated capacity of an AA cell equals 600 mAhr, then 1C equals 600 mA. Equation 1 describes this differential-temperature-to-charging-current system:

Temperatures T_{B} and T_{A} are monitored separately by standard negative-temperature-coefficient (NTC) thermistors (10 kΩ at 25°C) with corresponding resistance values of R_{T(B)} and R_{T(A)}, respectively *(Fig. 2)*. Both sensor output voltages, V_{B} and V_{A}, are then applied to the inputs of a basic passive adder created by R2 and R3. At T_{B} = T_{A} = 20°C (i.e., T_{DIFF} = 0°C) V_{B} = +2.75 V and V_{A} = -2.75 V, the passive adder’s output voltage is given by single-ended control voltage V_{T} = (V_{A} + V_{B})/2 = (–2.75 V + 2.75 V)/2 = 0 V.

When T_{B} rises to 25°C due to the initial high charging current of 600 mA and T_{A} remains constant at 20°C (T_{DIFF} = 5°C), the sensor voltage V_{B} = +2.50 V and V_{A} = –2.75 V while control voltage V_{T} = (V_{A} + V_{B})/2 = (–2.75 V + 2.50 V)/2 = -0.125 V. As a result, the output of the passive adder produces a value for V_{T} that is inversely proportional to T_{DIFF}, *(Fig. 1b)*:

The voltage-to-high-current converter circuitry around IC1, whose output current is directly proportional to V_{T}, has both scale and offset capabilities and therefore can be designed to deliver the needed charging current I_{CH} to the battery *(Fig. 1c)*. Circuit performance is described analytically by:

Before proceeding, we can check the validity of this design by convolving Equation 2 with Equation 3 to reproduce Equation 1:

Begin the design implementation with T_{DIFF} at 0°C where V_{T} = 0 V. V_{SET} is chosen to equal 1.25 V, the maximum charging current is set at 600 mA, and the R_{SET} resistor value is determined by letting R_{SET} = V_{SET}/I_{CH} = 1.25 V/600 mA = 2 Ω (2 W). When the differential temperature T_{DIFF} rises to 5°C and V_{T} = -125 mV, the value of V_{SET} will have linearly decreased to 0 V, causing I_{CH} to drop to approximately 0 A, terminating the high-current charge. The performance equation for this voltage-to-high-current converter is given by.

However, dividing both sides of the equation by R_{SET} yields the more useful form for design:

Final component selection for this converter is accomplished by comparing both offset and scale terms of the design equation *(Equation 3)* with the converter’s corresponding performance equation terms in Equation 4b. Set feedback resistor R6 to 100 kΩ, 1% and equate offset terms in Equation 5. Then solve for the value of R5 by choosing –5 V for V_{REF}.

The calculated value of R5 (416.67 kΩ) is approximated by choosing a standard 412 kΩ, 1% resistor. Finally, calculate the value of R7 by comparing scaling terms in.

The calculated value of R7 is 11.96 kΩ, which can be satisfied with a standard 12-kΩ, 5% resistor. Circuit performance was simulated and verified by laboratory measurement over multiple charge/discharge cycles.

**Reference**

Villanucci, Robert S. and Diecidue, Joseph, “‘Intelligent’ NiCd Charger Avoids Battery Damage from High Currents,” *Electronic Design*, May 8, 2008, p 51-54, http://electronicdesign.com/power/intelligent-nicd-charger-avoids-battery-damage-high-currents

**Read more articles from the**** Ideas for Design**** Series: ****Vol. 3, No. 1**

*Robert S. Villanucci**, professor (retired), holds an AEng from the Wentworth Institute of Technology, Boston, Massachusetts, a BSET from Northeastern University, and an MSEE from Tufts University, Medford, Mass.*

*Joseph Diecidue**, electronics technician, holds a BSEE from the Wentworth Institute of Technology, Boston, Massachusetts.*