Battery charger control circuit is very useful now-a-days. You need not follow on battery charging or disconnect from ac power for avoiding over charge. This circuit is used to charge battery when the battery voltage drops below the minimum voltage that you want to connect it to a charger. When the battery voltage reaches the maximum voltage you want the charger to be connected.
This circuit is shown in figure. Let your battery voltage is 15 volt. When Ei drops below 10.5 V, V0 goes negative, releasing the relay to its normally closed position. The relay’s normally closed (NC) contacts connect the charger to battery Ei. Diode D1 protects the transistor against excessive reverse bias when V0 = -Vsat. When the battery charges to 13.5 V, V0 switches to disconnect the charger. Diode D2 protects both op-amp and resistor against transients developed by the relay’s collapsing magnetic field.
Suppose that the application requires an inverting voltage level detector with hysteresis. That is V0 must go low when Ei goes above Vut and V0 must go high when Ei drops below Vlt. For this application, do not change the circuit or design procedure for the non-inverting voltage level detectors, simply add an inverting amplifier, or inverting comparator, to the output Vo.