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A very simple battery charger circuit is described in this article, which uses just a single transistor for the voltage detection as well as for automatically disconnecting the battery from the supply when it gets fully charged.
Circuit Description
As shown in the diagram we can see a straightforward configuration where a single transistor is connected in it’s standard operating mode. 
The circuit functioning may be understood with the help of the following points:
Considering the battery to be charged is a 12 volt battery, we know that it is advised to charge the battery until it reaches between 13.5 and 14 volts.
The transistor base voltage is adjusted using the preset P1, such that the transistor just conducts and operates the relay at around 14 volts.
This adjustment becomes the high voltage trip point of the circuit and is used to switch OFF the charging voltage to the battery when it gets fully charged or its voltage reaches around 14 volts.
The lower trip point of the circuit cannot be adjusted as this circuit is too simple and does not incorporate the low voltage detection feature.
However the transistor is itself equipped with a switch OFF feature in case its base voltage becomes too low.
Typically a general purpose transistor like the one which is shown (BC547) when adjusted to switch ON at 14 volts may have the lower threshold of around 10 volts, when it might get just switched OFF.
This wide voltage difference between the high set threshold and the lower natural threshold is because of the involved big hysteresis with the design.
The lower threshold of 10 volts is dangerously low and we cannot wait for the circuit to restart the charging process until the battery voltage falls to this dangerous 10 volts level.
 Allowing the battery to discharge down to 10 volts can make the battery flat permanently and reduce its life.
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Therefore to eliminate this issue the circuit needed to somehow reduce the hysteresis level. This is done by introducing a couple of diodes at the emitter of the transistor.
We know that normally a 1N4007 diodes would drop around 0.7 volts across it and two if them would make a total of 1.4 volts.
By inserting the two diodes in series with the emitter of the transistor, we force the transistor to switch off 1.4 V earlier than its normal specified limit of 10 volts.
Therefore now the lower operating threshold of the circuit becomes 10 + 1.4 = 11.4 volts, which may be considered just OK for the battery and for the automatic restart of the charging process.
Having both the thresholds updated as per the standard charging requirements, we now have an automatic automotive battery charger that’s not only cheap to build but also smart enough to take care of the battery charge conditions very efficiently.


Parts List
R1 = 4K7
P1 = 10K preset,
T1 = BC547B,
Relay = 12V, 400 Ohms, SPDT,
TR1 = 0 - 14V, current 1/10th of the battery AH
Bridge diodes = Equal to the current rating of the transformer,
Emitter diodes = 1N4007,
C1 = 100uF/25V

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