Stabilizer LP2951 manufactured by National Semiconductors. Element values are taken from the article “Charging”, written by Chester Simpson.
Diode D1 can be any of a series of 1N400x, which can be purchased. It is used as a lock, to prevent reverse current from the battery to the chip LP2951 when disconnecting the input voltage.
The current charge is about 100 mA, and this value is the maximum current is limited to the internal circuits chips LP2951. For those who are interested, let us explain that any lithium-ion battery can be recharged up to charge current 1C (ie, the current in mA equivalent capacity in mAh, so that, for example, the battery capacity of 1100 mAh can be recharged current to 1100 mA). The lower charge current leads, respectively, to more charge time. In my humble opinion, 100 mA – relatively low charging current, so that the typical lithium-ion battery can be connected to this charger for the night.
Resistors specially selected high order (tens / hundreds of ohms and a range of MW) that during a power input voltage current through them has been as low as possible, about 2 microamps. To ensure good accuracy of the output voltage resistors must be within a tolerance of 1%. With the potentiometer 50 kOhm output voltage varies in the range between 8.4 V and 4.26 V. This allows, in accordance with the type of rechargeable battery, set it equal to 4.1 or 4.2 V. The capacitors, in particular, C2, are needed to ensure the sustainability of the scheme.