I have created a power supply which provides 5V and 15mA. My battery (3.7V,520mAh) doesn't charge because this current isn't strong enough,it starts charging from ~150mA - 200mA. But my application consumes 2mA in average. For my battery to accept the charge, I plan to use a shunt battery charger. Is it the good thing to do?
Use a dedicated charging chip like MCP73831. Maximum current is set with a single resistor.
Firstly you should not be charging with such a high voltage. Your charger should only supply a maximum of 4.2V to 4.3V. Secondly the charge current available is far too low and at that rate (15mA) it will take over 34 hours to charge.
First, if someone is concerned about efficiency, a shunt regulator is not the most efficient dc to dc regulator.
Secondly, LI-ion batteries are not forgiving of design flaws in their chargers. To avoid major problems (fire and explosion) their charging profiles need to be carefully observed - Voltage, current, time, battery temperature...
Here's a reference to app notes and data sheets to get the full story. http://www.linear.com/search/search.php?q=li-ion+charger