Li-ion battery powered circuit design
UPDATE TWO


  ltc4056 damaged 2 times, i'm try to understand the reason of this
  damage
  
  this is my typo mistake. U2 ltc4054, not ltc4056.  


Okay.  This is a very simple circuit. I do not know how 2 of them burned up on you.  



I only see one serious deficiency.
What will you do to keep the battery from being discharged so low the battery gets damaged? 

You may want to consider adding an LTC1998 Voltage Reference for Battery Monitoring.  You could use the BATTLO to shut down the LTC3240.  



Keep in mind the full featured MCP73871 costs about the same as the LTC4054.  Low battery detect, battery temperature monitor, multiple power sources (USB and adapter), set max charge voltage and cutoff voltage, charge status indicator, and power good signal.  All nice features you do not currently have. Just add resistors for settings and LEDs for status. 



UPDATE ONE


  ltc4056 damaged 2 times, i'm try to understand the reason of this
  damage


Notice in your schematic, pin 2 is connected to ground?  


  ISENSE (Pin 2): Sense Node for Charge Current. Current from
  VCC passes through the internal current sense resistor and out of the
  ISENSE pin  to supply current to the emitter of the
  external PNP transistor. The collector of the PNP provides charge
  current to the battery.
  Source: LTC4056 Datasheet


  







Notice BAT pin 3 in your schematic?
BAT is pin 6.
BAT is an input, not output.  


  BAT (Pin  6): Battery  Voltage  Sense  Input.
  Source: LTC4056 Datasheet





  Pin 3 is Base  Drive  Output, for the External PNP Pass Transistor. 
  Provides a controlled  sink  current  to drive the base of the PNP.
  This pin has current limiting protection
  Source: LTC4056 Datasheet






I asked:  


  I do not see an inductor. Is your chip a charge pump and linear step
  down?


You replied:  


  As i said this is stup up/down converter. I think there's a inductor
  inside this. – Berker Işık


There are no semiconductor inductors.
There are different types of step-up and step-down typologies.
Your step-down is not a buck step-down.  That is why I asked.  

The LTC3240-3.3 is a charge pump step-up.  That's okay.  

The LDO step-down mode efficiency (87%) of this chip is okay at 100 mA.
You could do better with a buck step-down without a step-up mode.  You should not need a step up mode.  An Li-ion should not drop below 3.3V  with a 100 mA load.  You should make 3.4V as your cutoff.  

  





Li-ion are sensitive to being drained too low.  You need to set an input voltage point where the regulator is shut down so the battery is not drained too low. 

The reason I recommend the MPC73871 is you can use the LBO low battery output to shut down the 3.3v regulator.  And the LBO voltage is programmable.  

You could also instead use a buck step-down regulator with a programmable LBO/UVLO input.     

END OF UPDATE




I would prefer a more sophisticated charger chip like the
MCP73871 Battery Charge 
Management Controller  

You can use the LBO low battery output to shut down the 3.3v regulator.  

 





The 3.3V Regulator

Not much to say here without part number or max current.

I do not see an inductor.
Is your chip a charge pump and linear step down? 

You do not need the buck/boost 3.3V regulator if your load is not too heavy. 
Use an LDO buck step down converter.
In the discharge curve of a 18650 Li-ion battery, the voltage does not reach 3.3V until near the end of the battery's capacity. 


Source: Panasonic 18650 datasheet