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The inductor needs to have a very low resistance. 0.0049 ohms or there about.At The inductor of 1uH, what does the 4.90m ohm there represent.
In the spice (computer) the battery has a resistance of 0.001 ohm. Not important to you.Also at the input I see R= 1m ohm.
Will use the normal lithium batteries.Where will you find a Lithium battery that is only partially charged or partially discharged at 3.6V to 3.8V? It will be 3.2V when its load should be disconnected and will be 4.20V when fully charged. Then its average voltage during a discharge is 3.7V.