This is a single-cell, single inductor, single transistor LED driver. The values are all my first wild guesses, none tuned or tweaked, so it could be improved.
Efficiency is 70% with 1.6 mW into the LED.
Version 4 SHEET 1 880 680 WIRE -144 64 -208 64 WIRE -16 64 -64 64 WIRE 80 64 -16 64 WIRE 240 64 160 64 WIRE 336 64 240 64 WIRE 400 64 336 64 WIRE 480 64 400 64 WIRE 336 112 336 64 WIRE 480 112 480 64 WIRE -16 128 -16 64 WIRE -208 176 -208 64 WIRE 240 208 240 64 WIRE 480 240 480 176 WIRE -16 256 -16 208 WIRE 64 256 -16 256 WIRE 176 256 64 256 WIRE -208 304 -208 256 WIRE 576 304 480 304 WIRE 672 304 576 304 WIRE 240 320 240 304 WIRE 288 320 240 320 WIRE 336 320 336 176 WIRE 336 320 288 320 WIRE -16 336 -16 256 WIRE 336 336 336 320 WIRE 480 336 480 304 WIRE 672 336 672 304 WIRE 240 352 240 320 WIRE -16 464 -16 400 WIRE 240 464 240 432 WIRE 336 464 336 400 WIRE 480 464 480 400 WIRE 672 464 672 416 FLAG -16 464 0 FLAG 336 464 0 FLAG -208 304 0 FLAG 240 464 0 FLAG 480 240 0 FLAG 480 464 0 FLAG 672 464 0 FLAG 576 304 Led_Test FLAG 400 64 A FLAG 64 256 B FLAG 288 320 E SYMBOL LED 464 112 R0 WINDOW 0 39 77 Left 2 WINDOW 3 32 106 Left 2 SYMATTR InstName D1 SYMATTR Value NSCW100 SYMBOL ind 64 80 R270 WINDOW 0 -32 56 VTop 2 WINDOW 3 -38 55 VBottom 2 SYMATTR InstName L1
SYMBOL npn 176 208 R0 WINDOW 0 -54 25 Left 2 WINDOW 3 -90 73 Left 2 SYMATTR InstName Q1 SYMATTR Value BC547C SYMBOL cap 320 112 R0 WINDOW 0 52 26 Left 2 WINDOW 3 48 60 Left 2 SYMATTR InstName C1 SYMATTR Value 33n SYMBOL cap 320 336 R0 WINDOW 0 49 23 Left 2 WINDOW 3 42 59 Left 2 SYMATTR InstName C2 SYMATTR Value 300n SYMBOL cap -32 336 R0 WINDOW 0 52 9 Left 2 WINDOW 3 53 44 Left 2 SYMATTR InstName C3
SYMBOL res -32 112 R0 WINDOW 0 53 44 Left 2 WINDOW 3 44 79 Left 2 SYMATTR InstName R1 SYMATTR Value 10K SYMBOL voltage -208 160 R0 WINDOW 0 54 44 Left 2 WINDOW 3 52 79 Left 2 SYMATTR InstName V1 SYMATTR Value 1.5 SYMBOL res 224 336 R0 WINDOW 0 -51 43 Left 2 WINDOW 3 -48 74 Left 2 SYMATTR InstName R2 SYMATTR Value 50 SYMBOL LED 464 336 R0 WINDOW 0 36 77 Left 2 WINDOW 3 27 103 Left 2 SYMATTR InstName D2 SYMATTR Value NSCW100 SYMBOL current 672 416 R180 WINDOW 0 -69 55 Left 2 WINDOW 3 -75 19 Left 2 SYMATTR InstName I1 SYMATTR Value 1m SYMBOL res -160 80 R270 WINDOW 0 -39 60 VTop 2 WINDOW 3 -47 55 VBottom 2 SYMATTR InstName R3
TEXT 664 184 Left 2 !.tran 100m TEXT 608 88 Left 2 ;Single-Cell LED driver TEXT 616 128 Left 2 ;J Larkin Jan 29 2020