This needs tweaking - lots of knobs to turn - but looks pretty good. It's outputting more voltage than I expected. It's behaving sort of flyback-y. It gets more traditional with less base current.
Version 4 SHEET 1 1248 772 WIRE 288 32 240 32 WIRE 336 32 288 32 WIRE 560 32 336 32 WIRE 336 112 336 32 WIRE 816 176 688 176 WIRE 880 176 816 176 WIRE 992 176 944 176 WIRE 1088 176 992 176 WIRE 1152 176 1088 176 WIRE -128 224 -304 224 WIRE -96 224 -128 224 WIRE 336 224 336 176 WIRE 336 224 176 224 WIRE 992 224 992 176 WIRE 336 240 336 224 WIRE 560 240 560 32 WIRE 688 240 688 176 WIRE -304 304 -304 224 WIRE 1152 304 1152 176 WIRE 688 352 688 320 WIRE 992 352 992 288 WIRE 992 352 688 352 WIRE 336 384 336 304 WIRE 480 384 336 384 WIRE 560 384 560 320 WIRE 560 384 480 384 WIRE 992 416 992 352 WIRE -304 432 -304 384 WIRE 1152 432 1152 384 WIRE 336 464 336 384 WIRE 816 496 816 176 WIRE 880 496 816 496 WIRE 992 496 992 480 WIRE 992 496 944 496 WIRE 496 512 400 512 WIRE 544 512 496 512 WIRE 656 512 624 512 WIRE 688 512 656 512 WIRE 992 544 992 496 WIRE 176 592 176 224 WIRE 336 592 336 560 WIRE 336 592 176 592 WIRE 336 624 336 592 WIRE 496 624 496 512 WIRE 336 752 336 704 WIRE 496 752 496 688 FLAG -304 432 0 FLAG -128 224 +5 FLAG 992 544 0 FLAG 1152 432 0 FLAG 1088 176 OUT FLAG 288 32 +5 FLAG 480 384 B FLAG 336 752 0 FLAG 496 752 0 FLAG 656 512 +5 SYMBOL voltage -304 288 R0 WINDOW 0 49 41 Left 2 WINDOW 3 55 73 Left 2 SYMATTR InstName V1 SYMATTR Value 5 SYMBOL ind2 544 224 R0 WINDOW 0 -59 32 Left 2 WINDOW 3 -64 65 Left 2 SYMATTR InstName L1 SYMATTR Value 1m SYMATTR Type ind SYMBOL cap 320 240 R0 WINDOW 0 -65 27 Left 2 WINDOW 3 -67 61 Left 2 SYMATTR InstName C3 SYMATTR Value 20n SYMBOL ind2 672 224 R0 WINDOW 0 69 36 Left 2 WINDOW 3 65 68 Left 2 SYMATTR InstName L2 SYMATTR Value 9m SYMATTR Type ind SYMBOL cap 976 224 R0 WINDOW 0 59 25 Left 2 WINDOW 3 63 57 Left 2 SYMATTR InstName C4 SYMATTR Value 330n SYMBOL cap 976 416 R0 WINDOW 0 59 7 Left 2 WINDOW 3 61 44 Left 2 SYMATTR InstName C5 SYMATTR Value 330n SYMBOL schottky 944 160 R90 WINDOW 0 -51 30 VBottom 2 WINDOW 3 -43 32 VTop 2 SYMATTR InstName D1 SYMATTR Value BAT46WJ SYMATTR Description Diode SYMATTR Type diode SYMBOL schottky 880 512 R270 WINDOW 0 -25 -2 VTop 2 WINDOW 3 -29 -1 VBottom 2 SYMATTR InstName D2 SYMATTR Value BAT46WJ SYMATTR Description Diode SYMATTR Type diode SYMBOL res 1136 288 R0 WINDOW 0 64 40 Left 2 WINDOW 3 61 74 Left 2 SYMATTR InstName R7 SYMATTR Value 60K SYMBOL cap 320 112 R0 WINDOW 0 -66 9 Left 2 WINDOW 3 -72 45 Left 2 SYMATTR InstName C1 SYMATTR Value 2µ SYMBOL npn 400 464 M0 WINDOW 0 108 21 Left 2 WINDOW 3 86 54 Left 2 SYMATTR InstName Q1 SYMATTR Value BC547C SYMBOL res 320 608 R0 WINDOW 0 65 25 Left 2 WINDOW 3 57 62 Left 2 SYMATTR InstName R1 SYMATTR Value 20 SYMBOL cap 480 624 R0 WINDOW 0 71 19 Left 2 WINDOW 3 68 51 Left 2 SYMATTR InstName C2 SYMATTR Value 10µ SYMBOL res 640 496 R90 WINDOW 0 69 56 VBottom 2 WINDOW 3 69 57 VTop 2 SYMATTR InstName R2 SYMATTR Value 1K TEXT -240 80 Left 2 !.tran 100m uic TEXT -304 -48 Left 2 ;DC/DC CONVERTER TEXT -280 0 Left 2 ;JL SEP 12, 2013 TEXT 600 120 Left 2 !K L1 L2 0.98 TEXT -248 -88 Left 2 ;COLPITTS TEXT 600 88 Left 2 ;COILCRAFT