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This inverter is very easy to construct, reliable, and even powerful enough to light up a 15W florescent tube (if you cool your transistor well). The only hard-to-find piece of this baby is the so-called yellow inverter transformer. It's a miniature high frequency transformer that has a 25mm x 20mm x 5mm ferrite core, 30 turns of primary, 15 turns of feedback, and 250 turns of secondary all concentric, wound on plastic frame than wrapped with a 'yellow' adhesive tape. If you can't find it in your local electronic shops then search for old portable rechargeble florescent lanterns since they have at least one yellow inverter. Of course you can wind a handmade transformer which would do the same but it is a very difficult task when you don't have an original to inspire and it will still need an appropriate ferrite core.
This is a single transistor oscillator circuit. Current passed through primary winding inducts a magnetic field to the core and the core gives the energy back to the feedback winding with a delay determined by the core material and windings. System then oscillates continuously on a frequency depending on this timing. You cannot use 2SD882 with voltages over 4.5 volts. It is only needed if you are going to feed the circuit with only 4.5 volts. Equivalent transistors may not work as good as 2SD882 (NEC Electronics, Japan).