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Self-charging can definitely be achieved if you know what you are doing.
Charging a battery which is driving the above circuit is perfectly possible.
For example, I run my battery for lightening up a lamp for several hours(10-hours).
The battery voltage was exactly the same after the test as it was before the test started.
It discharged and re-charged!
Here, the signal generator, which is probably just a simple 555 timer circuit, here am using the logic train pulse generator, which produces a train of pulses with a Mark-Space ratio(duty-cycle) of more than 50% On time. That signal is used to switch a transistor On and Off in rapid succession.
The transistor type is a NPN silicon transistor, an FET type of
transistor, or a Darlington pair IGBT devices.
Whatever the type chosen, the lamp will be switched on and off so rapidly that it will light up.
The fluctuating current through the transformer which produces
an alternating voltage in its secondary winding, which than passes through the diode "D", resistor "R" and capacitor "C"
to charge the battery in spite of the fact that the battery is powering the signal generator circuit and the lamp.
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