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This is a very simple charger. Transistors and capacitors have to be capable of 100 - 200 volts. Matching the amp output of the transformer to the transistor is another consideration.
To pick a transformer for this project, please do the math before choosing parts for example ; wall outlet of 120v in the transformer primary, secondary transformer output of 60v.
This is a RMS value shown on your meter of 120v & 60 volts when you pass the 60v through a bridge rectifier the voltage converts to peak 2 peak (P2P) pulsed DC with a value of approximately 84v P2P.
The math for this conversation can be calculated like this: 60v * 1.414 = 84v or use this calculations; 60v / .707 = 84v, both calcs are right, just a inverted calc from the other. This is what voltage you will expect from the output of your bridge rectifier seen on your DMM.
This value shows why 100 - 200 volt part's are needed to complete this project.
If you have access to a oscope, it will show P2P at all points. Meaning instead of 120v in, the scope shows 170v in to the transformer and not 60 volts out of the transformer but 84v out on the scope and only a frequency change across the bridge rectifier from 50 or 60hz AC to 100 or 120hz pulse DC.
When drawing on EC, the program works like a true oscilloscope and only shows P2P with no RMS consideration. If you see some strange voltage or frequency on a drawing it maybe from another country or needed to make a drawing work properly.
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