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I am creating a temporary setup for a lead acid charger, using a rewound Microwave transformer, a bridge rectifier, and a giant filter capacitor (30,000µF).

Wound turns until I got 14 volts filtered on the output of the capacitor.

I tried to charge the battery, but it seemed to get "stuck" at 11.8-12 volts, and not charge up to the 13.5 volt charge.

I know this might not be the best charger setup, but I fried my charger, and need a temporary set up. I AM watching the voltage constantly, and making sure it does not reach above 13.5.

The battery is a 17 amp hour 12 volt lead acid

And the reason I am using the Giant capacitor is I am using it for equipment in parallel with the battery and charger that is very sensitive to hum.

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When you measured the 14 volts I bet that was with the load and battery disconnected. Under load conditions, the transformer and bridge rectifier would drop a volt or two.

Transformers are never perfect and the coils have series resistance that cause imperfect "regulation". Series leakage inductance also contributes to the problem.

For the rectifier, the volts lost across a single silicon diode might be about 0.5 volts on very light loads but when charging, each diode voltage will be more like 0.7 volts and, for a bridge rectifier lose an extra 0.4 volts in total.

You know the answer by now, add 5% (ish) more turns to the secondary.

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Bang more turns on like Andy stated .Do something about the voltage wasting bridge rectifier .Consider mosfets and shottkies .If you are worried about the volts getting too high when left unattended you could rig up some comparetor that kills the charger at say 14.4 V and restarts it at say 13V .This wide deadband means that the setup wont chatter .In fact you could get away with a relay because the number of operations wont be too high .Whether you sense Battery volts with a Tl431 or a LM393 or an ardiouno is up to you . Now imagine that the battery is left there indefinately and the battery has no load .Clearly the system will run short on time long off time pulses .This pulsating operation will on average make less gas .There is a school of thought that its actually better for the battery compared to the orthodox constant float voltage of say 13.8 . I cant prove this but for your job it gives simple circuitry.

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