->  True, but the voltage is too high to be
-> of use (as it was originally designed) if
-> you use the bridge as you have suggested.

 I am getting Confused. Who in their Right Mind would replace the Two
Diodes with a Bridge. And How can one say it would be a doubling
Circult. You are Putting in Twice to voltage required for a Bridge
Rectifier circuit. OF course the Output would be Doubled. BUT that has
Nothing to do with the Rectifier Doubiling Voltage.
And incidently How many rembember the "Real" Voltage Doubling
Rectifier Circuit used in some old Transformerless Circuits??
There was as I recall even a trick to make a Voltage Quadrupiling
circuit.
 
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