Mini Power Supply Design Questions

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I call it a mini-power supply but really its just a standard 120:12 VAC transformer with a 7812 regulator. Mini; nothing complicated. I'm looking to add some functionality to a pre-made board that includes a transformer, 1N4007 diode (not a full-wave bridge), and a 7812 regulator and the obligatory caps. But of course, I have a some questions.

1) The original design has a 1000uF cap after the 1n4007 quarter wave rectifier. I know this is for smoothing. Is there a difference between a single 1000uF cap and a pair of 500uF caps? My gut tells me yes, but my head can't figure out what.

2) The additional functionality being added may incur a 'pulsed' load. I'm hopeful I can calculate the peak current and time duration. Anyone know if a formula I can use to determine the voltage droop based on the pulsed load and what size output capacitor would help reduce the droop.
 
1) Two 500uF capacitors in parallel create 1000uF.

2) The 7812 regulator will minimize voltage droop if the peak output current is not more than 1A and if it is cooled properly.
An output capacitor improves the transient response because a voltage regulator has a fairly slow response.
 
The slow response is what I'm looking to factor in. As of right now the load will go from 0mA to 250mA in a few milliseconds. So I'm A) worried about the voltage droop due to the sudden load; B) calculating what size capacitor(s) can be installed to optimize the voltage droop; and C) how well does a 7812 run with no load?
 
 
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According to this data sheet, the response time to a step change in output current is about 10μs, so a load change involving ms of time should give little change in output voltage as long as you have the normal small capacitor of at least 0.1μF at the 7812 output.
 
I looked at atleast four other manufacturers datasheets and they did not include that one graph that I was looking for; that was included in the ST datasheet you linked to. If they had, I wouldn't have asked the question.
 
I looked at atleast four other manufacturers datasheets and they did not include that one graph that I was looking for; that was included in the ST datasheet you linked to. If they had, I wouldn't have asked the question.
I looked at one other data sheet before I looked at the ST. Guess I lucked out.
 
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