If the DC current is 100mA then a filter capacitor value as low as 47uF will produce ripple of 14.4V peak-to-peak. Using 1000uF then the ripple is "only" about 0.5V peak-to-peak.
I have some small inexpensive 1000uF/16V capacitors.
Looking through my vast collection of small transformers (a number of which came from Radio Shack), I found that I have that very transformer. I notice that on the Radio Shack site (
12V CT 450mA Standard Chassis-Mount Transformer with Leads - RadioShack.com)
there is a tab for tech info, but it only gives the mechanicals. I measured the transformer I have and I found that the primary DC resistance is 140 ohms, the secondary is 1 ohms per each half of the center tapped secondary. The leakage inductance (with primary shorted) referred to the full 12 volt secondary is 3.35 mH.
If you add these parasitics to your model (I'm assuming you got the numbers in your post from a simulation), you may get somewhat different results.
The transformer has surprisingly good regulation for such a small transformer. With 120 VAC applied to the primary, the unloaded output voltage from the full secondary was 14.0 VAC. With a load current of .450 amps into a pure resistive load, the secondary voltage dropped to 12.18 VAC.
I soldered up a 2 diode circuit using the center tap arrangement. I made some measurements with a 100 mA load. With only 47uF of filter cap, I get about 5.6 volts of ripple, P-P, and a DC output voltage of 6.3 volts.
With 1000 uF of filter cap, I get about .445 volts of ripple, P-P and a DC output voltage of 8 volts.
I've attached 2 scope captures. The one labeled scope_7 is for the 47uF case, and the one labeled scope_8 is for the 1000uF case.
The yellow trace is the voltage across the capacitor, the green trace is the current into the resistive load and the red trace is the current out of one half of the center tapped winding.
In the scope_8 capture, the yellow and green traces have their ground references offset so that the ripple can be seen.