sim508 eval
Yes, the 4,700uF is a Huge cap. But our products are used in a variety of industrial applications, some with very nasty power sources. For our applications, we've found that that size cap works for all situations, and many of our applications cannot tolerate failures.
The power reuquirements you quote are for the SIM card, not the radio. While connected to the network, the radio can draw almost 500mA, depending on the mode and band. During actual transmission it can draw as much as 3 Amps about every 4.6mS. The power supply has to provide clean power while transmitting. Look at section 3.4 of this manual:
https://www.madeeasykits.com/Docs/Hardware Design SIM300DZ_HD_V2.03.pdf
It details the power requirements. In particular look at the section regarding the VBAT voltage where it states:
Voltage must stay within the min/max values, including voltage drop, ripple, and spikes.
Depending on your application, you can probably reduce the size of the input capacitor significantly. However, our experience has been that the cap connected to the VBAT lines needs to be about 2,200uF for reliable power in all modes and under all conditions - even though SIMCom documentation may suggest otherwise.
I've consulted on a lot of GSM applicaitons, and by far the major problem with most designs is poor power supply design. I've seen systems that were in the field for months and worked fine, that then started experiencing failures because of marginal power supplies. I'd recommend that you test your supply in the production environment, under the worse case for current draw and temperature, and look at the VBAT line with a good scope to ensure that you are meeting the device requirements.