Regarding energy storage for the rail, consider that 1 farad when discharged by 1 ampere will sag at 1 volt/second.
Let's assume you have 50 Hz power. Thus you can use a full-wave rectifier and have 100 recharge opportunities per second. Thus your TIME will be 0.01 seconds.
Assume you will accept 0.1 volt sag on the VDD. How big must your capacitor be?
dV/dT = I/C, derived from the derivative of Q = C * V, with C held constant.
Rearrange this, and C = I / (dV/dT) = I * T/ V
In the above case, C = 1 ampere (assumed) * 0.01 second / 0.1 volt = 0.1 farad or
================ example of selecting VDD filter for OpAmp =======
Now lets apply what we've learned to a precision opamp circuit, with DC to 100MHz signal (perhaps radar modulation) and we need 12 bit performance (or settling) despite the OpAmp having ZERO dB Power Supply Rejection at high frequencies. Can we design the VDD filtering?
Assume the Opamp must drive 15 picoFarad load at +- 2 volts (4 volts PP) as well as a 250 Ohm feedback resistor.
Summary: we need to provide the surge currents, occurring every 10 nanoSeconds and the VDD capacitor must settle very quickly or NOT SAG more than 1/2^12 or more than 1 Vquanta at the VDD pin.
Assume Vquanta is 1milliVolt (4vpp/4096).
Assume the surge current is I = C * dV/dT + Vout/Rload * Vout/Rfeedback
Isurge = 15pF * 2vPeak * 630Million volts/second + 0 + 2vpeak/250 ohm
Isurge = 15pF * 1.2GigaVolt/sec + 8mA = 18mA + 8mA = 26mA
What size cap (before we worry about VDD ringing, and settling)?
C = I * T/V = 26mA * 10nanoSec / 0.001 = 26mA * 10,000 nano = 260,000 picoF
C = 0.26uF
OK. Now suppose we don't want that cap (plus all the inductance of OpAmp package + PCB traces + PCBvias + 0.26uF inductance) to ring more than 1milliVolt? Can we dampen it? Assume 10nH inductance (to emphasize the seriousness of the challenge).
Fring of 1 uF (round up, to handle temperature deltaCapacitance effects) and 10 nanoHenry? Fring = 0.16 / sqrt(1uF * 10nH) = 0.16 / 1.0e-7 = 1.6MHz.
How to dampen? use resistor of value sqrt(L / C) = sqrt(10nH/ 1uF) = sqrt(0.01) or 0.1 Ohm. Which is an awkward value to find.
What to do? Think about this
simulate this circuit – Schematic created using CircuitLab
Is the 1nanoFarad cap a good idea?