My method of calculating C bulk for AC rectifiers is based on energy storage required to prevent dropout if AC input cuts out for 1 cycle at max load.
The typical design on page 1 of your IC spec shows a Cin=680uF for a 12V to 5V @ 5A.
Let’s how close I get to their recommended design.
also Figure 23 shows the ripple current rating for the typical bulk e-cap must have a larger ripple current rating , for larger cap values to withstand the current surges. The RMS current rating of a capacitor is determined by the amount of current required to raise the internal temperature approximately 10°C above an ambient temperature of 105°C. This is NOT the value you want to use in the design , rather the max rated for which capacitors are rated for often 1500 hrs lifespan at the rated temperature. Lower ESR, higher ripple current yet smaller C values are desired. Then ripple voltage in the cap can be further reduced by the circuit ESR added to the cap ESR.
However a lower input voltage a higher average current is needed to maintain a constant DC output power. So there are a lot of critical tradeoffs to balance in e-cap selection and the wrong one means poor reliability and efficiency from overall losses incurred.
Thus using 50 Hz for one cycle= 20 ms. Your output power specified was 5V*1.4A=7W and the suggested efficiency was 80%. So the required energy = E= P*t/80%= 180 mJ
The 24Vac bridge can produce 35V no load and about 24V average with lots of ripple so if we use this high ripple avg, \$E=1/2CV^2=180mJ\$ thus \$C=180mJ*2/24^2=625 uF\$
Hmm pretty close.
Next ESR or Ripple current.(rms) I use the same value as DC current as expected value ( but not a hard startup). so to reduce the stress on the heating up the cap, I am going to insert a power SMD resistor to this cap about 0.1 Ohm hopefully for reliability purposes for the cap without creating losses elsewhere. Then choose a cap with an ESR
value of 10 mOhm so it doesn’t heat up much. this results in a ESR*C=0.01*680uF=6.8us which I know is achievable in low ESR caps. (<10us)
so my recommendation is 625 uF or 680 uF ,10 mOhm + Rs=100 mOhms in series.