I have got a SEPIC converter design see here: http://www.linear.com/docs/27994 The calculation of the SEPIC converter starts at page 21. For the input capacitance on page 17 they tell you need:
\$I_{RMS}(C_{IN}) = 0.3 \cdot ∆I_L \$
This is a current and not a capacitance how can I calculate a capacitance value from this current?
On page 24 they calculate the coupling capacitor current:
\$I_{RMS}(C_{DC})\$
but again this is no capacitance. How can I calculate a capacitance from this current?
From the datasheet (on page 17, right above your \$I_{RMS} = 0.3 \Delta I_L\$ equation):
The input capacitor of a boost converter is less critical than the output capacitor, due to the fact that the inductor is in series with the input, and the input current waveform is continuous. The input voltage source impedance determines the size of the input capacitor, which is typically in the range of 10μF to 100μF. A low ESR capacitor is recommended, although it is not as critical as for the output capacitor.
This is basically saying: it depends. If your upstream source is close by and decently stiff, a smaller input capacitance (~10μF) will suffice. If the supply is further away or has a high output impedance, a larger capacitor (~100μF) is needed.
Similar to a boost converter, the input current is constant so the capacitors won't need to quickly supply a large amount of current. This is opposed to a buck converter whose input current is discontinuous and thus a higher amount of input capacitance is desired, especially for high-output-impedance upstream supplies.
In my experience, designing input capacitance can be kind of an iterative process. Put a reasonable amount (i.e. guess) in, observe the input voltage ripple (right at the input to the converter), and adjust as needed.
