That "8" is dimensionless.. so it is not a voltage.
You can ask yourself the same question for the ESR: why 7/8 ?
Same for Cin: why 4 multiplies Vin ripple ?
Probably are some values for safety margins Texas Instruments arrived to in their years of experience designing stuff.
Please my friend, do not use such formulae for capacitor ripple in output of boost...use the formula as follows.........ac(rms) ripple = sqrt(irms^2 - idc^2)
where
irms = the rms current coming out of the boost diode
idc = the dc output current of the boost.
....the above two things are easily found frm standard trapezoid wave eqautions.....
i post them here, the trapezoid equations are in there
Here is the eqaution for IRMS of a trapezoid current waveform
IRMS = SQRT[D * (I1^2 + I1.I2 + I2^2)/3]
where D = duty
I1 = the only thing it can be in that equation
I2 = ditto
This is one of the most key waveforms in hard switched SMPS as you know.
And a triagle wave is just a trapezoid with one side zero
A square wave is just a trapezoid with 2 sides equal.
...so its good for tri's and squares too.
NOT worth doing the integration every time...just see the equation.
OK!
I can understand that setting 8 mulitpler cap is to allow for a load transient.
So do you agree if we don't need to consider load transient, can I omit this "8"?
After carefully reading this document form TI, I think a bulk electrolytic cap is only for transients and ceramics is very one that for reducing the ripple.
Like the TPS40210 picture, TI designer seems always use a parallel combination of electroytic and ceramic.