Imagine a relatively large circuit made out of mosfets.

I need to calculate the effective capacitance that the entire circuit switches during each transition. This includes all the gate capacitances and short circuit currents, glitches etc.

My book tells me the formula is this:

C = I_average/ (f * Vdd)

But from my understanding the correct formula should be I_Average / (2pi * f * Vdd), because the impedance of a cap is 1/2pifVdd instead of 1/fVdd.

Please what is the correct formula? Is there a reason why they are removing the 2pi factor from it ?

THank you!!