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Finally, substiting Eq. (13) into Eq. (10) and using Eq. (7), gives another version of the exact equation that the ripple and the capacitance (more correctly, ωRC) must satisfy, i.e., cos[arctan(1 / ωRC)] exp(-[2π - arccos(1 - r) - arctan(1 / ωRC)] / (ωRC) = 1 - r ω is the angular frequency of the ripple C is the bulk capacitance R is the load resistance r is the ripple This equation has no closed-form solution and must be solved numerically.

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Finally, substiting Eq. (13) into Eq. (10) and using Eq. (7), gives another version of the exact equation that the ripple and the capacitance (more correctly, ωRC) must satisfy, i.e., cos[arctan(1 / ωRC)] exp(-[2π - arccos(1 - r) - arctan(1 / ωRC)] / (ωRC) = 1 - r ω is the angular frequency of the ripple C is the bulk capacitance R is the load resistance r is the ripple This equation has no closed-form solution and must be solved numerically.
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niconiconi (niconiconi@mk.absturztau.be)'s status on Thursday, 02-Jan-2025 10:05:33 JST niconiconi

Q: What is the formula of the ripple of a DC power supply derived from AC via a diode-capacitor rectifier?
A: Don't worry about it. Just pretend the diode is always off, so you're discharging a full capacitor in isolation as a standard RC circuit. Use small ripple approximation, and pretend the exponential discharge is linear too.
Q: Stop cheating, what is the exact solution for arbitrary loads?
A: Believe me, you don't want that anyway.

In conversation about a month ago from mk.absturztau.be permalink