1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Ripple Voltage Derivation (Full-Wave Rectifier)

  1. Jan 4, 2013 #1


    User Avatar
    Gold Member

    1. The problem statement, all variables and given/known data

    Derive the ripple voltage of a full-wave rectifier with a capacitor-input filter.

    2. Relevant equations


    Where [itex]V_{r(pp)}[/itex] is the peak-to-peak ripple voltage and [itex]V_{DC}[/itex] is the dc (average) value of the filter's output voltage.

    And [itex]V_{p(rect)}[/itex] is the unfiltered peak rectified voltage.

    3. The attempt at a solution


    [itex]t_{dis}\approx T[/itex] when [itex]v_C[/itex] reaches its minimum value.


    Since [itex]RC> > T[/itex], [itex]T/R_LC[/itex] becomes much less than 1 and [itex]e^{-T/R_LC}[/itex] approaches 1 and can be expressed as

    [tex]e^{-T/R_LC}\approx 1-\frac{T}{R_LC}[/tex]


    [tex]v_{C(min)}=V_{p(rect)}\left ( 1-\frac{T}{R_LC} \right )[/tex]

    [tex]V_{r(pp)}=V_{p(rect)}-V_{C(min)}=V_{p(rect)}-V_{p(rect)}+\frac{V_{p(rect)}T}{R_LC}=\frac{V_{p(rect)}T}{R_LC}=\left ( \frac{1}{fR_LC} \right )V_{p(rect)}[/tex]

    My issue is with the approximation that I bolded above. If [itex]e^0[/itex] approaches 1, then how does the expression [itex]e^{-T/R_LC}[/itex] approach [itex]1-\frac{T}{R_LC}[/itex]?
  2. jcsd
  3. Jan 4, 2013 #2


    User Avatar

    Staff: Mentor

    Those are the first 2 terms of the series expansion for e^x

    BTW, in your initial problem statement, that should be "with a capacitor-output filter", not "input" filter, right?

    Also, are you given as part of the problem statement that T << RC? That's certainly not always the case for FWRs with output filter caps. If you want to minimize ripple, that is a requirement though.
  4. Jan 4, 2013 #3


    User Avatar
    Gold Member


    Thanks for clarifying about the series expansion of e^x.

    The text does say "For a full-wave rectifier with a capacitor-input filter..." I took "input" to mean that the capacitor takes the full-wave rectified input waveform and transforms it into a ripple waveform.

    The T << RC approximation is simply given as "which is usually the case..." In the chapter I'm studying, it is an introduction to diodes/rectifier circuits and the goal is to get DC waveform that is as close to a horizontal line (constant voltage) as possible.
  5. Jan 4, 2013 #4


    User Avatar

    Staff: Mentor

    Got it, thanks for the clarifications. And yeah, being able to assume T << RC simplifies the math a lot! :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook