Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to calculate RMS voltage from triac phase angle

  1. Jan 31, 2012 #1
    In a system that uses a triac to switch mains voltage, how can one calculate the resultant peak voltage, RMS voltage and power for a given phase (conduction) angle e.g. 50°?

    Many thanks
  2. jcsd
  3. Jan 31, 2012 #2
    in the usual way. Draw the output wave form graphs. That will directly give you peak.
    RMS volatge = Sqrt of avg of square of instantaneous voltage. This you calculate by integration. And for finding the power, you need wave-form of current as well.
    The you find power = Avg of ( V(instantaneous) * I(instantaneous) ) over a cycle.
    In short, you need to do some work. :)
    And, welcome of PF.
  4. Jan 31, 2012 #3
    Thanks for your reply 'I_am_learning'

    Drawing graphs is one way but I need a more technical solution. I need the formula!

    Just a mathematical way to calculate the peak voltage based on a phase angle would be sufficient.
    Here's hoping...
  5. Jan 31, 2012 #4
    DC12, I believe if you draw some graphs of output voltage wave-forms for few values of firing angle (like, 30, 90, 150, 300 etc), then the formula you are trying to find will be apparent.
    Sorry, but we can't do your homework here.
  6. Jan 31, 2012 #5
    Thanks again I_am_learning. Graphs don't help at all. This needs to be done many times for many different levels and numerous angles - I just don't have enough ink and paper. No homework being done here sir.
  7. Jan 31, 2012 #6
    I think he's saying just work out one or a few cases, and find the relationships. Then you can apply what you see to a general case. I would tell you, but I don't know an equation for this off the top of my head.
  8. Jan 31, 2012 #7
    I think that equation for RMS voltage across the load look like this:

    [tex]V_{load} = Vpeak *\sqrt{\frac{2 \pi - 2 \varphi + sin2 \varphi}{4\pi}}[/tex]

    Where [tex]\varphi - triac- angle- delay = triggering -angle[/tex] .

    [tex]for-0\varphi - triac- is- full- on[/tex] .

    [tex]And for- \frac{\pi}{2} V_{load} = Vpeak/2[/tex] .

    Or use this graph

    Last edited: Jan 31, 2012
  9. Jan 31, 2012 #8
    I thought that I shows some example.
    For V = 230V we have 325V peak and conduction angle 50° so the triggering angle must be equal to 130°.


    First we must convert 130° degrees to radians:

    r = 130 * ∏/180 = 130 * 0.0174 = 2.26 [rad]

    I use Wolframalpha

    but you could use Google too

    Code (Text):
    sqr( (2pi - 2*2.26 + sin(2*2.26))/(4pi) )
    Vload = 325V * √ ( (2*pi - 2*r + sin(2r) ) / (4pi) ) = 325V * 0.249 = 80.9Vrms

    Attached Files:

    • 1.PNG
      File size:
      10.1 KB
    Last edited: Jan 31, 2012
  10. Jan 31, 2012 #9


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    You can calculate RMS by integrating the sin2θ function over the active time of the switch. Thats where the √2 comes from over the whole cycle.
    The peak value is just the value of the sin(θ) at the turn on time.
    This assumes a resistive load, of course.
  11. Jan 31, 2012 #10
    Perfect. Thanks Jony130 and others!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook