How to calculate the PWM (Pulse Width Modulation) of a Pure Sine Wave of a specified Hz rate?












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$begingroup$


I am trying to calculate the pulse waves for the PWM (Pulse Width Modulation) of a Pure Sine Wave with 60 Hz or 50 Hz.



Each pulse wave duration calculated, either to power on or power off, must be a whole number of 3 μs (microseconds) or greater. The challenge is to closely approximate a pure sine wave within the constraints specified above.



My best attempt is this:

p = power on microseconds (μs) as a whole number of 3 or greater.

n = no power (power off) (μs) as a whole number of 3 or greater.

h = Hz rate, which will be 60 or 50 Hz.

m = microseconds (μs) for a single sine wave cycle at h Hz

t = total microseconds (μs) for the previous pulse calculations


$$h = 60$$
$$m = frac{1000000}{h} = 16667$$
$$frac{p}{p+n} ≈ sin(frac{p+n+t}{m} times frac{pi}{2})$$



I started with the assumption to turn power on at the minimum 3 μs and then calculated the first power off duration to be 178 μs.



Then I added 1 to the 3 μs to turn power on again for 4 μs and then calculated to have it turned off for 132 μs; I suspect that just adding 1 each time to the power on duration is not correct, but I don't know how to determine when I should increase that duration more rapidly.
I want to calculate to sin(0.5) and then use these numbers backwards to zero, and then repeat the full cycle for the negative side of the sine wave.



I know my assumptions are wrong, the total μs exceeds 16667 μs for a single cycle, it came out to be 5676 x 4 = 22704 μs with 214 on-off pulse combinations. I'm close, but not quite there.



This problem has humbled me, I'm absolutely stuck and will appreciate any help. Thank you.






wave-equation







share|cite|improve this question











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    4












    $begingroup$


    I am trying to calculate the pulse waves for the PWM (Pulse Width Modulation) of a Pure Sine Wave with 60 Hz or 50 Hz.



    Each pulse wave duration calculated, either to power on or power off, must be a whole number of 3 μs (microseconds) or greater. The challenge is to closely approximate a pure sine wave within the constraints specified above.



    My best attempt is this:
    
p = power on microseconds (μs) as a whole number of 3 or greater.
    
n = no power (power off) (μs) as a whole number of 3 or greater.
    
h = Hz rate, which will be 60 or 50 Hz.
    
m = microseconds (μs) for a single sine wave cycle at h Hz
    
t = total microseconds (μs) for the previous pulse calculations


    $$h = 60$$
    $$m = frac{1000000}{h} = 16667$$
    $$frac{p}{p+n} ≈ sin(frac{p+n+t}{m} times frac{pi}{2})$$



    I started with the assumption to turn power on at the minimum 3 μs and then calculated the first power off duration to be 178 μs.



    Then I added 1 to the 3 μs to turn power on again for 4 μs and then calculated to have it turned off for 132 μs; I suspect that just adding 1 each time to the power on duration is not correct, but I don't know how to determine when I should increase that duration more rapidly.
    I want to calculate to sin(0.5) and then use these numbers backwards to zero, and then repeat the full cycle for the negative side of the sine wave.



    I know my assumptions are wrong, the total μs exceeds 16667 μs for a single cycle, it came out to be 5676 x 4 = 22704 μs with 214 on-off pulse combinations. I'm close, but not quite there.



    This problem has humbled me, I'm absolutely stuck and will appreciate any help. Thank you.






    wave-equation







    share|cite|improve this question











    $endgroup$















      4












      4








      4





      $begingroup$


      I am trying to calculate the pulse waves for the PWM (Pulse Width Modulation) of a Pure Sine Wave with 60 Hz or 50 Hz.



      Each pulse wave duration calculated, either to power on or power off, must be a whole number of 3 μs (microseconds) or greater. The challenge is to closely approximate a pure sine wave within the constraints specified above.



      My best attempt is this:
      
p = power on microseconds (μs) as a whole number of 3 or greater.
      
n = no power (power off) (μs) as a whole number of 3 or greater.
      
h = Hz rate, which will be 60 or 50 Hz.
      
m = microseconds (μs) for a single sine wave cycle at h Hz
      
t = total microseconds (μs) for the previous pulse calculations


      $$h = 60$$
      $$m = frac{1000000}{h} = 16667$$
      $$frac{p}{p+n} ≈ sin(frac{p+n+t}{m} times frac{pi}{2})$$



      I started with the assumption to turn power on at the minimum 3 μs and then calculated the first power off duration to be 178 μs.



      Then I added 1 to the 3 μs to turn power on again for 4 μs and then calculated to have it turned off for 132 μs; I suspect that just adding 1 each time to the power on duration is not correct, but I don't know how to determine when I should increase that duration more rapidly.
      I want to calculate to sin(0.5) and then use these numbers backwards to zero, and then repeat the full cycle for the negative side of the sine wave.



      I know my assumptions are wrong, the total μs exceeds 16667 μs for a single cycle, it came out to be 5676 x 4 = 22704 μs with 214 on-off pulse combinations. I'm close, but not quite there.



      This problem has humbled me, I'm absolutely stuck and will appreciate any help. Thank you.






      wave-equation







      share|cite|improve this question











      $endgroup$




      I am trying to calculate the pulse waves for the PWM (Pulse Width Modulation) of a Pure Sine Wave with 60 Hz or 50 Hz.



      Each pulse wave duration calculated, either to power on or power off, must be a whole number of 3 μs (microseconds) or greater. The challenge is to closely approximate a pure sine wave within the constraints specified above.



      My best attempt is this:
      
p = power on microseconds (μs) as a whole number of 3 or greater.
      
n = no power (power off) (μs) as a whole number of 3 or greater.
      
h = Hz rate, which will be 60 or 50 Hz.
      
m = microseconds (μs) for a single sine wave cycle at h Hz
      
t = total microseconds (μs) for the previous pulse calculations


      $$h = 60$$
      $$m = frac{1000000}{h} = 16667$$
      $$frac{p}{p+n} ≈ sin(frac{p+n+t}{m} times frac{pi}{2})$$



      I started with the assumption to turn power on at the minimum 3 μs and then calculated the first power off duration to be 178 μs.



      Then I added 1 to the 3 μs to turn power on again for 4 μs and then calculated to have it turned off for 132 μs; I suspect that just adding 1 each time to the power on duration is not correct, but I don't know how to determine when I should increase that duration more rapidly.
      I want to calculate to sin(0.5) and then use these numbers backwards to zero, and then repeat the full cycle for the negative side of the sine wave.



      I know my assumptions are wrong, the total μs exceeds 16667 μs for a single cycle, it came out to be 5676 x 4 = 22704 μs with 214 on-off pulse combinations. I'm close, but not quite there.



      This problem has humbled me, I'm absolutely stuck and will appreciate any help. Thank you.






      wave-equation




      wave-equation






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      edited Jan 12 at 16:00







      Mark Main

















      asked Jan 12 at 9:20









      Mark MainMark Main

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          $begingroup$

          If you want to produce a sine wave as nearly as possible, you need merely vary the on-pulses as multiples of 3 microseconds as a function of sine with time with, e.g., 3 microsecond off-pulses between them. If you want just the full-wave power equivalent, I recommend exploring RMS which effectively reflects the duty cycle requirement I think you are looking for.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I really appreciate your help. I got lost in the forest, thanks again.
            $endgroup$
            – Mark Main
            Jan 12 at 21:10











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          $begingroup$

          If you want to produce a sine wave as nearly as possible, you need merely vary the on-pulses as multiples of 3 microseconds as a function of sine with time with, e.g., 3 microsecond off-pulses between them. If you want just the full-wave power equivalent, I recommend exploring RMS which effectively reflects the duty cycle requirement I think you are looking for.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I really appreciate your help. I got lost in the forest, thanks again.
            $endgroup$
            – Mark Main
            Jan 12 at 21:10
















          2












          $begingroup$

          If you want to produce a sine wave as nearly as possible, you need merely vary the on-pulses as multiples of 3 microseconds as a function of sine with time with, e.g., 3 microsecond off-pulses between them. If you want just the full-wave power equivalent, I recommend exploring RMS which effectively reflects the duty cycle requirement I think you are looking for.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            I really appreciate your help. I got lost in the forest, thanks again.
            $endgroup$
            – Mark Main
            Jan 12 at 21:10














          2












          2








          2





          $begingroup$

          If you want to produce a sine wave as nearly as possible, you need merely vary the on-pulses as multiples of 3 microseconds as a function of sine with time with, e.g., 3 microsecond off-pulses between them. If you want just the full-wave power equivalent, I recommend exploring RMS which effectively reflects the duty cycle requirement I think you are looking for.






          share|cite|improve this answer









          $endgroup$



          If you want to produce a sine wave as nearly as possible, you need merely vary the on-pulses as multiples of 3 microseconds as a function of sine with time with, e.g., 3 microsecond off-pulses between them. If you want just the full-wave power equivalent, I recommend exploring RMS which effectively reflects the duty cycle requirement I think you are looking for.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 12 at 17:45









          poetasispoetasis

          405117




          405117












          • $begingroup$
            I really appreciate your help. I got lost in the forest, thanks again.
            $endgroup$
            – Mark Main
            Jan 12 at 21:10


















          • $begingroup$
            I really appreciate your help. I got lost in the forest, thanks again.
            $endgroup$
            – Mark Main
            Jan 12 at 21:10
















          $begingroup$
          I really appreciate your help. I got lost in the forest, thanks again.
          $endgroup$
          – Mark Main
          Jan 12 at 21:10




          $begingroup$
          I really appreciate your help. I got lost in the forest, thanks again.
          $endgroup$
          – Mark Main
          Jan 12 at 21:10


















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