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How to calculate the PWM (Pulse Width Modulation) of a Pure Sine Wave of a specified Hz rate?
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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
asked Jan 12 at 9:20
Mark MainMark Main
655
$endgroup$
add a comment |
$begingroup$
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
asked Jan 12 at 9:20
Mark MainMark Main
655
$endgroup$
add a comment |
$begingroup$
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
asked Jan 12 at 9:20
Mark MainMark Main
655
$endgroup$
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
asked Jan 12 at 9:20
Mark MainMark Main
655
asked Jan 12 at 9:20
Mark MainMark Main
655
edited Jan 12 at 16:00
Mark Main
asked Jan 12 at 9:20
Mark MainMark Main
655
asked Jan 12 at 9:20
Mark MainMark Main
655
asked Jan 12 at 9:20
Mark MainMark Main
655
655
add a comment |
add a comment |
1 Answer
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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.
answered Jan 12 at 17:45
poetasispoetasis
405117
$endgroup$
$begingroup$
I really appreciate your help. I got lost in the forest, thanks again.
$endgroup$
– Mark Main
Jan 12 at 21:10
add a comment |
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1 Answer
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1 Answer
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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.
answered Jan 12 at 17:45
poetasispoetasis
405117
$endgroup$
$begingroup$
I really appreciate your help. I got lost in the forest, thanks again.
$endgroup$
– Mark Main
Jan 12 at 21:10
add a comment |
$begingroup$
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.
answered Jan 12 at 17:45
poetasispoetasis
405117
$endgroup$
$begingroup$
I really appreciate your help. I got lost in the forest, thanks again.
$endgroup$
– Mark Main
Jan 12 at 21:10
add a comment |
$begingroup$
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.
answered Jan 12 at 17:45
poetasispoetasis
405117
$endgroup$
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.
answered Jan 12 at 17:45
poetasispoetasis
405117
answered Jan 12 at 17:45
poetasispoetasis
405117
answered Jan 12 at 17:45
poetasispoetasis
405117
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
add a comment |
$begingroup$
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
add a comment |
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