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I know PWM with dense and loose duty cycle is used to generate sine wave for applications such as 3-phase motor driving. But, How fast does it require to properly generate a sine wave to drive a motor?

I mean, if a sine wave is 1 Hz, how many times of the PWM base frequency is required to properly generate a sine wave PWM?

I guess 100 times would be fast enough, 1000 times would be perfect, 50 is barely enough, and 10 is not enough based on my imagined drawing of PWM in my mind.

Is there a standard or commonly used number of times to generate a sine wave? Thank you!

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    \$\begingroup\$ Depends on the filtering you are putting it through (i.e. the motor). You don't want to go too fast either since that means more switching losses in the transistors and more high frequency losses in the motor. \$\endgroup\$ – DKNguyen Mar 16 at 2:13
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In the early days of VFDs, PWM was successfully used to control motors at less than 10 times the frequency of the synthesized sine wave. At that frequency, motor losses were increased a little, but careful selection of motor ratings to suit the duty compensated for that. The acoustical noise made by the motors was ok for factory environments.

PWM at 30 or 40 times motor frequency is sufficient to reduce motor losses to an almost insignificant increase above pure sine wave losses.

Offering a customer adjustment in the range of 30 X to 300 X provides the opportunity to find an operating point at which acoustical noise is not a problem. Operating in the upper end of that range may come at the cost of reduced VFD efficiency and the need to upsize the VFD for a given motor. As devices with reduced switching losses become more competitive, higher PWM multiples may become more common.

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In my experience as a post-doctoral researcher in motor drives, 10x fundamental frequency is generally accepted as a minimum PWM frequency. I searched the literature to find precedents for this when writing papers/my PhD thesis, but found surprisingly little formal research on this.

Source: experience (https://scholar.google.com/citations?user=N7P5-hUAAAAJ)

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For practical purposes, the most important limit is to go above the acoustic threshold, i.e. the frequency should be more than 20 kHz. Above that it is a matter of mechanical vibrations caused by torque jitter.

Electrically the torque jitter is determined by the motor coil characteristics, most importantly the coil inductance, operating voltage and operating current.

For example, for a small brushless motor the coil inductance could be 100 µH, operating voltage 10 volts and operating current 1 ampere. If the PWM frequency is 20 kHz, the low and high duration is around 25 µs. During this time, the coil current will change by 25 µs * 10 V / 100 µH = 2.5 A. The magnetic field follows the current, which causes the torque to jitter by +- 125%. If the PWM frequency could be raised to 100 kHz, current would change only by 0.25 A and the torque jitter would be +- 25%. Larger motors usually have more inductance, permitting lower PWM frequency.

The velocity jitter is not as large, because the inertia of the motor will smooth it out. But the torque jitter directly causes vibrations in the surrounding structure, and the strength of the vibrations depend on mechanical properties of mass and elasticity.

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  • \$\begingroup\$ In my experience, very few VFD's in the sub 5 HP range allow switching at 20 kHz or above. I have no experience above 5HP, but I imagine it is a similar situation. Some VFD's are down around 5 KHz. They are very noisy. \$\endgroup\$ – mkeith Mar 17 at 4:31
  • \$\begingroup\$ @mkeith Hmm yeah, my background is more in the e-bike kind of brushless motors, which are usually 0.2-2kW. The most common PWM frequencies used there are in range of 20-50 kHz. \$\endgroup\$ – jpa Mar 17 at 5:08
  • \$\begingroup\$ Yes. I also worked on an E-skate and E-scooter design. We ran at 20kHz or higher to avoid acoustic noise. At 15 kHz it is not too bad. It mainly depends on your age. Most people have at least a little bit of hearing loss at 15kHz unless they are quite young. I am not that young and I can't even hear it at 15 kHz. \$\endgroup\$ – mkeith Mar 17 at 5:27

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