You can place all the switching noise up in the ultrasonic domain with PWM, this method can't do that...
No offence, but that is not entirely true, to be honest. The spectrum of a PWM waveform typically contains components at (fc ± n.fo) where fc and fo are the carrier / modulating frequencies respectively and n = 1, 2, 3 etc. In other words, a PWM waveform carries sidebands well below the carrier frequency at substantial strengths, as shown in the picture below (Courtesy: DGHolmes, TA Lipo, PWM for power converters Principles and Practice).
Besides, lower order harmonic components of the fundamental (causing THD) are also generated by high frequency PWM and no harmonic elimination is guaranteed.
Besides, according to TI (pg 15 of below), the THD of an 8-bit waveform itself is around 0.5% and performing high frequency PWM with this waveform is not going to significantly improve this THD anyway. So what is the takeaway, especially with a filter and an inductive load in place ?
https://www.ti.com/lit/an/snoa665c/snoa665c.pdf
HF PWM maybe convenient (especially to the uninitiated) and Harmonic Elimination PWM may be old, but it still remains a principal method among others in what is today known as 'Programmed PWM'.
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Not sure what 'fast PWM' is but I guess 'phase perfect' refers to an advancement by half a carrier cycle. And in a 3-phase environment, the third harmonic is easily rejected and is therefore of no consequence.
Yes, different kinds of PWM result in different harmonic profiles. However, the one that is recommended is asymmetrically sampled sine-triangle PWM in which the sine reference is sampled at the both the peaks and troughs of the triangular carrier as shown below. The phase advancement is by a quarter carrier cycle. The advantages are that the odd / even harmonic sidebands around odd / even multiples of the carrier frequency (respectively) are automatically eliminated.
Further, there could be some improvement if an odd carrier / fundamental frequency ratio (fc / fo).
(Courtesy: DG Holmes, TA Lipo, PWM for power converters Principles and Practice)
The term comes from microcontroller datasheets. Most support various PWM modes. These are synthesized waveforms, not analog generated.