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I'm implementing PWM for a three-phase inverter.

The documentation on the subject, especially the technical implementations, is very good but as far as I am able to understand none of the one I read talks about why the reference signal is a triangle or a sawtooth. In one document I found that this type of modulation is the oldest in the game (PWM concerned) so maybe is a thing of old technology that becomes standard?

Jhonathan Asimov
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  • who says that a triangle reference was "standard"? Far as I'm concerned, the proper reference would be sinusoidal. And we do see such things in the wild. – Marcus Müller Mar 20 '20 at 20:01
  • @DKNguyen so the sawtooth/triangle is the smoothed output of the value of a timer? – Jhonathan Asimov Mar 20 '20 at 20:10
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    @MarcusMüller A triangle is standard, though, like in sine-triangle PWM? Sure, SVM has advantages, but sine-triangle is easier to implement. – Hearth Mar 20 '20 at 20:16
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    @MarcusMüller the triangle wave is standard for the PWM reference. You then compare the triangle to a sine-wave to get the gate pulses. – Ben Mar 20 '20 at 21:37
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    Ah, sorry, I've been stupid; my head was stuck with the waveform the PW**M** *is modulated with*, not the one that's being used in a comparator to generate the PWM. My apologies! – Marcus Müller Mar 20 '20 at 21:41
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    @Hearth SVM still uses triangular references for PWM modulation, it's the generated signals that are different. – Dmitry Grigoryev Mar 21 '20 at 11:24

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The "triangle reference" method that has some history as a standard or popular method was more formally known as the "triangle interception method." It was based on generating switching commands based on the interception of a triangle wave with a sine wave as shown below. It was not too difficult to implement and it provided reasonably good results for variable frequency drives (VFDs). Results were improved by changing the ratio of the triangle wave frequency to the sine wave frequency over the range of the operating frequencies.

After the invention of large scale integrated circuits and microprocessors, more sophisticated PWM strategies became preferred.

enter image description here

Image from Zubek, Abbondanti & Nordby “Pulsewidth Modulated Inverter Motor Drives with Improved Modulation” IEEE Trans. Ind. Appl., Nov./Dec. 1975

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    People still use the triangle wave for PWM. But instead of a sine wave they will often use space vector modulaiton. – Ben Mar 20 '20 at 22:35
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You don't need to have a triangle-wave or a PWM for that matter to generate a sine wave. You could use hysteresis modulation which does not require a PWM. However, the switching frequency is variable with a hysteresis modulation and it might require more computing power.

If you need a PWM, a triangle wave is the way to go, a sawtooth wave would cause problems for H-Bridges and 3-phase inverters/rectifiers. The top transistors or the bottom transistors would all stop conducting at the same time. While with a triangle wave, the top and bottom transistor of different branches will not start conducting at the same time except if the duty cycle is the same for all branches.

Edit : In the case of 3-phase rectifier/inverter using, here's the comparison between sawtooth PWM and triangle PWM. As you can see, with the sawtooth, your transition from the zero-vector "000" to the zero-vector "111" , something you don't see with the triangle wave. With the triangle wave, transistors do not switch at the same time

Another reason why a triangle wave is better. It is easier to sample signals. With the triangle wave, you can set the ADC trigger when the triangle wave is at 0 or 100%, because at these points you are assured that no transistors will switch. I added arrows on the graph to highlight the sampling instants. With the sawtooth wave, no matter where you sample, there could be a transistor switching.

Edit 2 : The last image represents the PWM for a space-vector modulation from 0 to 60 degrees with 1 zero-sequence vector "000". You can see easily that only one transistor switch at a time. The PWM frequency used is 2400 Hz. In real-life, 2400 Hz is a bit low, it's more usual to see 10 kHz and more for PWMs. You can also see Va, Vb and Vc

Sawtooth PWM

Triangle PWM

SVM 0 - 60 degrees

Ben
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For sinewave PWM generation (or audio applications like Class-D amplifiers) triangle waves are preferred over sawtooth, because of their symmetry. This gives 2-sided PWM where both the rising edge and falling edge are modified as the duty cycle changes.

This means that the centre of each PWM pulse stays in the same position in a PWM period, whereas with a sawtooth waveform (single sided PWM), the centre of the pulse moves as the duty cycle changes, which adds distortion to the reconstructed sinewave.

  • And symmetry allows for easier sampling. If you sample at the top and/or bottom of the triangle wave, you're assured that no transistors will switch at the sampling instant. – Ben Mar 21 '20 at 14:04
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Think of it numerically/digitally instead of with waveforms: You would need a period timer. What does a period timer that counts up or down at the same rate look like? If it wraps around to zero at the end, it looks like a sawtooth. If it reverses direction once it reaches the top or bottom, it looks like a sawtooth or triangle wave.

If you graphed a digital timer it would look like a staircase or ziggurat. But if the timer is analog it looks like a sawtooth or triangle.

DKNguyen
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  • Having a sawtooth instead of a symmetric triangle would create problems for H-Bridges and 3-phase inverters/rectifiers. All top transistors would stop conducting at the same time and all bottom transistors would start conducting at the same time. – Ben Mar 21 '20 at 00:15
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Sawtooth / triangular reference waveforms can be trivially generated using widely available hardware counters (timers), with minimum CPU involvement. Signals generated by such modulation become asymptotically precise as PWM frequency increases, so unless you can't increase the PWM frequency to be 20-50 times higher than the signal frequency, there will be no improvement from a different reference waveform. This is the reason they are so widely used.

Dmitry Grigoryev
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Your question is answered by analyzing the intrinsic benefits of the triangle sine wave PWM from a harmonic point of view. Normally PWM sine modulation in three-phase inverters is implemented in digital form using a microprocessor. There are three forms of discrete sine wave PWM, which are:

--Sawtooth carrier regular sample PMW

--Triangle carrier symmetrical PWM

--Triangle carrier asymmetrical PWM

The 'Sawtooth carrier regular sample PMW' induces a huge amount of 2nd harmonic component, so it is the worse PWM strategy for three-phase inverters. This is so because the 2nd harmonic component is unwanted for any application of a three-phase inverter, specially in grid-tied applications. The 'Triangle carrier symmetrical PWM' induces less 2nd harmonic, so it is preferred over the 'Sawtooth carrier regular sample PMW'. However, the best sine wave PWM is the 'Triangle carrier asymmetrical PWM' because it does not induce any 2nd harmonic component. As a consequence of this, the 'Triangle carrier asymmetrical PWM' is the most used PWM technique in sine wave PWM inverters. I hope this answer your question. If you want more information about this issue, I recommend you to check the following book, it has the answer you are looking for:

"Pulse Width Modulation For Power Converters Principles and Practice, D. Grahame Holmes"

Daniel Memije Garduño
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