Software generation of Three Phase Sinusoidal PWM

In a sinusoidal PWM, signals are modulated sinusoidally, as shown in figure below. Note how duty-cycles of PWM changes in proportion to amplitudes of a reference sine wave. 

A single phase sinusoidal PWM (ref)

For three phase sinusoidal PWM (SPWM) waves, simply generate PWMs using three such modulating sine waves 120° from each other, as shown below:

                                     A three-phase Sinusoidal PWM (ref)

How to generate PWMs - 

(A) Analog approach

The SPWM (three phase or a single) can be generated by continually comparing a reference sine wave (three phase or a single) with a triangular wave using an opamp comparator.

(B) Digital approach - 

Digitally (using FPGAs, microcontrollers or dedicated ICs), one approach would be to calculate signals.

However, a much preferred (and a usual) approach  makes use of predefined look-up tables of signal pulse widths.

Lets use an 8-bit for our look up tables. 

First, let us quantize the amplitude of the sinusoidal wave in 8 bits. The negative peak of the sine wave will be zero and the positive peak as 255 as given by the following equation.

PWM_duty-cycle= 127*sin f+128, 0 £ f £ 2p .      

Above equation is for a single phase. For three phase, equations will be:

Phase R PWM_duty-cycle=127*sin f+128

Phase Y PWM_duty-cycle=127*sin (f+120°) +128

Phase B PWM_duty-cycle=127*sin (f+240°) +128

However, "f" has to be digitized too. Using 8-bits, f_8-bit= (k/256) x 2p, where 0 £ k £ 255.

This will result in: (for a single phase)

PWM_duty-cycle= 127*sin {(k/256) x 2p} + 128, 0 £ k £ 255                

Above final equation will give us a 8-bit value for PWMs that we can store in a look-up table 256 long (each storing a byte). Note, the equation will result in floating numbers which needs to rounded up or down as appropriate.

A Verilog snippet code below shows the data in the look-up table: (best viewed in Chrome browser)

//note 256 locations each storing 8-bit long data (PWM)   //each location represents an angle location/time  case(addr)                                            //angle:   data=PWM;                               8'd00:      data=8'd128;                           8'd01:      data=8'd131;                           8'd02:      data=8'd134;                           ....                                                      8'd254:      data=8'd122;                          8'd255:      data=8'd125;                        endcase

(We can create similar table using C/C++ or any other language).

The table is for a single phase. For three phase, we may be inclined to create three different look-up tables, one for each phase. However, such an approach will require more memory space. Rather what we should do is to read from three locations (each 120° apart).In other words, if a duty-cycle value for the first phase is read at 0° (0th place) for the first phase, values from 120° (85th place) and 240° (171th place) are read for the second and the third phase, respectively from the look-up table.

How to establishing the desired sinusoidal frequency? 

It is Simple. The rate of reading the duty-cycles from the look-up table will give us the desired sinusoidal  frequency - simply read from the table at the desired frequency rate.