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generate sin wave with PWM

Discussion in 'Embedded' started by ivan, Oct 10, 2006.

  1. ivan

    ivan Guest

    hi all,

    How do I generate a sin wave using PWM?
    The way I have thought is just to create a triangular wave with equal steps
    of the PWM duty cycle (depending on freq) and then filter out the harmonics
    with a hw filter.
    But what if I want to generate a sin wave instead of a triangular wave, how
    do I calculate the steps for the duty cycle of the PWM? These steps are not
    equal, so I will need to store them in a table.
    Any ideas?

    ivan, Oct 10, 2006
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  2. ivan

    Ico Guest

    Well, the steps are not equal, so you will need to store them in a table :)

    Using sine tables is common for generating sine waves, since
    calculating sines is a very expensive operation.
    You could use something like the following snippet:

    #include <stdio.h>

    int main(int argc, char **argv)
    int x = 0, y = 64;

    while(1) {
    x += y/8;
    y -= x/8;

    printf("%d %d\n", x, y);
    return 0;
    Ico, Oct 10, 2006
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  3. ivan

    jetq88 Guest

    Write a program on your favorite computer in your favorite language
    that emits a bunch of .pword assembler directives with the sine values.

    Note that the table only needs to cover 1/4 cycle. At run time you use
    symmetry to get the values for other parts of the sine wave. All 4
    combinations of indexing into the table forwards and backwards, and
    negating the result or not yield the full sine wave.
    jetq88, Oct 10, 2006
  4. Or calculate them on the fly. Neither method seems challenging. After all if
    the PWM is clocking at the CPU frequency you've got lots of cycles to the
    next PWM update unless you got no resolution from the PWM. Now, is the sin
    wave you want at a fixed frequency or fixed amplitude?

    As to calculating you might want to apply you mind to the trig formula:

    sin(A+B) = sin(A)*cos(B) + cos(A)*sin(B)

    Peter Dickerson, Oct 10, 2006
  5. ivan

    Jerry Avins Guest

    You can output widths that are samples of a sine. they can be generated
    directly as you need them or taken from a table. The derivative of a
    sine is a cosine. The difference between the widths of successive pulses
    that simulate a sine follow a cosine. A pair of DDAs, like a pair of
    op-amps, connected back to back can generate sine and cosine waves
    simultaneously. (DDA stands for "digital differential analyzer". Nobody
    builds them any more, but they are easily created in software.) Software
    DDAs are often used for circle generation, and they can supply pulse
    widths for uni- or bipolar PWM.

    The software version is related to Bresenham’s algorithm. Look it up.

    Jerry Avins, Oct 10, 2006
  6. ivan

    Joerg Guest

    Not necessarily. You could, for example, run a square wave into a wave
    digital LP filter. If you use Chebychev or elliptic it won't consume
    much in terms of MIPS. One can play with the coefficients a bit to
    reduce the number of shift-adds as long as the stop band attenuation
    remains sufficient. And use CSD.
    Joerg, Oct 10, 2006
  7. Thats hugely more work than you need to do. We're talking a few multiplies
    (by constants) and adds at the most.

    Peter Dickerson, Oct 10, 2006
  8. ivan

    Joerg Guest

    Hello Peter,
    Depends on the hardware the OP is planning to employ. If it's a uC or
    DSP with a HW multiplier it is easy. If it has to be a low end garden
    variety without HW multiplier that is a different story. You can run a
    steep Chebychev WDF in about 500 cycles per sample. Probably similar
    with other shift-add schemes.
    Joerg, Oct 10, 2006
  9. ivan

    Arlet Guest

    Here are some ideas:

    Arlet, Oct 10, 2006
  10. Others will tell you of all sorts of formulae and about look-up tables but
    one technique that many forget is called a "Digital Differential Analyser".
    With some very simple maths and some logic these can be implemented and
    produce sine and cosine streams of data which could be used more-or-less
    directly by the PWM generation logic.

    Put the term "Digital Differential Analyser" and Sizer into Google's search
    string and you will get a number of references that may prove useful
    (especially if you register for the IEEE and CiteSeer sites.

    Paul E. Bennett ....................<email://>
    Forth based HIDECS Consultancy .....<http://www.amleth.demon.co.uk/>
    Mob: +44 (0)7811-639972
    Tel: +44 (0)1235-811095
    Going Forth Safely ..... EBA. www.electric-boat-association.org.uk..
    Paul E. Bennett, Oct 10, 2006
  11. ivan

    Ico Guest

    That's what I said, very expensive

    Ico, Oct 10, 2006
  12. ivan

    Jim Stewart Guest

    Don Lancaster got carried away with this awhile ago:

    Jim Stewart, Oct 10, 2006
  13. ivan

    Joerg Guest

    Hello Ico,
    You can do that for a buck fifty with an MSP :)
    Joerg, Oct 10, 2006
  14. The first task is to define the PWM:sine freq ratios, and also decide
    if you need to scale the Sine voltage, or Frequency, via the PWM.
    Then you'll know what quantize errors you are forced to live with, and
    from there, you can choose a coding scheme : you may find in small
    systems, that the quantize issues matter most.
    One system we did, was fixed Freq and Amplitude, so used this approach :

    We took care to match the slopes of the steepest sine portions, to a
    sensible step rate. Then chose a width for the flat top/bottoms, and
    finally chose widths for 'chamfers' to what is thus far a flattened
    This is effectively a slope-fit method, with carefully selected
    time-breaks. It does need maths to choose the corners, but needs no
    maths on the uC running the PWM.

    Jim Granville, Oct 10, 2006
  15. You don't. For that you need a moral height destabilizer, not a pulse
    width modulator. A PWM just ain't evil enough to trigger a wave of

    SCNR ;->
    Hans-Bernhard Broeker, Oct 10, 2006
  16. ivan

    Joerg Guest

    Hello Hans-Bernhard,
    But if it were connected to the FET gate of a switcher and the compare
    register ain't updated before the inductor current reaches kaboom level
    it is able to re-create Sodom and Gomorrha...
    Joerg, Oct 10, 2006
  17. ivan

    CBFalconer Guest

    Precisely. Set B = dA (the angular increment) and you have:

    sin(A + dA) = k1 * sin(A) + k2 * cos(A)

    which, for small dA, has k1 close to 1 and k2 close to 0. You can
    use cos(A) = sin(90-A) so that you don't need elaborate
    calculations for cos.

    Some informative links:
    CBFalconer, Oct 11, 2006
  18. ivan

    Jerry Avins Guest


    I have long felt that we shared a common way of seeing things. Did you
    see my response?

    Jerry Avins, Oct 11, 2006
  19. ivan

    ivan Guest

    ok.. this is the way I have done it and it seems to work althought there is
    some discontinuity between the last and first element of the table (however
    this can be solved calculating increments of the PWM values instead of the
    values itself).
    Well the value of the PWM dutycycle is directly proportional to the value of
    the output voltage, so for 24bits and a isr that updates the PWM value at
    about 60KHz I have:

    x = (int)(0x7fffff * sin(2*pi*n/N))


    N = 60KHz / TargetFreq;

    hence I generate my table with:

    for(n = 0; n < N; n++)
    x = (int)((16777216.0/2)*(sin(2*PI*n/N) + 1));

    thanks again
    ivan, Oct 11, 2006
  20. Only after I had posted and on my subsequent trawl through the newsgroups.

    Paul E. Bennett ....................<email://>
    Forth based HIDECS Consultancy .....<http://www.amleth.demon.co.uk/>
    Mob: +44 (0)7811-639972
    Tel: +44 (0)1235-811095
    Going Forth Safely ..... EBA. www.electric-boat-association.org.uk..
    Paul E. Bennett, Oct 11, 2006
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