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Arduino: R-2R: Sine On You Crazy Diamond

jc2048

Part one is here:
https://www.element14.com/community/people/jc2048/blog/2018/04/12/arduino-r-2r-experiment

 

I was going to do some hardware next but got sidetracked into playing with software instead.

 

Here's a very well-known waveform being produced by the simple resistor-ladder DAC I built in part one.

 

 

image

 

and here's what it looked like before I got the arithmetic right

 

 

image

 

That's generated by this sketch

 

//
//  --- Sine table - generated by sineTable.exe 
//

unsigned int sineTable[256] = {
   0x0000,0x00c9,0x0192,0x025b,0x0324,0x03ed,0x04b6,0x057f,0x0647,0x0710,0x07d9,0x08a2,0x096a,0x0a33,0x0afb,0x0bc3,
   0x0c8b,0x0d53,0x0e1b,0x0ee3,0x0fab,0x1072,0x1139,0x1201,0x12c8,0x138e,0x1455,0x151b,0x15e2,0x16a8,0x176d,0x1833,
   0x18f8,0x19bd,0x1a82,0x1b47,0x1c0b,0x1ccf,0x1d93,0x1e56,0x1f19,0x1fdc,0x209f,0x2161,0x2223,0x22e5,0x23a6,0x2467,
   0x2528,0x25e8,0x26a8,0x2767,0x2826,0x28e5,0x29a3,0x2a61,0x2b1f,0x2bdc,0x2c98,0x2d55,0x2e11,0x2ecc,0x2f87,0x3041,
   0x30fb,0x31b5,0x326e,0x3326,0x33de,0x3496,0x354d,0x3604,0x36ba,0x376f,0x3824,0x38d8,0x398c,0x3a40,0x3af2,0x3ba5,
   0x3c56,0x3d07,0x3db8,0x3e68,0x3f17,0x3fc5,0x4073,0x4121,0x41ce,0x427a,0x4325,0x43d0,0x447a,0x4524,0x45cd,0x4675,
   0x471c,0x47c3,0x4869,0x490f,0x49b4,0x4a58,0x4afb,0x4b9e,0x4c3f,0x4ce1,0x4d81,0x4e21,0x4ebf,0x4f5e,0x4ffb,0x5097,
   0x5133,0x51ce,0x5269,0x5302,0x539b,0x5433,0x54ca,0x5560,0x55f5,0x568a,0x571d,0x57b0,0x5842,0x58d4,0x5964,0x59f3,
   0x5a82,0x5b10,0x5b9d,0x5c29,0x5cb4,0x5d3e,0x5dc7,0x5e50,0x5ed7,0x5f5e,0x5fe3,0x6068,0x60ec,0x616f,0x61f1,0x6271,
   0x62f2,0x6371,0x63ef,0x646c,0x64e8,0x6563,0x65dd,0x6657,0x66cf,0x6746,0x67bd,0x6832,0x68a6,0x6919,0x698c,0x69fd,
   0x6a6d,0x6adc,0x6b4a,0x6bb8,0x6c24,0x6c8f,0x6cf9,0x6d62,0x6dca,0x6e30,0x6e96,0x6efb,0x6f5f,0x6fc1,0x7023,0x7083,
   0x70e2,0x7141,0x719e,0x71fa,0x7255,0x72af,0x7307,0x735f,0x73b5,0x740b,0x745f,0x74b2,0x7504,0x7555,0x75a5,0x75f4,
   0x7641,0x768e,0x76d9,0x7723,0x776c,0x77b4,0x77fa,0x7840,0x7884,0x78c7,0x7909,0x794a,0x798a,0x79c8,0x7a05,0x7a42,
   0x7a7d,0x7ab6,0x7aef,0x7b26,0x7b5d,0x7b92,0x7bc5,0x7bf8,0x7c29,0x7c5a,0x7c89,0x7cb7,0x7ce3,0x7d0f,0x7d39,0x7d62,
   0x7d8a,0x7db0,0x7dd6,0x7dfa,0x7e1d,0x7e3f,0x7e5f,0x7e7f,0x7e9d,0x7eba,0x7ed5,0x7ef0,0x7f09,0x7f21,0x7f38,0x7f4d,
   0x7f62,0x7f75,0x7f87,0x7f97,0x7fa7,0x7fb5,0x7fc2,0x7fce,0x7fd8,0x7fe1,0x7fe9,0x7ff0,0x7ff6,0x7ffa,0x7ffd,0x7fff};

void setup() {
  // set the digital pin as output:
  pinMode(0, OUTPUT);
  pinMode(1, OUTPUT);
  pinMode(2, OUTPUT);
  pinMode(3, OUTPUT);
  pinMode(4, OUTPUT);
  pinMode(5, OUTPUT);
  pinMode(6, OUTPUT);
  pinMode(7, OUTPUT);
}

void loop() {
    for(i=0;i<256;i++)
        PORTD = (sineTable[i] + 0x8000) >> 8;
    for(i=255;i>0;i--)
        PORTD = (sineTable[i] + 0x8000) >> 8;
    for(i=0;i<256;i++)
        PORTD = (0x8000 - sineTable[i]) >> 8;
    for(i=255;i>0;i--)
        PORTD = (0x8000 - sineTable[i]) >> 8;
}

 

The sine is done with a look-up table rather than the floating point library in order to save space and because it's much faster. I generated the table (only the first quadrant, to save space) using the following simple C program. That was compiled in Visual C++ on a PC and run simply by double-clicking on the filename (the text file ends up in the same directory and it's quicker than typing into a console window). Then I simply open it with Notepad and copy and paste it into the Arduino sketch. Probably not a very elegant approach, but it works.

 

/****************************************************************/

/* sineTable.c                                                  */

/*           Data values for one-quadrant sine look-up table    */

/*           256 values in int array                            */

/*           Output file is called sineTable.txt                */

/*           13th April 2018    Jon Clift                       */

/*--------------------------------------------------------------*/

/* Rev   Date     Comments                                      */

/* 1.0   13/04/18                                               */

/****************************************************************/

#include 

#include 

#include 

#include 

#include 

#include 

// variables

FILE *handle;

char temp_string[256];

unsigned int sineTable[256];

// main routine

void main(int argc,char *argv[])

{   int i,j;

    /* print banner */

    printf("\n--- sineTable DOS UTILITY PROGRAM V1.0 ---\n");

    printf("Builds sine table for Arduino R-2R experiment blog.\n");

 

    /* generate sine table in array */

   for(i=0;i<256;i++) {

        sineTable[i]=(unsigned int) (((sin((3.1415926/512)*i)) * 32768) + 0);

        }

     /* open output file */

    if((handle=fopen("sineTable.txt","wt"))==NULL) {

        printf("Failed to open output file.\n");

        _fcloseall();

        }

 else {

  /* write file banner */

  fprintf(handle,"//\n");

  fprintf(handle,"//  --- Sine table - generated by sineTable.exe \n");

  fprintf(handle,"//\n");


  fprintf(handle,"unsigned int sineTable[256] = {");

  /* write table to file */

  fprintf(handle,"\n");

  for (i=0;i<16;i++) {

   fprintf(handle,"   ");

   for(j=0;j<16;j++) {

    fprintf(handle,"0x%04x",sineTable[(i*16) + j]);

    if(j<15)

     fprintf(handle,",");

    else {

     if(i==15)

      fprintf(handle,"};\n");

     else

      fprintf(handle,",\n");

     }

    }

   }

  /* close output file */

  fclose(handle);

     printf("Done.\n");

  }

 

 

Part one: Arduino: R-2R Experiment

Part two: Arduino: R-2R: Sine On You Crazy Diamond

Part three: Arduino: R-2R: Buffer, Attenuate, and Filter

Part four: Arduino: R-2R: "We Interrupt This Programme..."

Part five: Arduino: R-2R: "Resistance is..."?

Part six: Arduino: R-2R: Setting the Output Frequency

Part seven: Arduino: R-2R; "A Sweep is as Lucky, as Lucky Can Be..."

Part eight: Arduino: R-2R: Setting the Signal Amplitude

Parents

  • Now I'm thinking - what kind of circuit would produce this concave square wave......

    It might be one example where performing a Fourier transform would provide insight into the answer.

  • in reply to dougw

    I don't normally use the FFT on the scope because it's not very useful for anything and very fiddly to get the settings right.

     

    This shows the waveform (yellow) and the FFT it produces (red). The waveform has a fundamental frequency of 568Hz. A square wave would have odd harmonics, which would be 1704Hz, 2841Hz, 3977Hz, 5113Hz for the 3rd to 9th. The horizontal scale of the FFT is 5kHz per division, so the square wave harmonics are there where you'd expect them to be. I'm not very sure what's going on at the very far left of the trace where the fundamental is, nor even whether I've adjusted it to start at the fundamental or at 0Hz; the scope isn't really good enough to look at this in any more detail.

     

    image

     

    What I need is a decent audio spectrum analyser. Based on an Arduino. So who's going to do that one? Any offers?

  • in reply to jc2048

      wrote:

     

    ...

     

    What I need is a decent audio spectrum analyser. Based on an Arduino. So who's going to do that one? Any offers?

    I made this one for an e14 design challenge. 64 buckets, 38 kHz sampling frequency.

    Not decent, just good enough to create a 3 channel light organ by grouping the 64 buckets into bass, mid and high..

  • in reply to Jan Cumps

    Disco lights! I knew there was something missing from my test equipment shelf.

     

    Although not many people know this, the original screenplay for Grease was called Glitch! and featured an electronic engineer rather than an auto mechanic.

    In one memorable scene he sits before a screen looking at a very nice R&S oscilloscope that's up for roadtest on element14 and sings

     

    "Oh my bugs, they're multiplying
    And my loops, they lose control
    Those digital chips,
    they sit there frying

     

    "You're the 'scope that I want,
    the 'scope that I want,
    ooh, ooh, ooooooh!

     

    etc...

     

    Of course, this may not be true at all (mischievous old people make up stories like this all the time).

     

    Thanks for the link. Nice project you did there. And it's interesting to see how someone else did the FFT, though it would need more buckets (as it is, one bucket would contain two of the harmonics, which isn't very useful). I'd quite like to try programming one myself sometime - I'll add it to the list of things to do.

Comment
  • in reply to Jan Cumps

    Disco lights! I knew there was something missing from my test equipment shelf.

     

    Although not many people know this, the original screenplay for Grease was called Glitch! and featured an electronic engineer rather than an auto mechanic.

    In one memorable scene he sits before a screen looking at a very nice R&S oscilloscope that's up for roadtest on element14 and sings

     

    "Oh my bugs, they're multiplying
    And my loops, they lose control
    Those digital chips,
    they sit there frying

     

    "You're the 'scope that I want,
    the 'scope that I want,
    ooh, ooh, ooooooh!

     

    etc...

     

    Of course, this may not be true at all (mischievous old people make up stories like this all the time).

     

    Thanks for the link. Nice project you did there. And it's interesting to see how someone else did the FFT, though it would need more buckets (as it is, one bucket would contain two of the harmonics, which isn't very useful). I'd quite like to try programming one myself sometime - I'll add it to the list of things to do.

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