Digital Sine wave...

Beau Schwabe

Anyone have some clever code to generate a pseudo sine wave?
Eventually this will be implemented in a frequency sweep application for doing Bode plots.

(Bean, your audio generation project gave me an idea for this.)

Right now I have a scheme that requires two I/O pins that are "flipped" at the same time,
with one lagging the other by 60 Deg.

        
A >----/\/\----o--||--> +V
               |
               0------> Out
               |  
B >----/\/\----o--||--> GND


A  B   SinePhase
0  1       0
0  0      60
0  0     120
1  0     180
1  1     240
1  1     300

In the attached image, Green is the ideal sine, while the Red is the actual sine wave.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

Post Edited (Beau Schwabe (Parallax)) : 2/5/2006 6:49:06 PM GMT

Tracy Allen

Hi Beau

There are Don Lancaster's "magic sine" algorithms, a special form of PWM that minimizes harmonics.

www.tinaja.com/magsn01.asp

PIC code is there, but it is a sure bet the SX could do it more efficiently. What frequency range are you looking at?

There are also the MF10 series digital filter chips, that can generate sine waves (with feedback from output to input) dependent on the input clock frequency. Audio range and below. There are also the DDS chips, like the AD9850, that cover a huge frequency range from sub Hertz to 60 mhz.

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Tracy Allen
www.emesystems.com

Beau Schwabe

Thanks Tracy,

I have seen this, and actually have implemented it, but it eats up allot of CPU cycles.

"What frequency range are you looking at?"
To start off, I would be happy with DC to a few MHz (5? 10?)... Once you get to 10MHz
or so, a square wave starts looking like a sine, and I could just go up from there.

I'm still not sure what step increment I want though. I have an idea for a wide range
VCO that could drive the OSC pin of an SX for the lower frequencies.

I will look into the AD9850 as an option.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

Tracy Allen

Beau,

Is there some reason you can't use a whole 8-bit port for this, to push out the sine wave in parallel?

There have been several threads on the Stamps list about how to calculate the control word (24 bits) for the AD9850 DDS.

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Tracy Allen
www.emesystems.com

Beau Schwabe

Tracy,

I don't have a problem with using the entire 8-bit port to bit-bang a sine wave via a R2R dac, but I don't gain any more
CPU time doing it that way vs with the 2-pin method I mentioned above. I think even a triangle wave would work using the
two pin method with a 90 Deg phase lag.

A  B    Sine Phase
0  1       0 Deg
0  0      90 Deg
1  0     180 Deg
1  1     270 Deg

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

pjv

Hi Beau;

What kind of distortion can you tolerate?

I figure to generate a so-so sinewave with a single RC pin PWM can be done with 15 instructions per sine value, and there would need to be an absolute minimum of 8 segments to one sine cycle.....the more the purer the result. So that sounds like 120 instructions at 20 nanoseconds each, for a one cycle total of 2.4 usec. That's only about 400 Khz; quite a ways from your target.

Cheers,

Peter (pjv)

Beau Schwabe

pjv,

I would be willing to see what you have in the way of code for this.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

pjv

Hi Beau;
In the Parallax contest I entered a "Small Hardware and Development Board" project which incidentally had dual sinewaves with separately selectable frequencies generated by the "single pin PWM" method. While the sine waves were not the primary purpose of the entry, they demonstrate a reasonable way of getting good results, albeit quite a bit slower than what you are looking for.

If you poke at that entry (sorry, I don't know how to make the link for you), you can see the photograph of two sine traces on the 'scope.
Take a peek at the code to see how the ISR updates each PWM accumulator, and how the scheduler selects the sine value. The scheduler also drives the raise/lower buttons to control each frequency. It can very easily be modified to have the sceduler sweep through a range of frequencies. And of course, the amplitude is frequency independent.

Again, that project was not as fast as you would like, but by carving off the "niceties", I think it's possible to get things down to the speeds I indicated; about 400 KHz.· If you would like me to spend some time poking at that, I'd be happy to oblige.

;==============================================================================
;TITLE:··Sines.src
;
;PURPOSE:·Demonstrate a the effectiveness of an SX development board by
;··implementing a simple non-preemptive multi tasking scheduler
;··operating a dual pulse density modulation sine wave generator.
;
;AUTHOR:·Peter Van der Zee, Datek Industries Inc.
;
;REVISIONS:·Feb 27, 2005 Original.
;
;CONNECTIONS:·Port:·b.0·button to lower frequency 1
;···b.1·button to raise frequency 1
;···b.2·button to lower frequency 2
;···b.3·button to raise frequency 2
;
;··Port:·c.0·output as frequency 1· PWM output to RC filter 1.
;···c.2·output as frequency 2· PWM output to RC filter 2.
;
;DETAILS:·Each of two independent simple sine wave generators operate by
;··pulse density modulating an output bit in a deterministic
;··Interrupt Service Routine. A tick based task scheduler controls
;··frequency selection control and sine value calculation for each
;··of the generators.
;
;··The scheduler demonstrates multiple independent tasks operating
;··without much concern of each other with·the exception of being
;··non-preemptive in nature. In other words, a task that requires
;··more rapid response will not interrupt a slower task already
;··running or scheduled to run. For greater determinism it is
;··important that no task "hogs" a lot of processor time in any
;··run instance, and it is absolutely crucial that no task uses
;··long delay loops. The purpose of the scheduler is to remove the
;··in-line·requirement for delays by letting the scheduler provide
;··those instead.
;
;··In the generators, the sine value resolution is purposely left
;··coarse so on an oscilloscope the user can see the fixed effect
;··of frequency adjustment through raise/lower buttons.
;··Finer resolution can be conveniently made by expanding access
;··and granularity of the sine lookup table, albeit at the expense
;··of maximum frequency.
;
;··It should be obvious that replacing the sine lookup table with
;··a ramp value table, a sawtooth table or·any random function table
;··that other functions can be equally easily generated.
;
;··The scheduler time ticks are set to convenient numbers, in this
;··case permitting task threads to be executed at even decades of
;··time from the base tick of 1 usec for the ISR, to 10 and 100 usec,
;··1, 10 and 100 msec, and 1 sec. The scheduler can be easily altered
;··for more or less resolution, the major stipulation being that each
;··slower tick is an integer multiple of the previous tick.
;··More complicated arrangements can of course be made. Where mutiple
;··tick (non-decade) delays are required in a thread, then the thread
;··itself is tasked with the requirement to do so.
;==============================================================================

;---------------DEVICE DIRECTIVES----------------------------------------------

id  'Sines'

  DEVICE SX28,oschs3,stackx,turbo

  FREQ 50_000_000  ;default run speed = 50MHz
  RESET ResetEntry  ;jump to start label on reset

;---------------CONSTANTS------------------------------------------------------

Dac1Bit  equ rc.0   ;pulse density modulator 1 output to RC integrator
Dac2Bit  equ rc.2   ;pulse density modulator 2 output to RC integrator
IntValue equ -50   ;interrupt reload value for 1 micro second; 50 instructions at 50 MHz 
Ram1  equ $10   ;

;---------------VARIABLES------------------------------------------------------

  org 8
Flags          ds 1
Intflag        equ Flags.0   ;interrupt occurred flag

  org Ram1
Timer10uS      ds 1   ;counter to get to 10uSec
Timer100uS     ds 1   ;counter to get to 100uSec
Timer1mS       ds 1   ;counter to get to 1mSec
Timer10mS      ds 1   ;counter to get to 10mSec
Timer100mS     ds 1   ;counter to get to 100mSec
Timer1S        ds 1   ;counter to get to 1Sec

Dac1Value      ds 1   ;value for the PWM 1 output
Dac1Accum      ds 1   ;accumulator for PWM 1
Period1        ds 1   ;duration of one cycle of frequency 1
Period1Load    ds 1   ;duration of one cycle load source for frequency 1
F1index        ds 1   ;index into sine table for frequency 1
Dac2Value      ds 1   ;value for the PWM 2 output
Dac2Accum      ds 1   ;accumulator for PWM 2
Period2        ds 1   ;duration of one cycle of frequency 2
Period2Load    ds 1   ;duration of one cycle load source for frequency 2
F2index        ds 1   ;index into sine table for frequency 2

;---------------INTERRUPT ROUTINE----------------------------------------------

  org 0
Intsvc
;For each of two one byte PWMs, calculate the rollover carry and then clear or set the PWM bit accordingly
;The add-with-carry option must be disabled unless carry is specifically cleared before the add.

  setb    Intflag             ;advise scheduler an interrupt has occurred
  add     Dac1Accum,Dac1Value ;calculate PWM 1 overflow
  sc                          ;
  clrb    Dac1Bit             ;clear PWM 1
  snc                         ;
  setb    Dac1Bit             ;set PWM 1
  add     Dac2Accum,Dac2Value ;calculate PWM 2 overflow
  sc                          ;
  clrb    rc.2                ;clear PWM 2
  snc                         ;
  setb    rc.2                ;set PWM 2
  mov     w,#IntValue         ;
  retiw    ;return from interrupt and reset for 50 instructions

;---------------INITIALIZATION-------------------------------------------------

ResetEntry
  ;Initialize the ports
SetLevels mov m,#$0d           ;Set 0 for CMOS levels
          mov !ra,#%0000       ; 
          mov !rb,#%0000_0000  ; 
          mov !rc,#%0000_0000  ;
SetPullups mov m,#$0e          ;Set 0 for pullups
          mov !ra,#%0000       ;port a not used
          mov !rb,#%0000_0000  ;input buttons
          mov !rc,#%1111_1111  ;
SetTris   mov m,#$0f           ;Set 0 for output
          clr ra
          mov !ra,#%1111       ;port a not used
          clr rb               ;
          mov !rb,#%0000_1111  ;X,X,X,X _ F2up,F2dn,F1up,F1dn  
          clr rc               ;
          mov !rc,#%0000_0000  ;X,X,X,X _ X,DAC2,X,DAC1

  ;Clear memory
Clearmem  mov fsr,#$10         ;point to first memory bank
Clearone  setb fsr.4           ;stay in proper half
          clr ind              ;clear this location
          incsz fsr            ;point to next location
          jmp Clearone         ;not at end so clear one more

  ;Initialize the scheduler timers
          mov w,#10            ;timer decade value
          mov Timer10uS,w      ;10 microseconds
          mov Timer100uS,w     ;100 microseconds
          mov Timer1mS,w       ;1 millisecond
          mov Timer10mS,w      ;10 milliseconds
          mov Timer100mS,w     ;100 milliseconds
          mov Timer1S,w        ;1 second

  ;Initialize the variables
         clr rtcc              ;
         mov !option,#%1000_1000 ;internal rtcc
         clr Flags             ;
         mov Dac1Value,#128    ;set initial value of dac1 half way
         mov Dac2Value,#128    ;set initial value of dac2 half way
  
;---------------MAIN PROGRAM---------------------------------------------------

;The scheduler keeps time for the whole system and triggers sine calculations
;for both generators each 10 microseconds.
;Every 100 milliseconds it looks for raise/lower buttons being pushed, and if so,
;calls the corresponding generator's raise/lower routine.

Main     sb Intflag           ;test for interrupt occurred
         jmp Main             ;wait for interrupt
         bank Ram1            ;
Usec1    clrb Intflag         ;clear that fact
         decsz Timer10uS      ;scheduler 1 usec base tick
         jmp Main             ;wait for occurrence of next interrupt
Usec10   mov Timer10uS,#10    ;reload 10usec timer
  ;put 10 uSec routines here
         call Sine1           ;determine freq 1 step
         call Sine2           ;determine freq 2 step
         decsz Timer100uS     ;scheduler 10 usec tick
         jmp Main             ;wait for occurrence of next interrupt
Usec100  mov Timer100uS,#10   ;reload 10usec timer
  ;put 100 uSec routines here
         decsz Timer1mS       ;scheduler 100 usec tick
         jmp Main             ;wait for occurrence of next interrupt
Msec1    mov Timer1mS,#10     ;reload 100usec timer
  ;put 1 mSec routines here
         decsz Timer10mS      ;scheduler 1 msec tick
         jmp Main             ;wait for occurrence of next interrupt
Msec10   mov Timer10mS,#10    ;reload 1msec timer
  ;put 10 mSec routines here
         decsz Timer100mS     ;scheduler 1 usec base tick
         jmp Main             ;wait for occurrence of next interrupt
Msec100  mov Timer100mS,#10   ;reload 10usec timer
  ;put 100 mSec routines here
         sb rb.0              ;test button for lower frequency 1
         call Lower1          ;decrease frequency 1
         sb rb.1              ;test button for higher frequency 1
         call Higher1         ;increase frequency 1
         sb rb.2              ;test button for lower frequency 2
         call Lower2          ;decrease frequency 2
         sb rb.3              ;test button for higher frequency 2
         call Higher2         ;increase frequency 2
         decsz Timer1S        ;scheduler 1 usec base tick
         jmp Main             ;wait for occurrence of next interrupt
Sec1     mov Timer1S,#10      ;reload 10usec timer
  ;put 1 Sec routines here
         jmp Main             ;wait for occurrence of next interrupt

;---------------SUBROUTINES----------------------------------------------------

Lower1  ;reduce frequency of generator 1 but not below zero
         incsz Period1Load    ;increase the period of frequency 1
         skip                 ;
         dec Period1Load      ;underflow not permitted
         retp                 ;

Higher1  ;increase frequency of generator 1 but not above $ff
         decsz Period1Load    ;decrease the period of frequency 1
         skip                 ;
         inc Period1Load      ;overflow not permitted
         retp                 ;

Lower2  ;reduce frequency of generator 2 but not below zero
         incsz Period2Load    ;increase the period of frequency 2
         skip                 ;
         dec Period2Load      ;underflow not permitted
         retp                 ;

Higher2  ;increase frequency of generator 2 but not above $ff
         decsz Period2Load    ;decrease the period of frequency 2
         skip                 ;
         inc Period2Load      ;overflow not permitted
         retp                 ;

Sine1  ;calculate lookup time for generator 1, and if so, get sine value
         decsz Period1        ;step frequency 1 period duration
         retp                 ;not time for next sine lookup; return to scheduler
         mov Period1,Period1Load ;reload period 1 timer
         inc F1index          ;step to next sine value in lookup table
         mov w,F1index        ;
         call SineLookup      ;get sine value for this index
         mov Dac1Value,w      ;setup new dac 1 value for the ISR
         retp                 ;done freq1; return to scheduler

Sine2  ;calculate lookup time for generator 2, and if so, get sine value
         decsz Period2        ;step frequency 2 period duration
         retp                 ;not time for next sine lookup; return to scheduler
         mov Period2,Period2Load ;reload period 2 timer
         inc F2index          ;step to next sine value in lookup table
         mov w,F2index        ;
         call SineLookup      ;get sine value for this index
         mov Dac2Value,w      ;setup new dac 2 value for the ISR
         retp                 ;done freq2; return to scheduler

SineLookup ;lookup the sine value of index in w
         and w,#%0000_1111    ;only use 16 steps in lookup table
         add pc,w             ;calculate offset into lookup table
Sin0     retw 128             ;$80 
Sin1     retw 177             ;$b1
Sin2     retw 218             ;$da
Sin3     retw 245             ;$f5
Sin4     retw 255             ;$ff
Sin5     retw 245             ;$f5
Sin6     retw 218             ;$da
Sin7     retw 177             ;$b1
Sin8     retw 128             ;$80
Sin9     retw 79              ;$4f
SinA     retw 38              ;$26
SinB     retw 11              ;$b
SinC     retw 1               ;$1
SinD     retw 11              ;$b
SinE     retw 38              ;$26
SinF     retw 79              ;$4f

Cheers,
Peter (pjv)

Beau Schwabe

Thanks Peter,

I'll have a look and see what I can do.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

James Newton

http://www.sxlist.com/techref/new/letter/news0404.htm ·Has an interesting method of making pretty good sine waves in very few cycles.

The biggest problem you face is the lack of IO pins and your desire to avoid PWM.

The first thing that jumps to mind is to calculate the exact sinewave value (table or the link above) and then just use the top 2 or three bits of it, but accumulate the error from the other bits that are not used and total that into the next value. The result will be that at lower frequencies, you will have some PWM "effect" where one or both of the pins switch on and off rapidly to compensate for the error and at higher frequencies, there will be no time for that and you will get more like a squarewave.

Not sure if that makes sense...

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