Linearizing an LED for 800 pwm steps'?

[Ioannis]

There is no difference (significant at least) whether you use bipolar or mosfet since the transistor will work in linear region. So, since it works linearly, cap will make calculation easier, because you will have to deal with dc voltages in base of the transistor in regard with the ground.


So, after PWM fltering the resulting dc voltage is the sum of Vbe (~0,6) and V(R1). V(R1) will define the current through the LED.

Have not tested in comparisson with the table but seems easier to control.

Ioannis

[Mike, K8LH]

Hi Hank,

Have you tried using fewer discrete brightness level steps spread across the much larger pwm width? For example, I get very smooth fades using between 64 and 100 gamma corrected brightness level steps spread across a much larger 512 pwm steps.

You can also "bend" the duty cycle curve to help match the characteristics of the LEDs.

Regards, Mike

[HankMcSpank]

Hi Mike,

Thnaks for the input...no I've not tried fewer brightness steps - I figured my problem was an insufficient number of brightness steps ......especially at the low end of the brightness scale, where for example the first 20 steps at 256 pwm levels sees quite a swing in the perceived LED brightness.....this is why I whacked it right up to 1024 brightness levels....which is much better from a less 'steppy' LED response perspective , but I'm still not happy with the overall fade curve, so your formula is of high interest! (there's aplethora of curves out there...and it's difficult to decide which one is best for this application!)

I've copied your formula into an excel spreadsheet for LUT of 1024 (well, I have the code space so may as well use it!) & 10 bit PWM.....the curve looks more like what I'm aiming for (if you look at my earlier curve further up the thread, the last part of the curve was almost vertical - this is too extreme)....I see yours is a little more gradual/linear towards the upper/final part of the plot ....and I shall give this a try tomorrow...many thanks.


What's with the 0.3 at the end of the formula ...where did that come from?

[Mike, K8LH]

Hank,

The PWM "step" size makes a significant difference at the low end too. It's amazing how much more light you get from a LED running at 1/1024th duty cycle with 1-usec PWM steps compared to, say, 125-nsec steps. Getting more brightness resolution at the lower duty cycle range seems to pay off with better smooth fade capability.

What's with the 0.3 at the end of the formula ...where did that come from?

Oh, the 0.3 was for rounding. Sorry if it caused any confusion.

BTW, here's a little program I use for building my gamma array tables. It uses the free JustBASIC program. After running it I copy the array from the console into my PIC source file. Hope it may be of some use.

Regards, Mike

 '  Leo Bodnar's 'antilogarithmic' 
 '  gamma correction algorithm (Mike, K8LH)
 '
 '  JustBASIC (free) interpreter
 '
 Input "Gamma array size: "; arraysize
 Input " Total PWM steps: "; width
 Input "Gamma correction: "; gamma       ' try 0.5 to 1.0


 FOR index = 0 to arraysize-1
    dcyval = INT(width^(((index+1)/arraysize)^gamma)+.3)
    if(index = 0) then
      dcyval = 0
      PRINT
    else
      if(index MOD 10 = 0) then
        PRINT ","
      else
        PRINT ",";
      end if
    end if
    if(dcyval < 100) then print " ";
    if(dcyval < 10) then print " ";
    PRINT dcyval;
 NEXT index
 PRINT
 PRINT
 REM CLOSE

And here's what the output looks like when you run the program;

Gamma array size: 64
 Total PWM steps: 256
Gamma correction: .84


  0,  1,  1,  2,  2,  2,  2,  2,  3,  3,
  3,  4,  4,  4,  5,  5,  6,  7,  7,  8,
  9,  9, 10, 11, 12, 13, 14, 16, 17, 19,
 20, 22, 24, 26, 28, 30, 33, 36, 39, 42,
 45, 49, 53, 57, 62, 67, 72, 78, 84, 90,
 98,105,113,122,132,142,153,165,177,191,
205,221,238,256

[Mike, K8LH]

Hank,

You got a 12F683? If so, and if you want to experiment, connect an LED to GP0 (anode) and GP5 (cathode) and try the program below. The circuit doesn't use a current limiting resistor, relying instead on the RDS(on) resistance of the I/O pin output FETs.

The program fades the LED through sixty four gamma corrected brightness levels spanning 256 1-usec BAM duty cycle steps with a 1280-usec frame rate (781-Hz refresh rate).

:020000040000FA:0600000083018501F128D7
:08000800F000030EF10083017A
:100010000A08F2008A010408F3008C1074088500B5
:1000200083167608850077088500162878088500ED
:100030000030FF3E031819281D287908850002307A
:10004000FF3E0318202824287A08850074087407C6
:1000500074191030F41A0130F4000430FF3E031814
:100060002E28322800007B0885002030F418243028
:1000700074192830741A2C30F41A303084000C3083
:10008000FF3E031840287C0885007D08F5007409B0
:10009000F600F700F800F900FA00FB00FC00FD0094
:1000A0000130741820300018F6068018F706001981
:1000B000F8068019F906001AFA06801AFB06001BDA
:1000C000FC06801BFD06840A0230F418203000185C
:1000D000F6068018F7060019F8068019F906001AC6
:1000E000FA06801AFB06001BFC06801BFD06840A2C
:1000F0000430741920300018F6068018F70600192D
:10010000F8068019F906001AFA06801AFB06001B89
:10011000FC06801BFD06840A1030741A203000187B
:10012000F6068018F7060019F8068019F906001A75
:10013000FA06801AFB06001BFC06801BFD06083031
:10014000FF3E0318A0287508850073088400720814
:100150008A00030E8300F00E700E09008A013F39F9
:10016000820700340134023402340234023403348E
:1001700003340334043404340534053406340634BB
:1001800007340834083409340A340B340C340D3481
:100190000E340F3411341234143415341734193426
:1001A0001B341D341F342234243427342A342D3494
:1001B0003134353439343D34413446344B345134A0
:1001C00057345D3464346B3472347B3483348C3410
:1001D0009634A134AC34B734C434D134E034EF3481
:1001E000FF340730990083169F0170308F000F1D78
:1001F000F72883123F30840080018403841AFC288E
:100200002030F4000130AA000230AB000330AC0013
:100210000430AD000530AE000630AF000730B0004E
:100220000830B1000930B2000A30B3008C019101EE
:100230000530920083167F3092008C148312C030F8
:100240008B0010303321B60A361B2C293608AE201D
:10025000A000212910303321B603B61B212936080E
:10026000AE20A0002A29B500740820393406B4064F
:0C027000340503193429350B332908002C
:02400E00D43F9D
:00000001FF

I'll also write something using the PWM module so that we can try 125-nsec PWM steps (with an 8-MHz clock).

Cheerful regards, Mike

[HankMcSpank]

Hi Mike,
exactly
I haven't got a 12f683 to hand .... I'm still a rather weak/n00by programmer, so wondering what exatly that program is you've posted?!!!

I tried 1024 PWM levels with a gamma (0.8 & 1.6), but actualy neither of them seemed to fade any better than what I had in place already (which was some anti log kludge).

The hassle for me here is converting any lookup table to a DW table (to be able to use lots of available code space to store the lookup values), presently, I'm doing the test curves in excel, then saving to a csv...but my version of excel only allows 256 columns wide, so I have to put 1024 values the curve on 4 rows, then save it as a csv.

Worse still the 'DW' command seems to have a restriction of somewhere in the order of 70 bytes per line entry, so I can't just use a hulking 256 byte long lines, but having to break the 4 long CSV lines, into smaller snippets....

    DW 0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,10,11,11

& so on...what I really need is to knock up a program that takes an excel 'column' 1024 deep coverts it into blocks of lines 70 bytes long (like the above) all rpefaced with a DW on the front...because presently it's about 30 minutes work just to trial a different curve - it get tiring very quickly!

While I'm here, can anyone field an elegant way of rescaling....let's say I have 10 bit ADC that I want to scale to a maximum of 800 PWM steps (if you are wondering what I'm trying to achive....a max LED brightnesss setting ...I hoping to have a maximum PWM value (which will differ depending upon the maximum brightness setting required) & need to rescale the incoming ADC to it ...therefore a MAX ADC value of 1023 -> max PWM value of 800 (or 600, 400...whatever I've chosen to be the maximum PWM value)....it's easy to outside of picbasic...

(max PWM value/1023) * incoming ADC value ...but the first part of the caclulation results in a floating point number. (for example 800/1023 = 0.78201368523949169110459433040078 !!!) ....now I realise you have to gear everything up, but just wanted a little bit of guidance how this is done in Picbasic to set me on my way!

[HankMcSpank]

re the scaling...I found the floating point thread....

http://melabs.com/resources/fp.htm

but adding that particular bas file wiped my program out (I'm at the edge of my PIC's variable limit), so here's what I'm doing...

I scale up the max PWM value (which will be the maximum LED brightness) by 64 (the maximum multiplier that still keeps me within 'word' constraints), then divide this value by the maximum possible incoming ADC reading (10 bit = 1023) ... I then mulitply that result by the actual incoming ADC reading ......and then divide by 64.

I lose about 0.5% of resolution but that's pretty close for my needs.