Dividing by 1023 or 1024? The final verdict on analogRead

[TolpuddleSartre]

I'll just leave this here.
(Drops mic)

[GoForSmoke]

If you can't answer points, imply everything comes down to a single issue.

With a 1.024V ref I can work the 10 bits of the ADC ladder value as factors of 1 mV, knowing instrument error from specs.
Please understand that doing so does not involve conversion to volts and treats the ADC value as a range.

If you fixate on hardware details you may lose signt of the what you're doing with them part. Or you're a EE.

[Robin2]

Do you mean?

Look back at the 0-5 example in Reply #21

At least work to the ADC value where possible, it's the conversion of ranges to values that forces errors.

I agree 100%. I am just pursuing this Thread for intellectual fun.

...R

[GoForSmoke]

The fun part is that with a 1.024V Vref, just going by 1mV x ADC the most you get is 1.023mV.

AVR has a built-in 1.1V Vref for 1.074mV steps x highest possible read 1023 = 1.099V.

If that 1.1V could be voltage divided to a 1.023Vref (perfect world), that would be conversion-friendly IF you're into converting.

[Budvar10]

ADC/1024 is correct, and ADC/1023 is wrong!

Let say we have just 1 bit ADC, 0 or 5V. Just two possible values. Should be /0 used?

And here is for n=5:

Code: [Select]


First *x/(n-1) math:                                                              
input voltage   ADC value   ADC*x/(n-1)   result   average error   output
4.00-4.99       4           *5/4          5.00     +0.50           5          
3.00-3.99       3           *5/4          3.75     +0.25           3
2.00-2.99       2           *5/4          2.50      0.00           2
1.00-1.99       1           *5/4          1.25     -0.25           1
0.00-0.99       0           *5/4          0.00     -0.50           0
Note that for the 5 possible ADC values, the output scale now has 6 values (0-5)
and the value 4 can never occur! And although the average error might look to be
nicely distributed +/- the centre of scale, the actual output result proves to be
much uglier. For slowly increasing voltage, the ADC would read; 0, 1, 2, 3, 5!!!
The maximum error in real world use is 2V, because that very tiny change of
3.999V - 4.001V would cause an output change of 3V -> 5V or a change of 2V!
Correct scaling math *x/n:
input voltage   ADC value   ADC*x/n       result   average error   output  
4.00-4.99       4           *5/5          4.00     -0.50           4          
3.00-3.99       3           *5/5          3.00     -0.50           3          
2.00-2.99       2           *5/5          2.00     -0.50           2          
1.00-1.99       1           *5/5          1.00     -0.50           1          
0.00-0.99       0           *5/5          0.00     -0.50           0                                                                                            #
All output values are properly scaled and all are represented. The average error
is never greater than 0.5 (no more average error than the /(n-1) example),      
the average error is always one fixed value (-0.5) making it very easy
to compensate. The maximum error at any time is 1V, this is half the max error of
the /(n-1) example, which can introduce extra error up to 1 in high value ADC
readings

[Robin2]

Referring to Reply #34 ...

I think the assumption that 4.00 to 4.99 gives 4 and 3.00 to 3.99 gives 3 is incorrect. I would expect 4.5 to 4.99 to give 5 and 3.5 to 4.49 to give 4

...R

[TolpuddleSartre]

Please, can someone put this thread out of its misery?
Oh, the humanity!

Let say we have just 1 bit ADC, 0 or 5V. Just two possible values. Should be /0 used?

No, because 2¹ is 2, so by GoForSmoke's logic, we would divide by 1.

[Robin2]

Maybe it is time to move it to Bar Sport ?

...R

[lastchancename]

...and this thread explains why binary logic wins!
We don't need no stinkin' analog!

Zero or One - none of this warm, fuzzy stuff. It just confuses things.

Can we kill this thread?  Although it has had interesting moments!

[GolamMostafa]

Maybe it is time to move it to Bar Sport ?

It's very interesting that the OP has not yet made any comment; but, you want move to the Bar Sport leaving him behind?

[lastchancename]

Bar Sport is Probably better than TUTORIALS.
Maybe Programming Questions?

[Robin2]

It's very interesting that the OP has not yet made any comment; but, you want move to the Bar Sport leaving him behind?

No. He must come with us.

...R

[GoForSmoke]

ADC/1024 is correct, and ADC/1023 is wrong!

Let say we have just 1 bit ADC, 0 or 5V. Just two possible values. Should be /0 used?

And here is for n=5:

Code: [Select]


First *x/(n-1) math:                                                              
input voltage   ADC value   ADC*x/(n-1)   result   average error   output
4.00-4.99       4           *5/4          5.00     +0.50           5          
3.00-3.99       3           *5/4          3.75     +0.25           3
2.00-2.99       2           *5/4          2.50      0.00           2
1.00-1.99       1           *5/4          1.25     -0.25           1
0.00-0.99       0           *5/4          0.00     -0.50           0
Note that for the 5 possible ADC values, the output scale now has 6 values (0-5)
and the value 4 can never occur! And although the average error might look to be
nicely distributed +/- the centre of scale, the actual output result proves to be
much uglier. For slowly increasing voltage, the ADC would read; 0, 1, 2, 3, 5!!!
The maximum error in real world use is 2V, because that very tiny change of
3.999V - 4.001V would cause an output change of 3V -> 5V or a change of 2V!
Correct scaling math *x/n:
input voltage   ADC value   ADC*x/n       result   average error   output  
4.00-4.99       4           *5/5          4.00     -0.50           4          
3.00-3.99       3           *5/5          3.00     -0.50           3          
2.00-2.99       2           *5/5          2.00     -0.50           2          
1.00-1.99       1           *5/5          1.00     -0.50           1          
0.00-0.99       0           *5/5          0.00     -0.50           0                                                                                            #
All output values are properly scaled and all are represented. The average error
is never greater than 0.5 (no more average error than the /(n-1) example),      
the average error is always one fixed value (-0.5) making it very easy
to compensate. The maximum error at any time is 1V, this is half the max error of
the /(n-1) example, which can introduce extra error up to 1 in high value ADC
readings

Please, can someone put this thread out of its misery?
Oh, the humanity!
No, because 2¹ is 2, so by GoForSmoke's logic, we would divide by 1.

These are rather poor strawmen.

TS, how do YOU convert a single bit into voltage with any more accuracy than what you think to ridicule?
Oh? What? You can't?

Bud, if you measure only 5 steps, the CONVERSION error is no longer 3 orders of magnitude below instrument error.
The error diminishes at n(n-1) rate. I argue on practicalities that do not scale freely. Please at least stay in the ballpark!

I gave clear reasons that you don't address at all and instead erect these pre-broken strawmen.

[TolpuddleSartre]

Proofreading fail.

[Coding Badly]

Let say we have just 1 bit ADC, 0 or 5V.

That is not how the AVR analog-to-digital converter works.  A one bit successive approximation converter with a reference of 5 volts makes just a single comparison: Is the voltage less than 2.5 volts?  If the answer is "yes" then the converted value is zero.  If the answer is "no" then the converted value is one.