recently I played wth a LM35 temperature sensor that is normally very easy to handle. Connect directly to your arduino. No calibration needed on the analog side. But sometimes problems can occur and you read wrong data. This happened to me and I found a solution now documented in my latest blog entry. It is about a output swing of the LM35 and how to avoid it. Additionally you find some tips for better accuracy.
nope: i had that idea, too,
but 1024 is faster and correct, because:
there r really 1024 intervals:
lets say we have an 1bit (one bit) resolution ADC:
then we can distinguish 2 voltage ranges: [0,Vref/2[ and [Vref/2,Vref]...
so n-bit resolution delivers 2n voltage ranges... q.e.d. 8)
You are right there are 1024 values, but there are 1023 intervals and the MAX value is 1023 and this latter is the important param for analogRead() formulas.
Let me explain
analogRead reads typically from 0..5V which is mapped from 0..1023
Yes using 1024 is far faster as /1024 can be replaced by a shift >> 10 ..........but it is fast wrong. OK only 0.1% but even 0.1%'s add up.
In your example of a 1 bit ADC there are two values 0 (minimum) and 1 (maximum)
the formula would be
voltage = 5.0 * analogRead() / 1;
if analogRead == 0 => voltage = 0
if analogRead == 1 => voltage = 5.0
Suppose we had an analogRead that had only 4 values from 0..1023. What would the divider be then? 4, 8, 1024 or 1023 or 17 or ..
There are 3 voltage ranges with 4 values :
0..341
342..682
683..1023
so n-bit resolution delivers 2^n voltage ranges... q.e.d.
an analogRead() value maps to a whole interval, but not to a single point...
analogRead()==1023 maps to the biggest interval: [Vref-Vref/(2n),Vref]...
in fact the last interval is not limited at its right side: [Vref-Vref/(2n),oo[... theoretically...
if u were right, a 1-bit ADC would say 0 if the input is lower than Vref and 1 if the input is Vref or higher, which is not the case...
what u mean is an ADC that can say voltage too high/too low (out of range symbols)... but the atmega doesnt do that...
furthermore the datasheet of the ATmega168 says 23.7 ADC Conversion Result ADC=Vin*1024/Vref (page 256)...
I thought about this problem for a while (hope it helped...). In my opinion the problem is not that easy.
When you say 1023 is correct then this is easy to explain: The maximum value of the AD converter is 1023 and it equals to Vref (in this case 1.1V). So when you want to rescale it divide it by 1023 and multiply it with the new scaling factor.
On the other hand another easy explanation for 1024 is that you have 1024 steps so you divide by 1024 and multiply with your new scaling factor.
The problem is that we don't know exactly what the AD does in detail. It is about at which voltage the AD switches from 1022 to 1023 and at which voltage it would switch to 1024 if it would be possible. This is the background to the assumption that 1023 equals to Vref (or not...). So perhaps 1023 equals to Vref or 1024 equals to Vref. In theory 1024 equals to Vref but is never reached.
This really depends on what the AD does in detail. I haven't read the docs of the AVR so far so I don't know it in detail (yet).
nope - it is easy...
just take a look at the datasheet...
ADCs basically compare the input voltage to a common fraction of Vref, where the denominator is 2n, where n is the resolution of the ADC in bits... some do it iteratively with a DAC and some do it with 2n comparators in parallel...
what I meant with "it is not that easy" is you have to look in the datasheet. And yesterday evening it was too late for me to begin reading a datasheet. When you read it then it is easy.
where VIN is the voltage on the selected input pin and VREF the selected voltage reference (see
Table 23-3 on page 262 and Table 23-4 on page 263). 0x000 represents analog ground, and
0x3FF represents the selected reference voltage minus one LSB.
0x400 = 1024 represents the reference voltage. So dividing by 1024 is correct.
Rob had it right in the first place. When VIN = VREF, the ADC cannot return a value of 1024, only 1023. See chart below, simple linear algebra, y=mx+b. b is zero, so the equation of the line can only be: ADC = 1023 VIN / VREF.
At least that's correct for a perfect world. But don't just read section 24.7. Also read 24.6 about the various maladies a real-world ADC is subject to: Offset error, gain error, integral and differential non-linearity, quantization error. Then in section 29.8, typical characteristics for the various types of error are 2-4.5 LSB.
So my conclusion is that I probably shouldn't expect 0.1% accuracy from the ATmega's ADC. And whether I use 1023 or 1024 to scale the returned value probably makes little or no practical difference, it will probably be lost in the various other errors.
yeah, this is the kind of discussion I like Division by 1024 is correct but it doesn't matter if you divide by 1023 or 1024 because the other errors are much bigger than one LSB. This is true and because of that point among other reasons I took the internal 1.1V reference to get maximum resolution with the LM35. With the reference voltage of 5V the errors increase by a factor of almost 5.
The discussion about the 1023 or 1024 thing looks like a rather theoretical one but in my opinion it is nevertheless sensefull to exclude ervery source of errors possible.
After reading and thinking some more, I think that 1024 is right after all. Another way to look at it is that the ADC cannot actually represent a voltage equal to the reference voltage, since according to the datasheet, "0x000 represents analog ground, and 0x3FF represents the selected reference voltage minus one LSB." Similarly, as Elektrix said, 0x400 = 1024 represents the reference voltage, but of course 1024 isn't in the range of possible return values. And Rob's calculation where 1023 represents 4.995V is actually correct.
To me, the concept of "interval" is not the same as the number of steps. As the datasheet says, there are 2n steps. To me that means 2n-1 intervals, but I think to RIDDICK steps are the same as intervals. So maybe just a different way of arriving at the same conclusion. Actually I probably wouldn't even use "steps", I'd say the ADC can return one of 1024 values, i.e. 0 through 1023.
Good discussion indeed. I think I have a better understanding and will be able to sleep now XD
