Update 1: After the OP's edit, we now have a completely different question. The question is now: how come the readings do depend on the reference voltage that is used, whereas in theory they should not.
Update 2: If I had to program this in an Arduino, I would rather simplify the calculations as much as possible before coding:
- do not compute the measured analog voltage, nor the resistance, as they are not needed
- compute instead the ratio R/Rref directly from the analog reading
- rewrite the calibration polynomial as a function of log(R/Rref) instead of log(R) (which actually means log(R/(1 Ω)))
- optimize the evaluation of the polynomial by using Horner's method .
With these optimizations, we get:
// Coefficients of polynomial fit of log(R/Rref) -> 1/T.
const float c0 = 3.3540165e-3;
const float c1 = 2.5416075e-4;
const float c2 = -2.5959644e-6;
const float c3 = -9.3951087e-8;
// Convert ADC reading to temperature in deg. C.
static float temperature(int reading)
{
float R_ratio = reading / (1024.0 - reading); // = R / Rref
float x = log(R_ratio);
float inverse_T = c0 + x*(c1 + x*(c2 + x*c3));
return 1/inverse_T - 273.15;
}
void loop()
{
int reading = analogRead(A3);
Serial.println(temperature(reading));
deay(500);
}
Update: After the OP's edit, we now have a completely different question. The question is now: how come the readings do depend on the reference voltage that is used, whereas in theory they should not.
Update 1: After the OP's edit, we now have a completely different question. The question is now: how come the readings do depend on the reference voltage that is used, whereas in theory they should not.
Update 2: If I had to program this in an Arduino, I would rather simplify the calculations as much as possible before coding:
- do not compute the measured analog voltage, nor the resistance, as they are not needed
- compute instead the ratio R/Rref directly from the analog reading
- rewrite the calibration polynomial as a function of log(R/Rref) instead of log(R) (which actually means log(R/(1 Ω)))
- optimize the evaluation of the polynomial by using Horner's method .
With these optimizations, we get:
// Coefficients of polynomial fit of log(R/Rref) -> 1/T.
const float c0 = 3.3540165e-3;
const float c1 = 2.5416075e-4;
const float c2 = -2.5959644e-6;
const float c3 = -9.3951087e-8;
// Convert ADC reading to temperature in deg. C.
static float temperature(int reading)
{
float R_ratio = reading / (1024.0 - reading); // = R / Rref
float x = log(R_ratio);
float inverse_T = c0 + x*(c1 + x*(c2 + x*c3));
return 1/inverse_T - 273.15;
}
void loop()
{
int reading = analogRead(A3);
Serial.println(temperature(reading));
deay(500);
}
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancels out. It's not an error. The readings you get with this setup are indeed independent of your reference voltage.
Update: After the OP's edit, we now have a completely different question. The question is now: how come the readings do depend on the reference voltage that is used, whereas in theory they should not.
The answer lies most likely in the ADC calibration. If high accuracy is a requirement, the correct formula for the measured voltage is
V = Vref ×ばつ (reading + Eoff) ÷ (1024 + Egain)
where Eoff and Egain are the offset error and the gain error respectively. These errors are not knows a priori, and they are usually neglected when the accuracy requirement is low. The datasheet only gives constraints on how big these errors can be. The actual values depend on the specific microcontroller and can somewhat depend on the reference voltage. The only solution to get rid of these errors is to calibrate your own ADC. See Response of the Arduino ADC for an example on how this could be done.
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancels out. It's not an error. The readings you get with this setup are indeed independent of your reference voltage.
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancels out. It's not an error. The readings you get with this setup are indeed independent of your reference voltage.
Update: After the OP's edit, we now have a completely different question. The question is now: how come the readings do depend on the reference voltage that is used, whereas in theory they should not.
The answer lies most likely in the ADC calibration. If high accuracy is a requirement, the correct formula for the measured voltage is
V = Vref ×ばつ (reading + Eoff) ÷ (1024 + Egain)
where Eoff and Egain are the offset error and the gain error respectively. These errors are not knows a priori, and they are usually neglected when the accuracy requirement is low. The datasheet only gives constraints on how big these errors can be. The actual values depend on the specific microcontroller and can somewhat depend on the reference voltage. The only solution to get rid of these errors is to calibrate your own ADC. See Response of the Arduino ADC for an example on how this could be done.
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancelsVref cancels out. It's It's not an error. The readings you get with this setup are indeed independentindeed independent of your reference voltage.
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancels out. It's not an error. The readings you get with this setup are indeed independent of your reference voltage.
The formula to get the analog voltage from the ADC reading is:
V = Vref ×ばつ reading ÷ 1024
(yes, it's 1024, not 1023). The formula to get the thermistor resistance from the measured voltage is:
R = Rref ×ばつ V ÷ (Vref − V)
where Rref is your 10 kΩ pull-up. You can combine these two formulas in order to get the resistance directly from the ADC reading:
R = Rref ×ばつ reading ÷ (1024 − reading)
You may notice that, while doing this simplification, Vref cancels out. It's not an error. The readings you get with this setup are indeed independent of your reference voltage.