Note:
Values that must be entered by the user of this program are highlighted in yellow.
Values returned by the program are highlighted in light blue.
Some variables, constants, or points of interest are highlighted in light violet.
Warnings are highlighted in red.
yellow
light violet
light blue
red
This document studies the use of a single "non linear thermistor" as temperature sensing device. The subsequent circuit will linearize the thermistor response and the software will further linearize the circuits output.
Let's assume we try to use the 30K5A (30Kohm at 25
Temperature Range -->
The Steinhart-Hart equation is:
Table of thermistor resistance in 1 degree C intervals from 0 to 150
The typical linearization circuit used is shown below.
The capacitors are provided for filtering only, so they don't affect the steady state response of the circuit. The equations are:
Substituting and arranging the equation, we get:
The power dissipated in the thermistor is:
Which has a maximum when Rtherm=R
The maximum power dissipated in the thermistor will occur when its resistance is equal to R
Note:
Let's calculate the thermistor value in this temperature range (variable "i" is just to handle negative "t
Now, we calculate what the ideal linear response would be, and chose R
Make variable assignments for temperature range, ADC counts, Vref, Thermistor Coefficients, and resistors below:
These values define constants for resistance,power,temp, and counts
for 30 K5 thermistor:
R1 span
R2 linearity / midpoint crossing
R3 offset
R4 and R5: thermsitor power
<== Max Vout
<== Mid Vout
<== Min Vout
Adjust R1 - R5 above to achieve the desired temperature range within the working range of the ADC and to optimize the linearization curve below.
<== Span Vout
must be <
Note:
To calculate the temperature in terms of output voltage or data from the A/D converter:
The following matrix shows the response for every count of the data conversion. The first column is the temperature conversion, the second is the temperature conversion slope (increment of temperature per A/D count), and the third column is the difference with the linear response.
Translation table for use by software to implement a lookup table mapping ADC counts to temperature
This creates a file with the values in
the lookup table.
this function.
Thermistors are useful when they can be used interchangebly.
Let's first check that a thermistor tolerance of about 0.85% translates into a temperature tolerance of better than 0.2
Thermistor Resistance Tolerances @ 25C and Temperature Tolerance and Range for Betatherm / Measurement Specialties Thermistors are as follows:
Now, according to Betatherm / Measurement Specialties catalog, the thermistor resistance tolerance as a function of temperature for materials
We'll use a linear interpolation to calculate the thermistor tolerance at other temperatures. Also, we define the variable "t
When thermistors are required to be interchangable, then standard BetaCURVE high precision toleranced devices specified over a temperature range are utilized.
(Material must be 3, 5 or 6)
(Grade must be 1=standard, or 0.5=special)
Grade 1 --> 0.2C from 0 to 70,
Grade 0.5 --> 0.1C from 0 to 70, and 0.2C from 0 to 112
(
The thermistor tolerance in the temperature range defined by "t" is:
The maximum and minimum thermistor resistance values are:
This is just another expression of the information contained in the previous graph with the the "grade" and material type set by the user of this document.
The resistors tolerance is:
Set to zero to simulate ideal conditions
We'll consider also a gain and offset error in the A/D converter
Set values to zero
to simulate ideal
conditions.
The A/D data in terms of temperature is:
To see in what direction each element tolerance affects the "D
Depends on the temperature (depends on "Th
Now, it also depends on the temperature (depends on "Th
An increment in R
An increment in R
An increment in Th
Now the sign depends on the value of "Th
If
an increment in R
If
an increment in R
If
an increment in D
If
an increment in D
We define new variables to use these last conditionals below.
With all this, we can express the maximum and minimum data results as follows:
Now, to calculate the temperature error, we need to convert these data results back to temperature using the formula or look-up table that software is going to use:
Table of thermistor resistance to temperature conversion error in 1 degree C intervals across the temperature span of interest.
Note To determine the error band attributable to just the thermistor, set the circuit resistors and the ADC parameters to be ideal by setting their tolerances / values to zero in Section 5.3
The typical Waters thermistor linearization circuit is shown below.
Assign the input offset voltage of the op-amp.
OPA2364
OPA2364A
AD8616
The minimum and maximum Vos values are determined and nominal assumed to be zero.
The minumum and maximum temperatures in Celcius are determined:
To determine the thermistor resistance at a particular temperature, assign temperature
value to the variable T.
Calculations for various nodes about the circuit
The positive input to the op amp is assumed to be at a fixed voltage due to the resistor network
The negative input to the op amp is assumed to Vpos +/- Vos
Maximums
Minimums
Nominals
Using the min and max Vos values to back calculate the perceived thermistor value
Using the min and max perceived thermistor values to determine temperature error band:
The resistors and A/D converter tolerances affect more as the measured temperature range increases.
The resistors tolerance affects greatly. Tolerance of 1% gives unacceptable results, 0.1% is good, and 0.01% (in combination with the special thermistor tolerance) gives excellent temperature tolerance even with a range of 25 to 150 oC.
It is not worth to use the special thermistor tolerance unless the temperature range is not too wide (75 oC max), or unless we use 0.01% resistors tolerance.
Moving "tflat" from 0 to 25 oC improves a little the temperature tolerance in the high end but this requires a specially selected thermistor.
Changing the resistor values to set a lower thermistor maximum power, tends to improve a little the temperature tolerance in the low end.
Choosing a different thermistor value does not seem to affect the temperature tolerance. However, the thermistor maximum power effect described above happens at different power settings for each thermistor. For example, the same temperature tolerance curve is obtained with resistances that create a maximum power of 0.1 mW in a 10 Kohm thermistor, and with resistances that create a maximum power of 0.01 mW in a 100 Kohm thermistor.
Choosing R
In general we can say that with 0.1% resistors tolerance and a special tolerance thermistor, it is possible to have a temperature tolerance smaller than +/-0.5 oC in a temperature span of about 75 oC. This decreases to +/-0.25 oC with 0.01% resistors tolerance.With a standard tolerance thermistor and 0.1% resistors tolerance, the temperature tolerance is smaller than +/-0.75 oC, in the same temperature span of about 75 oC.
The input offset voltage of operational amplifier has a relatively small effect on the overall error temperature error band when using either
double click above
to open Betatherm
NTC Thermistor Theory
double click above
to open Betatherm
NTC Thermistor Material Tables
double click above
to open Betatherm
NTC Thermistor Part Numbering Information
QTI is a second supplier of precision interchangable thermistors and have slightly different A, B, and C values as well as a different tolerance curve when compared to the Betatherm Betacurve devices.
These A, B, and C constants were calculated using the QTI website using 0 to 70 as the temperature range and thermistor curve M.
double click above
to open QTI Thermistor Max Deviation Specs
The nominal, maximum, and minimum thermistor resistance values for the QTI thermistors are:
These QTI thermistor resistance values are now compared to the nominal Betatherm thermistor to generate error bands with respect to temperature (Note: the Betatherm A, B, and C values were used in conjuction with the QTI min and max thermistor resistance as a means of calculating the error when using a QTI thermistor in a circuit designed for the Betatherm thermistor). These are the + / - temperature errors of the QTI thermistor when used in the Betatherm circuit.
To generate the error band, the errors associated with the Betatherm thermistors need to be subtracted out of the plots in Section 5.5 and the QTI errors summed back in.
Subract the Betatherm error out of the
original plots and then add in the error
associated with the QTI devices.
these errors to columns 3 and 4 of the error table.