AN2648 Application note
Increasing the resolution of analog temperature sensors
Introduction
For a recent trade show, a demonstration board was required to display ST's new low-cost temperature sensor, the STLM20. The idea was to connect it to a basic microcontroller with on-board analog-to-digital converter (ADC) and display the temperature on seven-segment LEDs. Any user would be able to affect the temperature by applying his finger directly to the sensor and then watch the display change as a result. The goal was to keep things simple and use the ADC converter on the micro thus avoiding the expense and engineering effort of using an external ADC.
Using the STLM20 temperature sensor with low-cost microcontrollers
The design flow used for the demonstration board can be applied in many applications. This document describes how any user can implement a temperature sensor design using the LM20 and a low-cost microcontroller with integral A-D converter. Figure 1. STLM20 demonstration board
200mm / ~8 144mm / 5.7
34mm / 1.34
280mm / ~11
December 2007
Rev 1
1/15
www.st.com
STLM20 temperature-to-output transfer function
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STLM20 temperature-to-output transfer function
Upon examining the temperature sensor's output characteristics, several issues become apparent. The STLM20 is a voltage output device with a 2nd order transfer function:
V0 = (-3.88 × 10 -6 × T 2 ) + (-1.15 ×10 -2 × T ) + 1.8639 V
This is rather unwieldy math for a simple 8-bit micro, but a linear approximation is available which matches the curve very closely. As shown in Figure 2, the dashed blue line is a very good fit to the pink parabola of the 2nd order equation above, and has the following equation: Equation 1
V0 = (-0.01169 V/C) × T + 1.8663 V
This is much more manageable for coding in assembly language without a math package. In this figure, the reader will note that the curve deviates only slightly from the line at the extreme ends. In the middle, they are almost indistinguishable. Figure 2. STLM20 transfer function
2.5
2.3
2.1
Output voltage, VO , (V)
1.9
2nd Order Linear
1.7
1.5
1.3
1.1
0.9
0.7
0.5 -60 -40 -20 0 20 40 60 80 100
Temperature, T (C)
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STLM20 temperature-to-output transfer function The second issue arises with the output voltage range. The micro's ADC performs ratiometric conversion on the input using VCC and ground as the upper and lower references, respectively. That means that when the input voltage equals VCC, the 8-bit ADC's output will be 255 (FFHEX), and when the input is ground, the output will be 0 (00HEX). Any voltage in the range VCC to ground is converted proportionally according to the following relationship:
ADC output (dec) = (VIN /VCC ) × 255
For this application, the nominal VCC is 5 V, so this equation becomes:
ADC output (dec) = (VIN /5) × 255 = VIN × 51
Referring to Figure 3, while the ADC can accept inputs over the full range 0 to 5 V, the temperature sensor output will vary over a much smaller range, between 0.87 and 2.33 volts across the temperature range 40 to +85C. Figure 3. STLM20 output voltage range
Output voltage, VO (V)
5 4. 5 4 3. 5 3 2. 5 2 1. 5 1 0. 5 0 -60 -40 -20 0 20 40 60 80 100
Available voltage range
STLM20 full range, linear, ind temp
STLM20 output voltage range
Temperature, T (C)
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This amounts to using only 1.46 V of the available 5 V range. Furthermore, in the intended demonstration board application, the necessary temperature range was approximately room temperature 15/+25, or 10 to 50C. For this target temperature range, the voltage range is 1.28 to 1.75 V, an interval of less than 0.5 V, less than one tenth the available 5 V range. This is depicted in Figure 4.
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STLM20 temperature-to-output transfer function Figure 4. Application temperature and voltage ranges
5
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4.5
4
3.5
Output voltage, VO (V)
3
2.5
Temperature range of interest
2
1.5
Us ed voltage range of application
1
STLM20 full temperature range
0.5
Available voltage range
0 - 60 - 40 - 20 0 20 40 60 80 100
Temperature, T (C)
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In Equation 1, the slope is 11.69 mV per C. For the 8-bit ADC, the step size is 5 V/255 steps or 0.019608 V/step. Comparing this to the slope, we get:
0.019608 V/step = - 1.677318 C/step - 0 .0 1169 V/ C
This means that, with the temperature sensor connected directly to the ADC, the resolution is only 1.68C/step. The smallest temperature increment the ADC can resolve is 1.68C. This is very coarse resolution.
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STLM20 temperature-to-output transfer function Given that the expected voltage range is less than 0.5 V, it should be possible to amplify the STLM20 output signal so that is uses more of the available voltage range. A 10x amplification should be possible without exceeding the available 5 V range. Furthermore, a positive slope is more intuitive to the user, so inverting it would be helpful, too. Hence, a gain of 10 should be used. Multiplying equation 1 by 10, we get the curve as shown at the bottom in Figure 5. Figure 5. Application transfer function after gain, inversion and offset
5.5
3.5
1.5
-50
-30
-0 -10.5 -2.5
10
30
50
70
90
-4.5
Voltage (V)
+17.5
-6.5
x 10
-8.5
-10.5
-12.5
-14.5
< 5V
-16.5
-18.5
Temperature, T (C)
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The result has positive slope and spans from 17.5 to 12.8, an interval of about 4.7 V, much closer to the available 5 V range.
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STLM20 temperature-to-output transfer function
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With an offset of approximately +17.5 V the curve is moved back into the range 0-5 V to give the transfer function shown as the light blue line in Figure 5. So how is this done? What circuit will perform this transformation without adding intolerable cost to the system? It turns out that a difference amplifier can be used to add gain and offset, and can do the inversion as well. And it requires only one op-amp to implement. An additional op-amp is used as a voltage follower out of the temperature sensor to prevent output loading from affecting the STLM20's output level. The net amplifier requirement then is a dual op-amp. A voltage reference is also required to provide the offset level going into the difference amp. The overall circuit is shown in Figure 6. The STLM20 output voltage, V0, appears identically at the first op-amp output. That then drives the inverting input of the difference amp with a gain of 50k/5k = 10. This translates the curve from a voltage range of 1.28 V to 1.75 V to a range of 12.8 V to 17.5 V so an offset of about +17.5 V must be applied. The 1.7676 V reference sees a gain of 10 (R4/R3 = ~50k/5k = 10) on the op-amp's non-inverting input. Thus, 17.676 volts is added back into the translation. With this gain and offset, the original curve, which had an interval of less than 0.5 V and a negative slope, is transformed to one which spans close to 5 V and has a positive slope as illustrated by the light blue line in Figure 5. Figure 6. STLM20 with gain and offset circuit
VCC VCC
0.1uF T 0.1uF VO STLM20 = VO LMV358 R1 5k VOUT V2
1.7676V
0.1uF
R3 50k V1
VCC
5k R2 LMV358 0.1uF R4 50k 0.1uF
TS431
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AN2648
STLM20 temperature-to-output transfer function Equation 2 is the basic difference amplifier equation. Equation 2
VOUT =
V2 ( R3 + R1) R4 V1 R3 - (R4 + R2) R1 R1
If R1 = R2 and R3 = R4, then it reduces to:
VOUT = (V2 - V1 )
R3 R1
However, obtaining perfectly identical resistors is nearly impossible. Thus, the more complex expression of Equation 2 is used. Starting with Equation 1 on page 2, for Figure 6, we have:
VO = -0.01169 T + 1.8663 V
In Figure 6, V1 is driven by V0, so Equation 2 becomes:
VOUT =
V2 ( R3 + R1) R4 VO R3 - (R4 + R2) R1 R1
Substituting the expression for V0 into this, we get:
VOUT = V2
( R3 + R1) R4 ( - 0.01169 T + 1.8663) R3 - (R4 + R2) R1 R1
VOUT = V2
( R3 + R1) R4 R3 R3 + 0.01169 T - 1.8663 (R4 + R2) R1 R1 R1
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STLM20 temperature-to-output transfer function Equation 3
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VOUT = V2
( R3 + R1) R4 R3 R3 - 1.8663 + 0.01169 T (R4 + R2) R1 R1 R1
The ADC inside the microprocessor is shown in Figure 7. Figure 7. ADC in microprocessor
VCC = 5V
VADC
VOUT
A/D 8-bit
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MICROCONTROLLER
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For the ADC output, we have the following, where INT means the integer portion of the expression:
255 VADC = INT VOUT VCC
Substituting Equation 3, we get:
255 ( R3 + R1) R4 R3 R3 V2 VADC = INT - 1.8663 + 0.01169 T (R4 + R2) R1 R1 R1 VCC
Rearranging, and ignoring the integer notation for now, we get:
VADC
VCC ( R3 + R1) R4 R3 R3 = V2 - 1.8663 + 0.01169 T 255 (R4 + R2) R1 R1 R1
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STLM20 temperature-to-output transfer function To get the measured temperature, TMEASA, we must solve for T above:
VADC
VCC ( R3 + R1) R4 R3 R3 - V2 + 1.8663 = 0.01169 T 255 (R4 + R2) R1 R1 R1
VADC
VCC R1 ( R3 + R1) R4 R1 R3 R1 R3 R1 - V2 + 1.8663 = 0.01169 T 255 R3 (R4 + R2)R1 R3 R1 R3 R1 R3
VADC
VCC R1 ( R3 + R1) R4 - V2 + 1.8663 = 0.01169 T 255 R3 (R4 + R2) R3
Equation 4
TMEASA = T = VADC
VCC R1 ( R3 + R1) R4 1 1.8663 1 - V2 + 255 R3 0.01169 (R4 + R2) R3 0.01169 0.01169
This has the form: Equation 4b
TMEASA = VADC K S + K O
But, rather than using this equation, it is better to filter the temperature, to average multiple samples together for display. This has two benefits. It smoothes the changes resulting in a displayed value which updates more gradually. And it increases the effective resolution of the sensor. By adding two more bits, this essentially makes the A/D appear to have 10-bit resolution. So, we use a modified version of the previous math, but sum four consecutive samples together:
255 VADC = INT VOUT VCC
255 ( R3 + R1) R4 R3 R3 V2 VADC = INT - 1.8663 + 0.01169 T (R4 + R2) R1 R1 R1 VCC
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STLM20 temperature-to-output transfer function VSUM4 = 4 samples of VADC, range 0 to 1020.
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255 ( R3 + R1) R4 R3 R3 V2 VSUM4 = 4 INT - 1.8663 + 0.01169 T (R4 + R2) R1 R1 R1 VCC
Rearranging and ignoring the integer operator, we get:
VSUM4
VCC ( R3 + R1) R4 R3 R3 = V2 - 1.8663 + 0.01169 T 1020 (R4 + R2) R1 R1 R1
VSUM4
VCC ( R3 + R1) R4 R3 R3 - V2 + 1.8663 = 0.01169 T 1020 (R4 + R2) R1 R1 R1
VSUM4
VCC R1 R3 R1 ( R3 + R1) R4 R1 R3 R1 - V2 + 1.8663 = 0.01169 T 1020 R3 (R4 + R2) R1 R3 R1 R3 R1 R3
VSUM4
VCC R1 ( R3 + R1) R4 - V2 + 1.8663 = 0.01169 T (R4 + R2) R3 1020 R3
Equation 5
TMEAS4 = T = VSUM4
VCC R1 ( R3 + R1) R4 1 1.8663 1 - V2 + 1020 R3 0.01169 (R4 + R2) R3 0.01169 0.01169
This is a linear equation and has the form: Equation 5b
TMEAS4 = VSUM4 K S /4 + K O
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STLM20 temperature-to-output transfer function Notice that the upper limit for the sum of four samples is 1020 (4 x 255) and not 1023 as might be inferred for a 10-bit number. The actual values of KS/4 and KO depend on the four resistors in the difference amp, the voltage reference output and VCC. In the case of the temperature sensor demonstration board, we have these values:
R1 = 5107 R2 = 5105 R3 = 50850 R4 = 50850 VCC = 4.9058 V V2 = VREF = 1.7676 V
For KS, we insert these values into Equation 4 and get this for a single sample:
TMEASA = T = VADC
VCC R1 1 ( R3 + R1) R4 1 1.8663 - V2 + 255 R3 0.01169 (R4 + R2) R3 0.01169 0.01169
TMEASA = VADC 0.16528 + 8.43771
Thus, for Equation 4b, KS = 0.16528 and KO = 8.43771. Therefore, KS/4 = 0.04132. Substituting this into Equation 5b, we get:
TMEAS4 = 0.04132 VSUM4 + 8.43771
This gives the four-sample average of the temperature. However, more processing is still required to get it into a form suitable for implementing in a simple processor. Since the processor is an 8-bit, integer machine, multiplication by a real number - in this case a fraction - is difficult and requires lots of math software. Instead of doing such complicated math, it's easier to first multiply by 1000, then later divide by 1000. So, Equation 5b becomes:
1000 TMEAS4 = 41 VSUM4 + 8438
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STLM20 temperature-to-output transfer function
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Since the numbers are strictly integers, some truncation error has occurred. Running error analysis on the calculated results shows an average error of 0.21C, so as a final adjustment, an additional 0.2(x1000) is added to get this equation:
1000 TMEAS4 = 41 VSUM4 + 8438 + 200 = 41 VSUM4 + 8638
The above equation is then implemented in the software. The final step is dividing the result by 1000 and writing it to the demonstration board's display. The overall solution looks like this (Figure 8): Figure 8. Overall solution
VCC STLM20 TEMPERATURE TO VOLTAGE VO = 11.69mV / C × T + 1.8663V slope is 0.01169 V/C
VOUT = V2 ( R3 + R1) R4 VO ·R3 (R4 + R2) R1 R1 ( R3 + R1) R4 R3 R3 1.8663 · + 0.01169 · · T (R4 + R2) R1 R1 R1
= V2 ·
VOUT = 0.1164 · T 0.9821
VADC = INT
255 VOUT VCC
VCC R1 ( R3 + R1) R4 V2 · + 1.8663 = 0.01169 T · · 255 R3 (R4 + R2) R3
VCC R1 1 ( R3 + R1) R4 1 1.8663 · · · + V2 · 255 R3 0.01169 (R4 + R2)R3 0.01169 0.01169
V1
R1
R3 VOUT
VADC ·
1.7676V
V2 VREF
TMEASA = T = VADC ·
R2
TMEASA = VADC · 0.165284 + 8.437709
R4
VCC = T = VSUM4 · 0.041321 + 8.437709 4.9058V MEAS4 41 8438 +
1000 1000
A/D 8-bit
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Thus, for the minor expense of a voltage reference and dual op-amp, the resolution has been improved from 1.677C per ADC step to better than 0.1C steps on the display.
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AN2648
Summary
2
Summary
The STLM20 is very accurate over a wide temperature range and has a nearly linear output which spans the voltage range 2.33 down to 0.87 volts over the corresponding temperature range 40 to +85C. While it can be directly connected to an 8-bit A-D converter such as those often found integrated into low-cost microcontrollers, the resolution may be too coarse for some applications, amounting to 1.677C per A-D step. For applications requiring higher resolution, users can use an op-amp and a voltage reference to add gain and offset to the STLM20 output. This has the effect of increasing the resolution over the temperature range of interest while avoiding the need for a more expensive, higher resolution A-D converter. Using averages of four samples also increases the effective resolution. The final result is that users can achieve resolution as fine as 0.1C with the STLM20.
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Revision history
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Revision history
Table 1.
Date 20-Dec-2007
Document revision history
Revision 1 Initial release. Changes
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