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july 2009 doc id 15627 rev 1 1/12 AN2971 application note using the typical temperature ch aracteristics of 32 khz crystal to compensate the m41t83 and th e m41t93 serial real-time clocks introduction typical real-time clocks employ 32 khz tuning fork crystals. while being well suited to the low-power needs of battery-backed applications, they can drift significantly over the industrial temperature range ?40 to +85c. at the extreme temperatures, drifts are somewhere between ?108 and ?177 parts per million (ppm), a lo ss of about 5 to 8 minutes per month. full temperature compensation is possible, but costly. however, a simplified technique can be employed which can greatly improve the drift, and hence improve the timekeeping accuracy of the rtc without adding significant cost. knowing the general shape of the tuning fork crystal's temperature curve, such a compensation scheme is possible in applications where a temperature sensor is in use. as shown in figure 1 below, in the shaded portion nearer the bottom, the accuracy of the 32 khz crystal falls off appreciably as the temperature approaches the limits of operation. the pink line in the middle of th at region is considered the typical behavior. if the oscillator is adjusted for the expected or typical curve, the accuracy approaches the shaded region depicted at the top of the figure, to something nearer the range 25 ppm, about 1 minute per month, a much more tolerable range of accuracy. essentially, this technique takes the bottom shaded region and straightens it out along the temperature axis. in many applications that level of accuracy is all that is required. this document describes how to implement such a compensation scheme. figure 1. 32 khz crystal drift versus temperature -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 temp (c) ppm min typ post-max post-min uncompensated range of drift versus temperature max -180 -130 -80 -30 20 -170 -120 -70 -20 30 -160 -110 -60 -10 -150 -100 -50 0 -140 -90 -40 10 am0 3 096v1 www.st.com
additional considerations AN2971 2/12 doc id 15627 rev 1 1 additional considerations the turnover point is the temperature at which the crystal is at its highest frequency. this is the maximum or highest point on the temperature parabola and is referred to as t 0 . in figure 1 , it was assumed the turnover point was 25c. it will in fact range between 20 and 30c for most 32 khz crystals. figure 2. typical temperature curves for three different turnover points after calibration to 0 ppm at 25c during factory calibration of the m41t83 an d m41t93, the oscillator frequency is adjusted until the device is very close to 0 ppm at 25c. this has the effect of moving the temperature curve up and down. if the turnover point is at 20c, after factory calibration, the device will be at 0 ppm at 25c, but will run at its fastest at 20c. this is depicted by the orange curve. similarly, if the turnover point is at 30c, a fter factory calibration, the device will be at 0 ppm at 25c, but will run at its fastest at 30 c. this is depicted by the blue curve. thus, the temperature turnover point moves up and down with calibration, but remains at the same temperature. three turnover points (k=0.036, typical) -35 -30 -25 -20 -15 -10 -5 0 5 0 1020304050 temp (c) ppm 30 25 20 t 0 (c) am0462 8 v1
AN2971 additional considerations doc id 15627 rev 1 3/12 when the minimum and maximum values are included for all three turnover points, the curves of figure 3 are derived. the pink region is the same as before in figure 1 and represents the minimum and maximum cases for a turnover of 25c. the pink brackets on either side of figure 3 help make this clear. figure 3. range of drift for three turnover points the blue shaded region covers the minimum and maximum cases for a turnover of 30c, and the orange shaded region covers the minimum and maximum cases for a turnover of 20c. the entire range of drift is indicated by the dashed black lines, and is the sum of the three cases. -210 -160 -110 -60 -10 40 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 temp (c) ppm 20/0.030 20/0.036 20/0.042 25/0.030 25/0.036 25/0.042 30/0.030 30/0.036 30/0.042 t 0 =30c t 0 =25c t 0 =20c t 0 =30c t 0 =25c t 0 =20c t 0 /k am04629v1
additional considerations AN2971 4/12 doc id 15627 rev 1 for the purposes of this application note, the net result of considering the turnover point is an increase in the amount of uncertainty in the drift at the temperature extremes. with this added, the straightened uncertainty region shown at the top of figure 1 becomes that of figure 4 below. figure 4. range of drift after compensation in figure 4 , the black dashed lines show the entire range of the drift after compensation. as before, in figure 1 , the gray region represents the parabolas after they have been straightened along the temperature axis. after compensation, the drift should be no worse than 20 ppm in the range ?10 to +50c, and typically less than 10 ppm in that range as shown by the gray dashed lines for t 0 = 25c crystal equation the drift of a tuning fork crystal is described by the equation below. here, the drift is expressed as a fraction of the nominal frequency, f 0 . the factory calibration adjusts for the deviation of f 0 from 32768 hz. t 0 is the turnover point, and t is the temperature, in celsius. k is a constant in the range 0.030 to 0.042, with a typical value of 0.036. when plotted, the equation gives the curves shown in figure 1 through 4 . the typical case in figure 1 is for k = 0.036. the other values of k give the minimum and maximum (dashed line) curves. drift (ppm) -60 -50 -40 -30 -20 -10 0 10 20 30 40 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100 temp (c ) t 0 = 25c t 0 =20 to 30c am046 3 0v1 () 2 0 0 t t k f f ? ? ? =
AN2971 application theory doc id 15627 rev 1 5/12 2 application theory as shown in figure 5 , the typical temperature characteristics of the 32 khz crystal are described by a parabola. away from the center point, at temperatures above and below 25c, the crystal tends to run at lower frequencies. a table can be derived from the curve from which the user can look up the approxim ate drift (in parts per million or ppm) of the clock for a given temperature. thus, if the application can measure the temperature, it can predict the drift of the real-time clock and compensate accordingly by adjusting the rtc's calibration circuit. the m41t83 and m41t93 employ analog calibration circuits which adjust the frequency of the oscillator by adding or re moving capacitance. the non-linear relationship between the load capacitance and frequency is depicted in the curve of figure 7 . note that, since the curve is non-linear, the incremental change in ppm of the oscillator varies with the position on the curve. that is, a small change in capacitance does not have the same effect on ppm at one point on the curve as at another. therefore, in order to determine how much incremental capacitance to add or remove to achieve a desired ppm shift, the user must first determine where on the curve the device is operating. in the cases of the m41t83 and m41t93, in the embedded crystal package, a factory- calibration value is programmed into a permanent (one-time programmable) register which can be read by the application. this provides the starting point for the calibration procedure. it indicates where on the curve the device is operating at room temperature. in summary, figure 5 (tabularized in figure 6 ) tells the user the necessary ppm of calibration required for a given temperature. in turn, figure 7 and figure 8 allow the user to determine the load capacitance setting necessary to achieve the desired ppm shift.
example AN2971 6/12 doc id 15627 rev 1 3 example the first step is to determine the temperature. that in turn is used to look up the expected amount of drift, as shown in step 2. the easiest way to do this is to use a table as illustrated in figure 6 , which shows an expected drift of ?43 pp m at 58c. thus, the oscillator should be adjusted for a 43 ppm shift in the opposite direction. in step 3, the factory calibration value is used as a starting point on the capacitance-ppm curve in figure 7 . the factory calibration value of 0x14 corresponds to a capacitance of +5 pf (above the nominal 12.5 pf). that corresponds to ?7.78 ppm as shown in figure 8 . adding 43 ppm to that gives +35.22 ppm. thus, capacitance must be removed to speed up the oscillator. in step 4, the user finds the ppm value nearest 35.22 in the list in figure 8 . in this case, that is 34.97 ppm, which calls for an analog calibration value of 0xa9 (which corresponds to ?10.25 pf). this value is then placed into the user analog calibration register at address 0x12, and the otp bit is cleared (address 0x 13) forcing the device to employ the user analog calibration value in lieu of the factory calibration value. this results in the oscillator runni ng at a slightly different spe ed which in turn helps it keep time more accurately at the ambient temperature. by performing this procedure periodically, the application can keep the timekeeping accuracy at an acceptable level. using these few simple steps, users can greatly improve the timekeeping performance of their m41t83 and m41t93 real-time clock devices.
AN2971 example doc id 15627 rev 1 7/12 figure 5. 32 khz crystal curve, ppm versus temperature C160 01020 3 040506070 frequency drift (ppm) temperature c 80 C10 C20 C30 C40 C100 C120 C140 C40 C60 C80 20 0 C20 = C0.036 ppm/c 2 0.006 ppm/c 2 k ?f = k x (t C t o ) 2 f t o = 25c 5c factory calibration value, fcal, places operation at ~0 ppm at 25c. step 1: read temperature step 2: look up ppm from ppm vs. temperature graph/table (figure 5 and figure 6) example: temperature read is 58c. ppm curve/table shows that clock will be ~43 ppm slow. thus, ppm should be +43 ppm (here, + means faster). fast slow 43 ppm steps analog calibration sequence: am0 3 097v1
example AN2971 8/12 doc id 15627 rev 1 figure 6. drift versus temperature temperature (c) drift (ppm) -30 -116.5 -29 -112.3 -28 -108.2 -27 -104.1 -26 -100.2 -25 -96.3 -24 -92.4 -23 -88.7 -22 -85.0 -21 -81.4 -20 -77.9 -19 -74.5 -18 -71.1 -17 -67.8 -16 -64.6 -15 -61.5 -14 -58.5 -13 -55.5 -12 -52.6 -11 -49.8 -10 -47.0 -9 -44.4 -8 -41.8 -7 -39.3 -6 -36.9 -5 -34.5 -4 -32.2 -3 -30.0 -2 -27.9 -1 -25.9 0-23.9 1-22.0 2-20.2 3-18.5 4-16.8 5-15.3 6-13.8 7-12.3 8-11.0 9-9.7 10 -8.5 11 -7.4 12 -6.4 13 -5.4 14 -4.6 15 -3.8 16 -3.0 17 -2.4 18 -1.8 19 -1.3 20 -0.9 21 -0.6 22 -0.3 23 -0.1 24 0.0 25 0.0 temperature (c) drift (ppm) 25 0.0 26 -0.1 27 -0.2 28 -0.4 29 -0.7 30 -1.0 31 -1.5 32 -2.0 33 -2.6 34 -3.3 35 -4.0 36 -4.8 37 -5.7 38 -6.7 39 -7.8 40 -8.9 41 -10.1 42 -11.4 43 -12.8 44 -14.2 45 -15.8 46 -17.4 47 -19.0 48 -20.8 49 -22.6 50 -24.5 51 -26.5 52 -28.6 53 -30.7 54 -33.0 55 -35.3 56 -37.6 57 -40.1 58 -42.6 59 -45.2 60 -47.9 61 -50.7 62 -53.5 63 -56.4 64 -59.4 65 -62.5 66 -65.7 67 -68.9 68 -72.2 69 -75.6 70 -79.0 71 -82.6 72 -86.2 73 -89.9 74 -93.7 75 -97.5 measur ed tem p am0 3 09 8 v1
AN2971 example doc id 15627 rev 1 9/12 figure 7. typical oscillator accuracy versus load capacitance step 3: example (continued): analog calibration value read was 0x14 (+5 pf). move +43 ppm from 5 pf (0x14). decreasing load cap. - 2 0 . 0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 0 1 0 0 . 0 - 18.0 - 1 5 . 0 5.0 9.75 a n a l o g c a l i b r a t i o n v a l u e, ac, register 0x12 p p m a d j u s t m e n t offset to c xi , c xo (pf) net equiv. load cap., c load , (pf) 10.0 3.5 5.0 12.5 15 17.4 0xc8 0xbc 0xa9 0x00 0x14 0x27 increasing load cap. slower faster decreasing load cap. - 2 0 . 0 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 0 1 0 0 . 0 - 18.0 - 1 5 . 0 a n a l o g c a l i b r a t i o n v a l u e, ac, register 0x12 p p m a d j u s t m e n t offset to c xi , c xo (pf) net equiv. load cap., c load , (pf) increasing load cap. slower faster read factory calibration value: set otp bit to 1, wait 4ms, then read analog calibration register (address 0x12). this will return factory calibration value (for 0 ppm @ 25c). step 4: find factory calibration value on the curve, then move ppm (from step 2) up/down from there and read new calibration value from ppm vs.load capacitance table/graph (figure 7 and figure 8) +4 3 ppm new c a li b r a tion v a l u e value read is C10.25 pf (0xa9). step 5: clear otp bit, then write new value to analog calibration register. clear otp bit at address 0x13. write 0xa9 to address 0x12. steps (continued) 0x94 C10.25 7.38 C5.0 0.0 am0 3 099v1
example AN2971 10/12 doc id 15627 rev 1 figure 8. load capacitance versus ppm cap analog cal ppm cload 9.75 0x27 -14.83 17.37 9.50 0x26 -14.56 17.25 9.25 0x25 -14.25 17.12 9.00 0x24 -13.95 17.00 8.75 0x23 -12.17 16.88 8.50 0x22 -11.92 16.75 8.25 0x21 -11.67 16.63 8.00 0x20 -12.63 16.50 7.75 0x1f -11.11 16.38 7.50 0x1e -10.81 16.25 7.25 0x1d -10.50 16.13 7.00 0x1c -11.08 16.00 6.75 0x1b -9.84 15.88 6.50 0x1a -9.49 15.75 6.25 0x19 -9.13 15.63 6.00 0x18 -9.64 15.50 5.75 0x17 -8.38 15.38 5.50 0x16 -8.00 15.25 5.25 0x15 -7.60 15.13 5.00 0x14 -7.78 15.00 4.75 0x13 -6.78 14.88 4.50 0x12 -6.36 14.75 4.25 0x11 -5.93 14.63 4.00 0x10 -6.20 14.50 3.75 0x0f -5.04 14.38 3.50 0x0e -4.59 14.25 3.25 0x0d -4.13 14.13 3.00 0x0c -4.27 14.00 2.75 0x0b -3.20 13.88 2.50 0x0a -2.72 13.75 2.25 0x09 -2.23 13.63 2.00 0x08 -2.50 13.50 1.75 0x07 -1.56 13.37 1.50 0x06 -1.19 13.25 1.25 0x05 -0.70 13.12 1.00 0x04 -0.27 13.00 0.75 0x03 0.31 12.87 0.50 0x02 0.70 12.75 0.25 0x01 1.25 12.62 0.00 0x00 1.71 12.50 -0.25 0x81 2.66 12.37 -0.50 0x82 3.05 12.25 -0.75 0x83 3.60 12.12 -1.00 0x84 4.09 12.00 -1.25 0x85 4.76 11.87 -1.50 0x86 5.22 11.75 -1.75 0x87 5.80 11.62 -2.00 0x88 6.32 11.50 -2.25 0x89 7.59 11.38 -2.50 0x8a 8.20 11.25 -2.75 0x8b 8.83 11.13 -3.00 0x8c 9.22 11.00 -3.25 0x8d 10.11 10.88 -3.50 0x8e 10.77 10.75 -3.75 0x8f 11.44 10.63 -4.00 0x90 11.78 10.50 anlog cal value versus ppm cap analog cal ppm cload -4.25 0x91 12.81 10.38 -4.50 0x92 13.52 10.25 -4.75 0x93 14.24 10.13 -5.00 0x94 14.89 10.00 -5.25 0x95 15.72 9.88 -5.50 0x96 16.48 9.75 -5.75 0x97 17.26 9.63 -6.00 0x98 17.85 9.50 -6.25 0x99 18.87 9.38 -6.50 0x9a 19.70 9.25 -6.75 0x9b 20.55 9.13 -7.00 0x9c 21.85 9.00 -7.25 0x9d 22.32 8.88 -7.50 0x9e 23.23 8.75 -7.75 0x9f 24.17 8.63 -8.00 0xa0 25.36 8.50 -8.25 0xa1 26.11 8.38 -8.50 0xa2 27.12 8.25 -8.75 0xa3 28.15 8.13 -9.00 0xa4 29.69 8.00 -9.25 0xa5 30.31 7.88 -9.50 0xa6 31.43 7.75 -9.75 0xa7 32.58 7.63 -10.00 0xa8 33.87 7.50 -10.25 0xa9 34.97 7.38 -10.50 0xaa 36.22 7.25 -10.75 0xab 37.51 7.13 -11.00 0xac 39.22 7.00 -11.25 0xad 40.18 6.88 -11.50 0xae 41.58 6.75 -11.75 0xaf 43.01 6.63 -12.00 0xb0 44.34 6.50 -12.25 0xb1 46.01 6.38 -12.50 0xb2 47.58 6.25 -12.75 0xb3 49.18 6.13 -13.00 0xb4 50.72 6.00 -13.25 0xb5 52.54 5.88 -13.50 0xb6 54.30 5.75 -13.75 0xb7 56.10 5.63 -14.00 0xb8 57.13 5.50 -14.25 0xb9 59.87 5.38 -14.50 0xba 61.84 5.25 -14.75 0xbb 63.86 5.13 -15.00 0xbc 65.80 5.00 -15.25 0xbd 68.09 4.88 -15.50 0xbe 70.30 4.75 -15.75 0xbf 72.57 4.63 -16.00 0xc0 74.19 4.50 -16.25 0xc1 77.31 4.38 -16.50 0xc2 79.78 4.25 -16.75 0xc3 82.32 4.13 -17.00 0xc4 85.17 4.00 -17.25 0xc5 87.62 3.88 -17.50 0xc6 90.39 3.75 -17.75 0xc7 93.23 3.63 -18.00 0xc8 96.68 3.50 anlog cal value versus ppm fcal add 43 ppm look up new value am0 3 100v1
AN2971 revision history doc id 15627 rev 1 11/12 4 revision history table 1. document revision history date revision changes 23-jul-2009 1 initial release.
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