热电偶与热电阻的分度表计算

(表中如-2.474 286 0 x 10-24后面可是-24次方, -2.131 507 1 x 10+2后面是2次方)
下面是根据温度求电动势的逆方程:
E ci (t 90 ) i
i 0
n
E=c0+c1t90+c2t90+2….cit90+i 常量取值表如下: 温度范围: c0= c1= c2= c3= c4= c5= c6= c7= c8= 0 to 630.615°C 0.000 000 000 0 .... -2.465 081 834 6 x10-1 5.904 042 117 1 x 10-3 -1.325 793 163 6 x 10-6 1.566 829 190 1 x 10-9 -1.694 452 924 0 x 10-12 6.229 034 709 4 x 10-16 630.615 to 1,820°C -3.893 816 862 1 x 103 2.857 174 747 0 x 101 -8.488 510 478 5 x 10-2 1.578 528 016 4 x 10-4 -1.683 534 486 4 x 10-7 1.110 979 401 3 x 10-10 -4.451 543 103 3 x 10-14 9.897 564 082 1 x 10-18 -9.379 133 028 9 x 10-22
设计热电偶/热电阻式温度采集电路,将采集值转换成温度值是件麻烦事,因为其温度关系曲线不是线性的, 可以近似看作高次方程曲线,而一般采集得到的数据都是用单片机来做温度值转换,让单片机去求解高次方 程显然不现实,所以一般都是采用分段线性化的方法来计算温度值,这个分段方法技巧就不去介绍了,这里主 要来探讨分段线性化对应表(分度表)的生成,网络上有不少这种表格,但是这种表格一般精度不高,而且不一 定符合我们的分段要求,所以这里介绍程序生成分度表.以 B 型热电偶为例: 其温度-电压关系曲线方程为:
对于热电阻,方法一样,公式为(PT100):
R R0 (1 AT BT 2 CT 3 (T 100))
R=R0(1+AT+BT+2+CT+3(T-100))
R是采集的阻值,T是求得的温度值,R0=100, A = 3.90830 x 10
> 0 否则C= -4.183 x 10
-12 -3
. B = -5.775 x 10
-7
来自百度文库
. C = 0 如果 T
.(注,那个-3是-3次方)
程序实现就略了,通过该公式开可以计算分段误差. 上面的程序在 Linux 下编译运行通过.其他类型的那些个公式可以在网上找到,曾经想做个小软件,用 Qt 写个 界面,计算 8 种热电偶和几种热电阻的分度表,可以设置精度自动分段,可惜没时间.
t 90 c0 c1 E c 2 E 2 c3 E 3 ...ci E i
t90=c0+c1E+c2E+2+c3E+3…ciE+i
其中t90是温度值(计算所得),E是热电偶产生的电动势(采集所得),c是常量,下面是c的取值表:
温度范围: 电压范围: c0 c1 c2 c3 c4 c5 c6 c7 c8 = = = = = = = = = 错误范围: 250 to 700°C 291 to 2,431 m V 9.842 332 1 x 10+1 6.997 150 0 x 10-1 -8.476 530 4 x 10-4 1.005 264 4 x 10-6 -8.334 595 2 x 10-10 4.550 854 2 x 10-13 -1.552 303 7 x 10-16 2.988 675 0 x 10-20 -2.474 286 0 x 10-24 0.03 to -0.02°C 0.02 to -0.01°C 700 to 1,820°C 2,431 to 13,820 m V 2.131 507 1 x 10+2 2.851 050 4 x 10-1 -5.274 288 7 x 10-5 9.916 080 4 x 10-9 -1.296 530 3 x 10-12 1.119 587 0 x 10-16 -6.062 519 9 x 10-21 1.866 169 6 x 10-25 -2.487 858 5 x 10-30
double t,e;//t=temperature e = electronictive force int i,j; for(i=0;i<631;i++) { t = (double)i; e = C00+C10*t+C20*t*t+C30*t*t*t+C40*t*t*t*t+C50*t*t*t*t*t+C60*t*t*t*t*t*t; printf("t = %g, e = %g\n",t,e); } printf("t from 0-630 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); for(i=631;i<1821;i++) { t = (double)i; e = C01+C11*t+C21*t*t+C31*t*t*t+C41*t*t*t*t+C51*t*t*t*t*t+C61*t*t*t*t*t*t+C71*t*t*t* t*t*t*t+C81*t*t*t*t*t*t*t*t; printf("t = %g, e = %g\n",t,e); } printf("t from 631-1820 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); for(j=291;j<2432;j++) { e = (double)j; t = C02+C12*e+C22*e*e+C32*e*e*e+C42*e*e*e*e+C52*e*e*e*e*e+C62*e*e*e*e*e*e+C72*e*e*e* e*e*e*e+C82*e*e*e*e*e*e*e*e; printf("e = %g, t = %g\n",e,t); } printf("t from 291- 2431 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); for(j=2432;j<13821;j++) { e = (double)j; t = C03+C13*e+C23*e*e+C33*e*e*e+C43*e*e*e*e+C53*e*e*e*e*e+C63*e*e*e*e*e*e+C73*e*e*e* e*e*e*e+C83*e*e*e*e*e*e*e*e; printf("e = %g, t = %g\n",e,t); } printf("t from 291- 2431 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n"); }
根据公式可以设计程序来完成计算,下面是一个计算分段为 1 摄氏度和 1uV 的小程序: #include <math.h> #include <stdio.h> #define C00 0.0000 //0-630.615 #define C10 -2.4650818346e-1 #define C20 5.9040421171e-3 #define C30 -1.3257931636e-6 #define C40 1.5668291901e-9 #define C50 -1.6944529240e-12 #define C60 6.2290347094e-16 //630.615-1820 #define C01 -3893.8168621 #define C11 28.571747470 #define C21 -8.4885104785e-2 #define C31 1.5785280164e-4 #define C41 -1.6835344864e-7 #define C51 1.1109794013e-10 #define C61 -4.4515431033e-14 #define C71 9.8975640821e-18 #define C81 -9.3791330289e-22 //291-2431uV;250-700 #define C02 98.423321 #define C12 6.9971500e-1 #define C22 -8.4765304e-4 #define C32 1.0052644e-6 #define C42 -8.3345952e-10 #define C52 4.5508542e-13 #define C62 -1.5523037e-16 #define C72 2.9886750e-20 #define C82 -2.4742860e-24 //2431-13820uV;700-1820 #define C03 213.15071 #define C13 2.8510504e-1 #define C23 -5.2742887e-5 #define C33 9.9160804e-9 #define C43 -1.2965303e-12 #define C53 1.1195870e-16 #define C63 -6.0625199e-21 #define C73 1.8661696e-25 #define C83 -2.4878585e-30 int main(void) {