Question

2.3 Analytic form of transfer function. In certain cases the transfer function is available as an analytic expression. One common transfer function used for resistance temperature sensors (to be discussed in Chapter 3) is the Callendar- Van Duzen equation. It gives the resistance of the sensor at a temperature T as R(T)= Ro(1+AT+ BT2 - 100CT3 +CT*) [2), where the constants A, B, and C are determined by direct measurement of resis tance for the specific material used in the sensor and Ro is the temperature of the sensor at 0°C. Typical temperatures used for calibration are the oxygen point (-182.962°C; the equilibrium between liquid oxygen and its vapor), the triple point of water (0.01°C; the point of equilibrium temperature between ice, liquid water, and water vapor), the steam point (100°C; the equilibrium point between water and vapor), the zinc point (419.58°C; the equilibrium point between solid and liquid zinc), the silver point (961.93°C), and the gold point (1064.43°C), as well as others. Consider a platinum resistance sensor witha nominal resistance of 25 2 at 0°C. To calibrate the sensor its resistance is measured at the oxygen point as 6.2 Q, at the steam point as 35.6 Q, and at the zinc point as 66.1 2. Calculate the coefficients A, B, and C and plot the transfer function between -200°C and 600°C

Answer 1

First A, B and C are found and then the transfer function is plotted using MATLAB.

RCTO = R C1+ATH+ BT2 100 CT3+C Ro=250, RC-183.162) = 62 RC0-35-6,RCA11 53)= 661 A1 62-25+ AC-182-192 1D CG182-11a +8-182 12 +C-182. 9a ラー182-192 A+ 33193.9a5 8 - O.75a +1706603404 C= @ス0 356= 25 (1+ 100 A +100 B -100x1008c + 100 う。424= 18 A + I aooo B 66-1-25(1+417 58A +417-5sB -100×419.58C 十411-581c -- 419-58A+ 17c047 3764 8 +2.360608 X109c 644


Soliny D,and 3 Calculator Jes) A = 4.167 X lo3 20= B=7.25a XIO C = 839 XJo

50 40 30 20 10 0 -200 300 400 -100 100 200 500 600 70 60


Command Window New to MATLAB? See resources for Getting Started. = 4.167*10^-3; >a = 7.252*10^-7: >> b > c=-9.839 10^-12: >>T -200:600; = 25* ( 1 a T b T.^2 100 c T.^3 c* T.^4); >>R >> plot (T, R) f >>